tag:blogger.com,1999:blog-81487925049596588202024-03-04T22:04:44.190-08:00ProbabilidadEduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.comBlogger43125tag:blogger.com,1999:blog-8148792504959658820.post-40040200154058572872014-03-20T17:46:00.001-07:002014-03-20T17:46:27.832-07:00Conjunto PotenciaConjunto potencia de <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;"> </span><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(1,2,3,4)</span><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;"><br /></span>
<a href="http://chart.apis.google.com/chart?cht=tx&chl=2%5E%7B4%7D%3D2%5Ctimes2%5Ctimes2%5Ctimes2%3D16&chs=&chf=&chco=" id="preview_img_link" style="font-family: sans-serif; font-size: 13px; text-align: center;" target="_blank" title="open in a new window"><img id="preview_img" src="http://chart.apis.google.com/chart?cht=tx&chl=2%5E%7B4%7D%3D2%5Ctimes2%5Ctimes2%5Ctimes2%3D16&chs=&chf=&chco=" style="max-height: 100%; max-width: 100%;" /></a><br />
<br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">( ( ) )</span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(1), (2), (3), (4)</span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(1,2), (1,3), (1,4)</span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(1,2,3), (1,2,4), (1,3,4)</span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(1,2,3,4)</span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(2,3), (2,4)</span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(2,3,4)</span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">(3,4)</span>Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-46200846800147792112012-02-17T18:51:00.000-08:002012-02-17T18:51:42.907-08:00Teaching Bayesian stats backward — The Endeavour<a href="http://www.johndcook.com/blog/2011/04/20/teaching-bayesian-stats-backward/">Teaching Bayesian stats backward — The Endeavour</a>: <br><br><a style="font-size:13px" href="https://chrome.google.com/webstore/detail/pengoopmcjnbflcjbmoeodbmoflcgjlk">'via Blog this'</a>Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-56224969793672860682012-02-09T11:56:00.000-08:002012-02-13T19:20:53.071-08:00Proyecto ChanceEn los EEUU, el gobierno apoyó a un grupo de profesores para mejorar la enseñanza y el aprendizaje de la Teoría de la Probabilidad.<br />
<br />
Pueden visitar su página web aquí.<a href="http://www.dartmouth.edu/~chance/">[vínculo]</a>Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-68697849483496003322011-10-01T19:02:00.000-07:002011-10-01T19:02:02.023-07:00acabo de subir mis tareas, pero veo que no llegan con el formato que le asigne en word y tampoco las imagenes...<br />
<br />Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-81056449522532883982011-10-01T18:59:00.000-07:002011-10-01T18:59:17.823-07:00 <b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Problema 25</span></b><br />
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">En una aurna hay pelotas
rojas numeradas del 1 al 10 y pelotas azules numeradas del 1 al 15. ¿Cuál es la
probabilidad de que al extraer al azar una pelota sea roja y no tenga el número
5?<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Introduccion<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Analisis del
problema: sabemos que tenemos 10 posibilidades de 25 de sacar una pelota roja y
15 de 25 de que sea azul, es decir 10/25 y 15/25 respectivamente. Pero como nos
piden una condicion de que sea roja y no tenga el numero 5.<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Entonces se hace este
planteamiento:<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Sea el evento A: cuando se
estrae una pelota roja.<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Sea el evento B: si la
pelota que se estrajo tiene el numero 5.<o:p></o:p></span></div>
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<span lang=ES-MX style='font-size:8.0pt;line-height:
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<!--[endif]--><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p> </o:p></span><br />
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<br clear="ALL" style="mso-ignore: vglayout;" />
<div class="MsoNoSpacing" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">Desarrollo <o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">Teniendo en cuenta que la probabilidad de que ocurra el
evento B es posible si ocurre el evento A, se hace referencia a la relacion
P(A-B)=P(A)-P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">B)<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">Como lo menciono anteriormente la probabilidad de que
ocurra el evento A de de 10/15, entonces la probabilidad de que ocurra el
segundo evento una vez ocurrido el primero es de 1/15. tomando en cuenta que
solo hay una pelota roja marcada con el numero 5 del total de 15 pelotas.<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;"><span style="mso-spacerun: yes;"> </span>10<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">P(A)= ―</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: "MS Shell Dlg"; mso-fareast-language: ES; mso-hansi-font-family: Batang;"><o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>15<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<br /></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>1<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">B)=</span><span lang="ES-MX" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;"> </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">―<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>15<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<br /></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">Apliacando la relacion para obtener la probabilidad.<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>10<span style="mso-spacerun: yes;"> </span>1<span style="mso-spacerun: yes;">
</span>9<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A-B)=</span><span lang="ES-MX" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;"> </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">―<span style="mso-spacerun: yes;"> </span>- ― =<span style="mso-spacerun: yes;"> </span>― = 0.6000 = 60% <o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>15<span style="mso-spacerun: yes;"> </span>15<span style="mso-spacerun: yes;">
</span>15<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<br /></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<br /></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Conclusion<o:p></o:p></span></b></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Cuando se aplicó la
anterior relacion,<span style="mso-spacerun: yes;"> </span>se nota que es
necesario conocer cuando aplicar la intercepcion, en dos conjuntos de datos.<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Ahora bien se presenta otra
alternativa mas facil, aplicando la frecuencia relativa: <o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Tomando en cuenta el
espacio muestral. <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">S= </span><span lang="EN-US" style="font-family: Batang; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">{</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">1,</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">2</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">3</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">4</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">5</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">6</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">7</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">8</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">9</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">10</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> A</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">1</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> A</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">2</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> A</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">3</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> A</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">4</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> A</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">5</span><span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;">}</span><span lang="EN-US" style="font-family: "MS Shell Dlg","sans-serif"; font-size: 8.5pt; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">A: la
pelota es roja y no es el numero 5<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">A= </span><span lang="EN-US" style="font-family: Batang; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">{</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">1,</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">2</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">3</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">4</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> <span style="mso-spacerun: yes;"> </span>R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">6</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">7</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">8</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">9</span><span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"> R</span><span lang="EN-US" style="font-size: 5.0pt; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;">10</span><span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;">}</span><span lang="EN-US" style="font-family: "MS Shell Dlg","sans-serif"; font-size: 8.5pt; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;"><o:p></o:p></span></div>
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<span lang="EN-US" style="mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-tab-count: 1;"> </span></span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Probabilidad
de casos<span style="mso-spacerun: yes;"> </span>9<o:p></o:p></span></div>
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<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">P(A)=<span style="mso-spacerun: yes;"> </span></span><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 7.5pt; mso-ansi-language: ES; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;">――――――――――――――<span style="mso-spacerun: yes;"> </span>=<span style="mso-spacerun: yes;"> </span>―<span style="mso-spacerun: yes;">
</span>=<span style="mso-spacerun: yes;"> </span></span><span lang="ES" style="font-family: "Arial","sans-serif"; mso-ansi-language: ES; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;">0.60= 60%</span><span lang="ES" style="font-family: "MS Shell Dlg","sans-serif"; font-size: 8.5pt; mso-ansi-language: ES; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;"><o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify; text-indent: 35.4pt;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Total de casos<span style="mso-spacerun: yes;"> </span>15<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Problema 26<o:p></o:p></span></b></div>
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<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">La probabilidad de que
Antonio gane un juego de tenis es de 2/5 y la probabilidad de que Juan gane es
de ¼. ¿Cuál es la probabilidad de que Antonio gane el torneo en que participa
si en el juego final se enfrenta a Juan?<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">introduccion<o:p></o:p></span></b></div>
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<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Sea el evento A: gane
Antonio<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Sea el evento B: gane Juan<o:p></o:p></span></div>
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<br /></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Nos damos cuenta que el
evento que nos interesa es el evento A, osea el que Antonio gane y Juan Pierda.
Aplico la siguiente relacion de intercepcion, tomando en cuenta que implica una
multiplicacion.<o:p></o:p></span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">desarrollo<o:p></o:p></span></b></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>2<span style="mso-spacerun: yes;"> </span>1<span style="mso-spacerun: yes;">
</span><span style="mso-spacerun: yes;"> </span>2<o:p></o:p></span></div>
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<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">B)=</span><span lang="ES-MX" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;"> </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">― *<span style="mso-spacerun: yes;"> </span>― =<span style="mso-spacerun: yes;"> </span>― <o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>5<span style="mso-spacerun: yes;"> </span>4<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>20<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A-B)=P(A)- P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">B)<o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify; text-indent: 35.4pt;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>2<span style="mso-spacerun: yes;">
</span>2<span style="mso-spacerun: yes;"> </span>8-2<span style="mso-tab-count: 1;"> </span>6<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none; text-indent: 35.4pt;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>=</span><span lang="ES-MX" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;"> </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">― *<span style="mso-spacerun: yes;"> </span>― =<span style="mso-spacerun: yes;"> </span>―--<span style="mso-spacerun: yes;"> </span>=<span style="mso-spacerun: yes;">
</span>-<span style="mso-spacerun: yes;"> </span>= 0.3 = 30%<span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>5<span style="mso-spacerun: yes;"> </span>20<span style="mso-spacerun: yes;">
</span>20<span style="mso-tab-count: 1;"> </span>20<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">conclusion<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Como se ce en el desarrollo del
problema, nos damos cuenta de que es una relacion dependiente, es decir para
que exista la probabilidad de que Antonio gane Juan tiene que perder.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Problema
27<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">introduccion</span></b><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
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<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Sea A
y B dos sucesos donde la probabilidad de A= ¾ y la probabilidad de B= 3/8. en
base a la siguiente relacion:<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; text-align: justify; text-indent: 35.4pt;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">B)=P(B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩A</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=1/8<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;">Calcular :<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 36.0pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18.0pt;">
<!--[if !supportLists]--><span lang="ES-MX" style="mso-bidi-font-family: Calibri; mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-list: Ignore;">a)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">B)<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 36.0pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18.0pt;">
<!--[if !supportLists]--><span lang="ES-MX" style="mso-bidi-font-family: Calibri; mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-list: Ignore;">b)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B’</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)</span><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 36.0pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18.0pt;">
<!--[if !supportLists]--><span lang="ES-MX" style="mso-bidi-font-family: Calibri; mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-list: Ignore;">c)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(AUB)</span><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 36.0pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18.0pt;">
<!--[if !supportLists]--><span lang="ES-MX" style="mso-bidi-font-family: Calibri; mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-list: Ignore;">d)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’U</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">B’</span><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)</span><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">Desarrollo:</span></b><b style="mso-bidi-font-weight: normal;"><span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></b></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Desarrollando el inciso a)<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A-B)=P(A)-P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)<span style="mso-tab-count: 2;"> </span>(1)<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-family: Batang; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A-B)=P(A</span><span lang="EN-US" style="font-family: Batang; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B’</span><span lang="EN-US" style="font-family: Batang; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)-P(B’</span><span lang="EN-US" style="font-family: Batang; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩A</span><span lang="EN-US" style="font-family: Batang; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">) <span style="mso-tab-count: 2;"> </span>(2)<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">De (2) intercambiamos A y B<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(B-A)=P(B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)-P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)<span style="mso-tab-count: 2;"> </span>(3)<span style="mso-tab-count: 1;"> </span></span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">De (1) intercambiamos A y B<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(B-A)=P(B)
-P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)<span style="mso-tab-count: 2;"> </span>(4)<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">De (3) y (4):<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=P(B)-P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">B)<span style="mso-tab-count: 2;"> </span><o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify; text-indent: 35.4pt;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>3<span style="mso-spacerun: yes;">
</span>1<span style="mso-spacerun: yes;"> </span>2<span style="mso-spacerun: yes;"> </span>1<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none; text-indent: 35.4pt;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>=</span><span lang="ES-MX" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;"> </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">― -<span style="mso-spacerun: yes;"> </span>― =<span style="mso-spacerun: yes;"> </span>―<span style="mso-spacerun: yes;"> </span>=<span style="mso-spacerun: yes;">
</span>-<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>(5)<span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;">
</span>8<span style="mso-spacerun: yes;"> </span>8<span style="mso-spacerun: yes;"> </span>8<span style="mso-spacerun: yes;">
</span>4<span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">b) de </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A-B)=P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)</span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A-B)=P(A)-P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)</span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Igualando estas dos relaciones tenemos<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=P(A)-P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)</span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNoSpacing" style="margin-left: 35.4pt; text-align: justify;">
<span lang="ES-MX" style="mso-fareast-language: ES-MX; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>3<span style="mso-spacerun: yes;">
</span>1 <span style="mso-spacerun: yes;"> </span>5 <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none; text-indent: 35.4pt;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span>=</span><span lang="ES-MX" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;"> </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">― -<span style="mso-spacerun: yes;"> </span>― =<span style="mso-spacerun: yes;"> </span>―<span style="mso-tab-count: 2;"> </span>(6)<span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<div class="MsoNoSpacing" style="text-align: justify;">
<span lang="ES-MX" style="font-family: Batang; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-spacerun: yes;">
</span>8<span style="mso-spacerun: yes;"> </span>8<span style="mso-spacerun: yes;"> </span>8<span style="mso-spacerun: yes;">
</span><span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">c) sustituyendo A por A’ en (2)<span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’-</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)<span style="mso-tab-count: 3;"> </span>(7)</span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Sustituyendo A por A’ en (1)<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’-</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=P(A’)-P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)<span style="mso-tab-count: 2;"> </span>(8)</span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">De (7) y (8) se
obtiene:<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=P(A’)-P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)<span style="mso-tab-count: 2;"> </span>(9)</span><span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=1-P(A)=1-</span><span lang="EN-US" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">¾</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"> = </span><span lang="ES" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">¼</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><span style="mso-tab-count: 2;"> </span>(10)</span><span lang="EN-US" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">De sustituir (5) y (10) en (9) se obtiene<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)= </span><span lang="ES" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">¼</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">-</span><span lang="ES" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">¼</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">=0<span style="mso-tab-count: 3;"> </span>(11)<span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">d) </span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’U</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)=P(A’)+P(B)-P(A’</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">∩B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">) (12)<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">sustituyendo (10) en (12)<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">P(A’U</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-bidi-font-family: Arial; mso-fareast-language: ES; mso-hansi-font-family: Batang;">B</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">)= </span><span lang="ES" style="font-family: Batang; font-size: 14.0pt; line-height: 115%; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">¼+3/8-¼</span><span lang="ES" style="font-family: Batang; mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-hansi-font-family: Batang; mso-no-proof: yes;">=3/8<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Conclusion:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Viendo la introduccion del
problema se tiene que P(A)¾ , P(B) 3/8 y la intercepcion de estos dos eventos
es 1/8.<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES; mso-fareast-language: ES-MX; mso-no-proof: yes;">Cabe aclarar que estos ejercicios también se pueden
representar de una forma mas facil para el lector si se utilizan los diagramas
de venn.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<!--[if gte vml 1]><v:line id="_x0000_s1054" style='position:absolute;
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strokeweight="2.25pt"/><![endif]--><!--[if !vml]--><span style="mso-ignore: vglayout; position: relative; z-index: 251658240;"><span style="height: 208px; left: 167px; position: absolute; top: -38px; width: 4px;"><img height="208" src="file:///C:/DOCUME~1/LEONIC/CONFIG~1/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_s1054" width="4" /></span></span><!--[endif]--><span lang="ES" style="mso-ansi-language: ES;">Evento A:<o:p></o:p></span></div>
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<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">1/4<o:p></o:p></span></div>
</td>
<td style="background: yellow; border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 62.8pt;" valign="top" width="84">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">2/4<o:p></o:p></span></div>
</td>
<td style="background: yellow; border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 54.0pt;" valign="top" width="72">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">3/4<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 63.0pt;" valign="top" width="84">
<div class="MsoNormal">
<br /></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">Evento B:<o:p></o:p></span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-left: 104.4pt; width: 276px;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;">
<td style="background: olive; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 18.0pt;" valign="top" width="24">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">1/8<o:p></o:p></span></div>
</td>
<td style="background: olive; border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 29.8pt;" valign="top" width="40">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">2/8<o:p></o:p></span></div>
</td>
<td style="background: olive; border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 22.7pt;" valign="top" width="30">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">3/8<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 19.5pt;" valign="top" width="26">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">4/8<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 27.0pt;" valign="top" width="36">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">5/8<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 27.0pt;" valign="top" width="36">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">6/8<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 27.0pt;" valign="top" width="36">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">7/8<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 36.0pt;" valign="top" width="48">
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">8/8<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">Entonces
resolviendo:<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;"><span style="mso-spacerun: yes;"> </span>a): El resultado es lo que no esta en A
multiplicado por lo que esta en B<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span lang="ES" style="mso-ansi-language: ES;">b): El resultado es lo que esta en A multiplicado por lo que no esta en B<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="ES" style="mso-ansi-language: ES;">c): El resultado
es lo que esta en A junto con lo que esta en B<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span lang="ES" style="mso-ansi-language: ES;">d): El resultado es lo que no esta en A multiplicado por lo que no esta en
B<o:p></o:p></span></div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-46079913352713241992011-10-01T18:52:00.000-07:002011-10-01T18:52:36.461-07:00<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaEBohoC4BLIwpKf48aLusburniAVRGcpU5nBlCO3-Ax8lcCOFalcMBrZW3gxR4lHL6wK_M6THAX7QyWePvyyf3_1xIfADq4nRUQ2lE-sPTNOctKF-dTw4sZk2CbUzZXO_32vog-JlZiE/s1600/TAREA+1.PNG" imageanchor="1" style="clear:left; float:left;margin-right:1em; margin-bottom:1em"><img border="0" height="300" width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaEBohoC4BLIwpKf48aLusburniAVRGcpU5nBlCO3-Ax8lcCOFalcMBrZW3gxR4lHL6wK_M6THAX7QyWePvyyf3_1xIfADq4nRUQ2lE-sPTNOctKF-dTw4sZk2CbUzZXO_32vog-JlZiE/s400/TAREA+1.PNG" /></a></div>
envio mis tareas, espero lleguen todas.Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-69023987773824561042011-10-01T11:17:00.001-07:002011-10-01T12:39:35.020-07:00MicaPROBABILIDAD
<br />
Introducción
<br />
El concepto de probabilidad nace con el deseo del hombre de conocer con certeza los eventos futuros. Es por ello que el estudio de probabilidades surge como una herramienta utilizada por los nobles para ganar en los juegos y pasatiempos de la época. El desarrollo de estas herramientas fue asignado a los matemáticos de la corte.
Con el tiempo estas técnicas matemáticas se perfeccionaron y encontraron otros usos muy diferentes para la que fueron creadas. Actualmente se continúo con el estudio de nuevas metodologías que permitan maximizar el uso de la computación en el estudio de las probabilidades disminuyendo, de este modo, los márgenes de error en los cálculos
<br />
ACTIVIDAD I
<br />
¿Cuál es la probabilidad de que una persona de 25 años de edad llegue hasta los 40 años, si de acuerdo con una tabla de mortalidad cada 93,745 personas de 25 años de edad solo 87,426 llegan a los 40 años?
R= 87,426 / 93,745= 0.9325
La probabilidad es de un 93%
<br />
ELABORACIÓN DE UN HISTOGRAMA CONSIDERANDO LAS ESTATURAS DE LOS ALUMNOS DE LA LIC. EN MATEMÁTICA EDUCATIVA.
<br />
ESTATURAS ni
156 1
157 1
158 2
160 1
165 2
168 1
169 1
170 1
172 1
174 1
180 1
TOTALES 13
<br />
Amplitud del rango
<br />
180-156 = 24
<br />
13= 3.6 = 4
<br />
24/ 4 = 6
<br />
Intervalo mi Ni fi Ni Fi
<br />
156--162 159 5 5/13=0.384 5 5/13=0.384
<br />
162--168 165 2 2/13=0.153 7 7/13=0.538
<br />
168--174 171 4 4/13=0.307 11 11/13=0.846
<br />
174--180 177 1 1/13=0.076 12 12/13=0.923
<br />
180--186 183 1 1/13=0.076 13 13/13=1
<br />
Total 13
<br />
HISTOGRAMA
<br />
ESTATURAS DE ALUMNOS
<br />
PROBABILIDAD COMO FRECUENCIA ABSOLUTA
<br />
Introducción a la probabilidad.
<br />
En la actualidad vemos que la teoría de la probabilidad ocupa un lugar importante en muchos asuntos de negocios.
Los seguros y prácticas actuariales se basan firmemente en los principios de la teoría de la probabilidad.
Las pólizas de seguros de vida dependen de las tablas de mortalidad, las cuales a su vez se basan en las probabilidades de muerte en edades específicas. Otras tasas de seguros tales como seguro de bienes raíces y de automóviles se determinan de manera similar. La probabilidad también juega un papel importante en la estimación del número de unidades defectuosas en un proceso de fabricación, la probabilidad de recibir pagos sobre cuentas por cobrar y las ventas potenciales de un nuevo producto. Incluso los apostadores profesionales en eventos deportivos deben tener una comprensión sólida de la teoría de la probabilidad.
<br />
Problema 1
<br />
¿Cuál es la probabilidad de que una persona de 25 años de edad llegue a sobrevivir hasta los 40 si de acuerdo con una tabla de mortalidad, de caa 93 745 personas de 25 años de edad sólo 87 426 llegan a los 40 años.
<br />
Solución:
<br />
Como h=87426
<br />
n=93745
<br />
Probabilidad S= personas que llegan a los 40 años = 87 426
<br />
Total de personas de 25 años 93 745
<br />
= 0.9325 (se tomaron cuatro cifras decimales)
<br />
Problema 2
<br />
En una caja hay 25 tornillos en buen estado y 80 defectuosos, ¿Cuál es la probabilidad de sacar de la caja un tornillo en buen estado?
<br />
Solución:
<br />
Como h=25
<br />
N=80+25
<br />
Probabilidad S= Numero de tornillos en buen estado = 25 = 25
<br />
Total de tornillos en la caja 25+80 105
<br />
=0.2380
<br />
Probabilidad en porcentaje = 0.2380 (100) =23.80%
<br />
Problema 3
<br />
De cada 1000 personas a las que se les practica una revisión médica, 35 tienen problemas de vista. ¿Cuál es la probabilidad de que una persona examinada tenga alguna enfermedad en los ojos?
<br />
Solución:
<br />
Como h=35
<br />
n= 1000
<br />
Probabilidad S = número de personas con problemas de la vista = 35 = 7
<br />
Total de personas examinadas 1000 200
<br />
Probabilidad en porcentaje = 0.035(100)= 3.5%
<br />
Problema 4
<br />
En una caja hay 75 canicas azules y 225 rojas, ¿Cuál es la probabilidad de obtener al azar una canica azul?
<br />
Solucion:
<br />
Como h= 75
<br />
n= 75+225
<br />
Probabilidad S= numero de canicas azules = 75 = 75
<br />
Total de canicas en la caja 75 + 225 300
<br />
=0.25
<br />
Probabilidad en porcentaje = 0.25 (100)=25%
<br />
CONJUNTO POTENCIA
<br />
En matemáticas, dado un conjunto S, se llama conjunto potencia o conjunto de partes de S (se denota por P(S) o 2S) al conjunto de todos los subconjuntos de S.
<br />
En la teoría de conjuntos basada en los Axiomas de Zermelo-Fraenkel, la existencia del conjunto potencia se establece por el axioma del conjunto potencia.
Por ejemplo, si S= {a, b, c} entonces el conjunto potencia de S es P(S) = {{ }, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}.
<br />
El conjunto potencia de un conjunto S, junto con las operaciones de la unión, de la intersección y del complemento forman el ejemplo prototípico de álgebra de Boole. De hecho, uno puede demostrar que cualquier álgebra de Boole finita es isomorfa al álgebra booleana del conjunto potencia de un conjunto finito. Para las álgebras booleanas infinitas esto no es verdad, pero cada álgebra booleana infinita es sub-álgebra de una álgebra booleana de parte.
<br />
INTRODUCCIÓN
<br />
La teoría de conjuntos es una rama de la matemática relativamente moderna cuyo propósito es estudiar unas entidades llamadas conjuntos, aunque otra parte de esta teoría es reconocida como los fundamentos mismos de las matemáticas. La teoría de conjuntos fue desarrollada por el matemático alemán Georg Cantor a finales del siglo XIX a partir de ciertas conclusiones hechas por él mismo al reflexionar en unos detalles de las series trigonométricas de Fourier. La teoría de conjuntos fue expuesta por Cantor en una serie de artículos y libros, de los cuales pueden destacarse sus Beiträge zur Begründung der transfiniten Mengenlehre.
<br />
El propósito de Cantor era proporcionar un método para lidiar con asuntos relacionados al infinito actual, un concepto que fue rehuido y rechazado por algunos matemáticos (Pitágoras, Gauss, Kronecker) por considerarlo sin significado.
<br />
PROBLEMA
<br />
Conjunto potencia de [ 1,2,3, 4]
<br />
S= { }, { 1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {3,2,4}, {4,3,1}, {1,2,3,4}
<br />
PROBABILIDAD DE UNA DIFERENCIA
<br />
La probabilidad de una diferencia se aplica cuando se quiere obtener la probabilidad de que un suceso determinado ocurra y que simultáneamente otro suceso, también determinado, no ocurra.
Se expresa así:
<br />
P(A-B) = P(A) – P(A B)
<br />
Problema 25
<br />
En una urna hay pelotas rojas numeradas del 1 al 10 y pelotas azules numeradas del 1 al 5. ¿Cuál es la probabilidad de que al extraer al azar una pelota sea roja y no tenga el número 5?
<p>
Solución:
<p>
A: Se extrae pelota roja
<p>
B: Sale el número 5
<p>
El suceso que nos interesa es A – B. Aplicamos la relación:
<p>
P(A – B) =P(A ) – P(A B)
Con
<p>
P(A)=10/15
<p>
P(A B)=1/15
Porque sólo hay una pelota roja marcada con el número 5 del total de las 15 pelotas.
Por lo tanto:
<p>
P(A-B)=10/15-1/15=9/15
=0.6000
=60%
<p>
Otro procedimiento para resolver este problema es revisando la probabilidad como frecuencia relativa , así:
Solución :
<p>
Espacio muestral
<p>
S=[R1, R2, R3, R4, R5, R6, R7, R8, R9, R10, A1, A2, A3, A4, A5] son sucesos
<p>
A: La pelota es roja y no es el número 5
<p>
A =[R1, R2, R3, R4, R6, R7, R8, R9, R10) SON 9 (no está R5)
<p>
P(A)=casos favorables= 9 = 0.60 =60%es el mismo resultado
<p>
-------------------- ---
<p>
Casos posibles 15
El resultado que obtuvimos con P(A B)=P(A). P(B)=1/15
<p>
También lo podemos obtener con las siguientes relaciones:
<p>
P(A - B) = P(A B´) =P(B’ A)
Problema 26
<p>
La probabilidad de que Antonio gane un juego de tenis es de 2/5 y la probabilidad de que Juan gane es de ¼. ¿cuál es la probabilidad de que Antonio gane el torneo en que participa si en el juego final se enfrenta a Juan?
<p>
Solución :
<p>
Sucesos
<p>
A: Gane Antonio
<p>
B: Gane Juan
<p>
El suceso que nos interesa es que Antonio gane y simultáneamente que Juan pierda. Por tanto, aplicamos la siguiente relación:
<p>
P(A B)= P(A y B) = P(A) . P(B)
<p>
=2/5[1/4]=2/20
P(A - B) = P(A) – P(A B)
<p>
=2/5-2/20=8-2/20=6/20=0.3
=30%
Otro procedimiento para resolver este problema consiste en aplicar la siguiente relación:
<p>
P(A –B) = P(A) – P(A B) = P(A B´)
<p>
P(A –B) = P(A B’)
<p>
Con
<p>
P(B’) =1-1/4=4/4-1/4=3/4
<p>
Sustituimos en:
<p>
P(A – B) =P(A B’)
<p>
=P(A) . (B)
<p>
=[2/5][3/4]=6/20=0.3
=30 %
<p>
PROBLEMA 27
<p>
A y B son sucesos donde:
<p>
P (A )= P (Aᴒ B´)
<p>
P (A ) = 3
4
P (B) = 3
8
<p>
P (AᴒB ) = P(BᴒA) = 1
8
Calcular
<p>
a) P(A´ᴒB)
<p>
b) P(AᴒB´)
<p>
c) P(Aᴗ B)
<p>
d) P(AᴒB´)
<p>
Solucion:
<p>
Recordando las relaciones de la probabilidad de una diferencia tenemos:
<p>
P(A-B) = P(A) – P (AᴒB)
<p>
P(A-B) = P(AᴒB´) – P(B´ᴒA)
<p>
a) De 2 intercambiamos A y B
<p>
P(B-A) = P(BᴒA´B) – P(A´ᴒB)
<p>
De 1 intercambiamo A y B:
<p>
P(B-A) = P(B) – P(AᴒB)
<p>
De 3 y 4:
<p>
P(A´ᴒB) = P(B) – P (AᴒB)
<p>
= 3/8-1/8 = 2/8 = ¼
<p>
b) De 2 P(A-B) = P (AᴒB´)
<p>
De 1 P(A-B) = P(A)-P (AᴒB)
<p>
Entonces:
<p>
P(AᴒB´) = P(A) – P (AᴒB)
<p>
= ¾-1/8 = 5/8
c) Sustituimos A por A´en 2:
<p>
P(A´-B) = P(A´ᴒB´)
<p>
Sustituimos A por A´ en 1:
<p>
P(A-´B) = P(A´) –P (A´ᴒB)
<p>
De (7) y (8) obtenemos:
<p>
P(A´ ᴒB´) = P(A´) – P (A´ ᴒ´B)
<p>
P(A´) = 1 – P(A) = 1 = -3/4 =1/4
<p>
d)(A´ᴗB) = P(A´) + P(B) –P (A´ᴒB)
<p>
Sustituyendo 10 y 5 en 12 tenemos:
<p>
P (A´ᴗB) = ¼+3/8-1/4=3/8
CONCLUSION
<p>
esta unidad se analizaron los conceptos básicos de probabilidad, y cómo se puede emplear el análisis de probabilidades para proporcionar ionformación útil para la toma de decisiones.
• Se analizó la diferencia de la probabilidad aplicándose deque un suceso determinado ocurra y que simultáneamente otro suceso también determinado no ocurra.
Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-45325427409988517832011-09-30T17:10:00.001-07:002011-09-30T17:11:26.548-07:00Marco Antonio Díaz<div align="center" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
INTRODUCCION</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
La
Probabilidad es un concepto muy amplio, que nos ayuda a tomar
decisiones acertadas de acuerdo a los sucesos presentados. La
probabilidad se encarga de medir la frecuencia con la que se obtiene
un resultado en un proceso aleatorio.</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Su estudio
y aplicación es muy extenso debido a que a mediados del siglo XVII y
hasta la fecha se han encontrado grandes aportaciones de personajes,
que son de gran utilidad en áreas como la Matemática, Estadística
Moderna, Física, Química, Filosofía, Biología, Ingeniera etc. Que
aunque no muestre resultado preciso o determinado como se comento con
anterioridad, su investigación nos permite incrementar el grado de
confianza para tomar una optima decisión.</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
En este
portafolio de evidencias se analizaran ejemplos de algunos tipos de
probabilidad como a continuación se detallan.</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0in;">
El primer ejemplo que se analizara será el de la probabilidad de la
frecuencia relativa, la presentación de un histograma y la expresión
en porcentajes de los casos presentados.</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0in;">
Posteriormente se estudiara un segundo ejemplo donde analizaremos la
probabilidad con base en sucesos compuestos.</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0in;">
Además encontraremos la solución al conjunto potencia donde P = {
1,2,3,4 } donde observaremos todas las posibles combinaciones que se
puedan dar.</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0in;">
Por último se estudiara la Probabilidad de una diferencia,
analizando 3 ejemplos para tener una mejor apreciación de este tema.</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
I. PROBALIDAD COMO FRECUENCIA RELATIVA</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
ACTIVIDAD 1</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
¿Cuál es la probabilidad de que una persona de 25 años de edad
llegue hasta los 40, si de acuerdo con una tabla de mortalidad cada
93745 personas de 25 años de edad solo 87426 llegan a los 40 años?</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
Solución:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Probabilidad
S = <u>Numero de veces que el suceso E</u><sub><u>1</u></sub><u>
ocurrió </u>= <u>h</u></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Total de sucesos realizados
n</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Como h =
87426</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
n = 93745</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Probabilidad
S = <u>Personas que llegan a los 40 años</u> = <u>87426</u></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Total de personas de 25 años 93745</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 0.9325
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">ACTIVIDAD
2</span></strong></div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">¿Cuál es la probabilidad
de que una persona de 25 años de edad llegue hasta los 40 años, si
de acuerdo con una tabla de mortalidad cada 93745 personas de 25 años
de edad solo 87426 llegan a los 40 años?</span></strong></div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">R=
87426 / 93745= 0.9325</span></strong></div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">La
probabilidad es de un 0.9325</span></strong></div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">ACTIVIDAD
3</span></strong></div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">ELABORACION
DE UN HISTOGRAMA CONSIDERANDO LAS ESTATURAS DE LOS ALUMNOS DE LA LIC.
EN MATEMATICA EDUCATIVA.</span></strong></div>
<dl>
<dl>
<dd><table border="1" bordercolor="#000000" cellpadding="7" cellspacing="0" style="width: 445px;">
<colgroup><col width="201"></col>
<col width="213"></col>
</colgroup><tbody>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">ESTATURAS</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">ni</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">156</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">157</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">158</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">2</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">160</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">165</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">2</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">168</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">169</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">170</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">172</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">174</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">180</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="201"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">Totales</span></strong></div>
</td>
<td width="213"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">13</span></strong></div>
</td>
</tr>
</tbody></table>
</dd></dl>
</dl>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong>
</strong><br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">Amplitud
del rango</span></strong></div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">180
– 156 = 24</span></strong></div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<img align="ABSMIDDLE" border="0" height="22" name="graphics1" src="CARPETA%20DE%20EVIDENCIAS.doc_html_m15eef65f.gif" width="27" /><strong>
<span style="font-weight: normal;">= 3.6 = 4
</span></strong>
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<strong><span style="font-weight: normal;">24/
4 = 6</span></strong></div>
<table border="1" bordercolor="#000000" cellpadding="7" cellspacing="0" style="width: 599px;">
<colgroup><col width="85"></col>
<col width="86"></col>
<col width="86"></col>
<col width="86"></col>
<col width="86"></col>
<col width="85"></col>
</colgroup><tbody>
<tr valign="top">
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">Intervalo</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">mi</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">ni</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">fi</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">Ni</span></strong></div>
</td>
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">Fi</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">156
– 162</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">159</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">5</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">5/
13 = 0.384</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">5</span></strong></div>
</td>
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">5/
13 = 0.384</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">162
– 168</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">165</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">2</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">2/
13 = 0.153</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">7</span></strong></div>
</td>
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">7/
13 = 0.538</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">168
– 174</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">171</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">4</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">4/
13 = 0.307</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">11</span></strong></div>
</td>
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">11/13=0.846</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">174
– 180</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">177</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1/
13 = 0.076</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">12</span></strong></div>
</td>
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">12/13=0.923</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">180
– 186</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">183</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">1/
13 = 0.076</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">13</span></strong></div>
</td>
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">13/13=1</span></strong></div>
</td>
</tr>
<tr valign="top">
<td width="85"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">Total</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<strong><span style="font-weight: normal;">13</span></strong></div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="86"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="85"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
</tbody></table>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /></div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
II. PROBABILIDAD CON BASE EN LOS SUCESOS COMPUESTOS. (PROBABILIDAD
AXIOMATICA)</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
ACTIVIDAD
1</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
1. Para
participar en la rifa de un reloj, los alumnos de primer año
compraron 18 boletos y los de segundo grado 12 boletos. ¿Cual es la
probabilidad de que un alumno de primero o segundo gane la rifa? Se
imprimieron 50 boletos.</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Solución:
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
A: Un
alumno de primer grado gana el premio.</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
B: Un
alumno de segundo grado gana el premio</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
El suceso
que nos interesa es E= A y B son mutuamente excluyentes, es decir, A
ᴖ B = Ø</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A o B)
= P (A) + P (B) = 18/50 + 12/50 = 30/50 = 3/5 = 0.6</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 60
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
ACTIVIDAD
2</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
La tabla
siguiente muestra el nivel de estudios de los profesores de una
escuela.</div>
<table border="1" bordercolor="#000000" cellpadding="7" cellspacing="0" style="width: 604px;">
<colgroup><col width="67"></col>
<col width="70"></col>
<col width="70"></col>
<col width="69"></col>
<col width="89"></col>
<col width="70"></col>
<col width="68"></col>
</colgroup><tbody>
<tr valign="top">
<td width="67"><div class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div class="western" lang="es-MX">
Escuela Nacional de Maestros</div>
</td>
<td width="70"><div class="western" lang="es-MX">
Escuela Normal Superior</div>
</td>
<td width="69"><div class="western" lang="es-MX">
Escuela Normal Privada</div>
</td>
<td width="89"><div class="western" lang="es-MX">
Especialización en la Universidad
Pedagógica Nacional</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX">
Hombre</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX">
Mujer</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M1</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M2</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M3</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M4</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M5</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M6</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M7</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
M8</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
X</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H1</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H2</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H3</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H4</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H5</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H6</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H7</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H8</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H9</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
H10</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
X</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
<br />
</div>
</td>
</tr>
<tr valign="top">
<td width="67"><div align="center" class="western" lang="es-MX">
18</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
12</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
6</div>
</td>
<td width="69"><div align="center" class="western" lang="es-MX">
6</div>
</td>
<td width="89"><div align="center" class="western" lang="es-MX">
12</div>
</td>
<td width="70"><div align="center" class="western" lang="es-MX">
10</div>
</td>
<td width="68"><div align="center" class="western" lang="es-MX">
8</div>
</td>
</tr>
</tbody></table>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
¿Cual
es la probabilidad de que un alumno le toque un profesor egresado de
la Escuela Nacional de Maestros o que tenga una especialización en
la Universidad Pedagógica Nacional?</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
Solución:
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
A:
Profesor egresado de la Escuela Nacional de Maestros</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
B:
Profesor egresado de la Universidad Pedagógica Nacional</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
A ᴖ B ≠
Ø Dado que hay docentes que son egresados de ambas instituciones.
Los sucesos no son mutuamente excluyentes.</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Entonces:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A o B)
= P (A) + P (B) – P (A ᴖ B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 12/18 + 12/18 – 8/18 = 16/18 = 0.8888</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 88.88 %</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
ACTIVIDAD
3</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div lang="es-MX" style="margin-bottom: 0.14in; margin-left: 0.5in;">
1. DADO EL CONJUNTO S= {1, 2,3,4}, DETERMINA CUALES SUBCONJUNTOS SE
PUEDEN FORMAR.</div>
<div lang="es-MX" style="margin-bottom: 0.14in; margin-left: 0.5in;">
<br /><br />
</div>
<div lang="es-MX" style="margin-bottom: 0.14in; margin-left: 0.5in;">
SOLUCION:</div>
<div lang="es-MX" style="margin-bottom: 0.14in; margin-left: 0.5in;">
<br /><br />
</div>
<div lang="es-MX" style="margin-bottom: 0.14in; margin-left: 0.5in;">
P
{S}= { }, {1}, { 2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4},
{3,4}, {1,2,3}, {1,2,4}, {3,2,4}, {4,3,1}, {1,2,3,4}.
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
III. PROBABILIDAD DE UNA DIFERENCIA</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
La
probabilidad de una diferencia se aplica cuando se quiere obtener la
probabilidad de que un suceso determinado ocurra y que
simultáneamente otro suceso, también determinado, no ocurra.</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Se
expresión así:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A –
B) = P (A) – P (A ᴖ B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Esta
relación se conoce como ley general de sustracción de
probabilidades. También se utilizan las relaciones:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
( A – B ) = P ( A ) – P ( A </span>ᴖ<span lang="en-US"> B ) = P
( A</span><span lang="en-US">´ </span>ᴖ<span lang="en-US"> B </span><span lang="en-US">)
= P ( B </span><span lang="en-US">ᴖ</span><span lang="en-US"> A )
( 1 )</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(A – B) = P (A) – P (A </span><span lang="en-US">ᴖ</span><span lang="en-US">
B)
(2)</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
</span><span lang="en-US">(A</span><span lang="en-US">´</span><span lang="en-US">)
– P (A</span><span lang="en-US">´</span><span lang="en-US"> </span><span lang="en-US">ᴖ</span><span lang="en-US">
B) = P (A</span><span lang="en-US">´</span><span lang="en-US"> </span><span lang="en-US">ᴖ</span><span lang="en-US">
B</span><span lang="en-US">´</span><span lang="en-US">) = P (A</span><span lang="en-US">´</span><span lang="en-US">
- B) (3)</span></div>
<div class="western" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
ACTIVIDAD
1</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
En una
urna hay pelotas rojas numeradas del 1 al 10 y pelotas azules
numeradas del 1 al 5. ¿Cual es la probabilidad de que al extraer al
azar una pelota sea roja y no tenga el numero 5?</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Solución:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
A: Se
extrae pelota roja</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
B: Sale el
numero 5</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
El suceso
que nos interesa es A – B. Aplicamos la relación:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A –
B) = P (A) – P (A ᴖ B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Con</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A) =
10/15</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A ᴖ
B) = 1/15</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Porque
solo hay una pelota roja marcada con el número 5 del total de las 15
pelotas.</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Por lo
tanto:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A –
B) = 10/15 – 1/15 = 9/15</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 0.6000</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 60%</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Otro
procedimiento para resolver este problema es revisando la
probabilidad como frecuencia relativa, así:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Solución:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Espacio
maestral</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
S = {
R<sub>1</sub>,R<sub>2</sub>,R<sub>3</sub>,R<sub>4</sub>,R<sub>5</sub>,R<sub>6</sub>,R<sub>7</sub>,R<sub>8</sub>,R<sub>9</sub>,R<sub>10</sub>,A<sub>1</sub>,A<sub>2</sub>,A<sub>3</sub>,A<sub>4</sub>,A<sub>5</sub>,
} son 15 sucesos</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
A = La
pelota es roja y no es el numero 5</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
A = {
R<sub>1</sub>,R<sub>2</sub>,R<sub>3</sub>,R<sub>4</sub>,R<sub>5</sub>,R<sub>6</sub>,R<sub>7</sub>,R<sub>8</sub>,R<sub>9</sub>,R<sub>10</sub>,
} son 9 ( no está R<sub>5</sub> )</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A) =
<u>Casos favorables</u> = <u>9</u> = 0.60 = 60 % es el mismo
resultado</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Casos posibles 15
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
El
resultado que obtuvimos con P (A ᴖ B) = P (A). P (B) = 1/15</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
También
lo podemos obtener con las siguientes relaciones:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
</span><span lang="en-US">(A – B) = P (A </span>ᴖ<span lang="en-US">
B</span><span lang="en-US">´</span><span lang="en-US">) = P (B</span><span lang="en-US">´</span><span lang="en-US">
</span>ᴖ<span lang="en-US"> A)</span></div>
<div class="western" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" style="margin-bottom: 0in;">
ACTIVIDAD 2</div>
<div class="western" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
La
probabilidad de que Antonio gane un juego de tenis es de 2/5 y la
probabilidad de que Juan gane es de 1/4 ¿Cual es la probabilidad
de que Antonio gane el torneo en que participa si en el juego final
se enfrenta a Juan?</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Solución:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
A: Gane
Antonio</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
B: gane
Juan</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
El suceso
que nos interesa es que gane Antonio y simultáneamente que Juan
pierda. Por tanto, aplicamos la siguiente relación:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A –
B) = P (A) – P (A ᴖ B). Con P (A) = 2/5, ahora es necesario
calcular P (A <span lang="en-US">ᴖ</span> B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Como A y B
son sucesos dependientes aplicamos la siguiente relación:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A ᴖ
B) = P (A y B) = P (A). <span lang="en-US">P (B)</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">= 2/5(1/4) = 2/20</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(A – B) = P (A) – P (A </span>ᴖ<span lang="en-US"> B)</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">= 2/5</span><span lang="en-US"> – 2/20 =
</span><span lang="en-US"><u>8 – 2</u></span><span lang="en-US"> =
6/20 = 0.3</span></div>
<div class="western" style="margin-bottom: 0in;">
20</div>
<div class="western" style="margin-bottom: 0in;">
= 30%</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Otro
procedimiento para resolver este problema consiste en aplicar la
siguiente relación:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(A – B) = P (A) – P (A </span>ᴖ<span lang="en-US"> B) = P (A </span>ᴖ<span lang="en-US">
B</span><span lang="en-US">´</span><span lang="en-US">)</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A –
B) = P (A <span lang="en-US">ᴖ</span> B ´)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Con</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A) =
2/5</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (B´) =
1 – 1/4 = 4/4 – 1/4 = 3/4</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Sustituimos
en:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A –
B) = P (A ᴖ B´)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= P (A). (B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= (2/5) (3/4) = 6/20 = 0.3</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 30 %</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
ACTIVIDAD
3</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
A y B son
sucesos donde:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P(A) = 3/4</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (B) =
3/8</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A ᴖ
B) = P (BᴖA) = 1/8</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Calcular:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
a) P (A´
ᴖ B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
b) P (A ᴖ
B´)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
c) P (A u
B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
d) P (A´
ᴖ B´)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Solución:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Recordando
las relaciones de la probabilidad de una diferencia tenemos:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A - B)
= P(A) – P (A ᴖ B)
(1)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(A - B) = </span><span lang="en-US">P (A </span>ᴖ<span lang="en-US">
B</span><span lang="en-US">´</span><span lang="en-US">) – P (B</span><span lang="en-US">´</span><span lang="en-US">
</span>ᴖ<span lang="en-US"> </span><span lang="en-US">A)
(2)</span></div>
<div class="western" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
a) De (2)
intercambiamos A y B:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(B - A) =</span><span lang="en-US"> P (B </span>ᴖ<span lang="en-US">
A</span><span lang="en-US">´</span><span lang="en-US">) – P (A</span><span lang="en-US">´</span><span lang="en-US">
</span>ᴖ<span lang="en-US"> B)
(3)</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
De (1)
intercambiamos A y B:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (B - A)
= P (B) – P (A ᴖ B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
De (3) y
(4):</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A´ ᴖ
B) = P (B) – P (A ᴖ B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
= 3/8 –
1/8 = 2/8 = 1/4
(5)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
b) De (2)
P (A - B) = P (A ᴖ B´)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
De (1) P
(A -B) = P(A) – P (A ᴖ B)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Entonces:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(A </span>ᴖ<span lang="en-US"> B</span><span lang="en-US">´</span><span lang="en-US">)
= P (A) – P (A </span>ᴖ<span lang="en-US"> B)</span></div>
<div class="western" style="margin-bottom: 0in;">
= 3/4 – 1/8 = 5/8
(6)</div>
<div class="western" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
c)
Sustituimos A por A´ en (2):</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A´ -
B) = P (A´ ᴖ B´)
(7)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Sustituimos
A por A´ en (1):</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A´ -
B) = P (A´) – P (A´ ᴖ B)
(8)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
De (7) Y
(8) obtenemos:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(A</span><span lang="en-US">´</span><span lang="en-US"> </span>ᴖ<span lang="en-US">
B</span><span lang="en-US">´</span><span lang="en-US">) = P (A</span><span lang="en-US">´</span><span lang="en-US">)
– P (A</span><span lang="en-US">´</span><span lang="en-US"> </span>ᴖ<span lang="en-US">
B) (9)</span></div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<span lang="en-US">P
(A</span><span lang="en-US">´</span><span lang="en-US">) = 1 – P
(A) = 1 – 3/4 = 1/4
(10)</span></div>
<div class="western" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
De
sustituir (5) y (10) en (9) obtenemos:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A´ ᴖ
B´) = 1/4 – 1/4 =0
(11)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
d) P (A´
u B) = P (A´) + P (B) – P (A´ ᴖ B)
(12)</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
Sustituyendo
(10) y (5) en (12) tenemos:</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
P (A´ u
B) = 1/4 + 3/8 – 1/4 = 3/8</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
CONCLUSION</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="center" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0in;">
Se concluye que la probabilidad es universal y que desde tiempos
atrás hasta la actualidad a evolucionado a pasos agigantados, está
presente en las diferentes actividades que día a día realizamos por
ejemplo: juegos de azar, es decir al lanzar una moneda, un dado, en
un juego de lotería, etc.; gracias a estos resultados obtenidos
podemos predecir lo que se quiera lograr, su influencia también se
ve reflejada en ciencias como la Matematica, Estadistica, Filosofia,
Quimica, etc. Ya que atra ves de la medición de la frecuencia de los
distintos resultados presentados en los experimento aleatorios, se
pueden tomar decisiones más eficaces y acertadas para el logro de
objetivos planteados.</div>
<div align="justify" class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
<br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0in;">
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
<div class="western" lang="es-MX" style="margin-bottom: 0.14in;">
<br /><br />
</div>
Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-64899247552920905412011-09-30T17:02:00.001-07:002011-09-30T17:09:16.800-07:00Marco Antonio<div class="separator" style="clear: both; text-align: center;">
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<br />Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-66386681311833411532011-09-30T14:00:00.001-07:002011-09-30T14:00:37.251-07:00Foto de Tabla de Daniel<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4M64rshs8BGLmAmmX9iBgl7hxdmw8jXv_1DM3Uh7omhDGsV6lzUiZmpiu9mMh_Ph4kDemENunoB-ZTKOEH8f5qe2M5YWlSkdbGHtjAyrqF6r_nE-9kwRXVn_ne72BIFkNnL9-jeIGKVs/s1600/daniel1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="460" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4M64rshs8BGLmAmmX9iBgl7hxdmw8jXv_1DM3Uh7omhDGsV6lzUiZmpiu9mMh_Ph4kDemENunoB-ZTKOEH8f5qe2M5YWlSkdbGHtjAyrqF6r_nE-9kwRXVn_ne72BIFkNnL9-jeIGKVs/s640/daniel1.png" width="640" /></a></div>
Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-37001149098131403342011-09-30T13:52:00.001-07:002011-09-30T15:15:41.451-07:00Tablas en HTML<table border="1">
<tbody>
<tr>
<td>¡Hola</td>
<td>mundo!</td>
<td>¡Hola</td>
<td>mundo!</td>
</tr>
<tr>
<td>¡Hola</td>
<td>mundo!</td>
<td>¡Hola</td>
<td>mundo!</td>
</tr>
<tr>
<td>¡Hola</td>
<td>mundo!</td>
<td>¡Hola</td>
<td>mundo!</td>
</tr>
<tr>
<td>¡Hola</td>
<td>mundo!</td>
<td>¡Hola</td>
<td>mundo!</td>
</tr>
<tr>
<td>¡Hola</td>
<td>mundo!</td>
<td>¡Hola</td>
<td>mundo!</td>
</tr>
<tr>
<td>¡Hola</td>
<td>mundo!</td>
<td>¡Hola</td>
<td>mundo!</td>
</tr>
</tbody></table>
<br />
<div>
<span class="Apple-style-span" style="color: blue;"><b>Esto está bonito</b></span></div>
Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-79010069895431434112011-09-29T10:53:00.000-07:002011-09-29T14:48:40.376-07:00TAREA 1 PROBABILIDAD<div><div><div><div align="justify">TAREA 1 PROBABILIDAD<br />PROBLEMA 1: ¿Cuál es la probabilidad de que una persona de 25 años de edad llegue una tabla de mortalidad, de cada 93 745 personas de 25 años de edad sólo 87 426 llegan Probabilidad = h/n<br /></div><div align="justify">h= 87 426<br /></div><div align="justify">n= 93 745<br /></div><div align="justify">Probabilidad = 93,26%<br /></div><div align="justify">CONCLUSIÓN: La probabilidad de que una persona de 25 años de edad llegue hasta los 40 es del 93.26%.<br /><br /></div><div align="justify"> </div><div align="justify">PROBLEMA 2: Realizar la tabla de frecuencias e histograma con los siguientes datos:<br />Estatura de los alumnos del grupo 101 de la Lic. de Matemática Educativa, modalidad semiescolarizada.<br /></div><div align="justify"> </div><div align="justify">1.70 m 1.80 m 1.60 m 1.65 m 1.56 m 1.58m 1.69m 1.57m 1.74m 1.65m 1.72m 1.58m 1.68m </div><div align="justify"> </div><div align="justify">1.80 m 1.74 m 1.72 m 1.70 m 1.69 m 1.68m 1.65m 1.65m 1.60m 1.58m 1.58m 1.57m 1.56m<br /><br />13 DATOS<br /><br />Rango = Dato mayor - Dato menor<br />Rango = 180 - 156 = 24<br /><br />Clase = Raíz cuadrada del núm. de datos<br />Clase = 3.60555 4<br /><br />Intervalo= Rango/Núm. de clase<br /><br />Intervalo= 6 <br /><br />TABLA DE FRECUENCIAS<br />Intervalos Frec. Abs. Frec Abs. Acum. Frec. Rel. Frec Rel. Acum. Marcas de clase<br />156-162 5 5 38.4 38.4 237<br />162-168 2 7 15.3 53.8 246<br />168-174 4 11 30.7 84.6 255<br />174-180 1 12 7.6 92.3 264<br />180-186 1 13 7.6 100 273<br />TOTAL 13 <br /><br /><br /></div><div align="justify"> </div><div align="justify"> </div><div align="justify"> </div><div align="justify"><br /><br /><br /><br /><br /><br /><br />CONCLUSIÓN: De acuerdo a los resultados obtenidos y lo que se puede apreciar en las gráficas de frecuencias, podemos decir que la mayor parte de los alumnos del grupo 101 de la licenciatura de matemática educativa tienen una estura aproximada que se encuentra entre los rangos de 1.56 y 1.74 m. De acuerdo a los datos y gráfica de frecuencia acumulada representan el 84.6% de los alumnos de este grupo.<br /><br />MARÍA VAZFELY VÁZQUEZ FELIPE.</div></div></div></div>Vazfelyhttp://www.blogger.com/profile/12992154019753128266noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-10067981515843594202011-09-27T12:29:00.001-07:002011-09-27T12:37:37.214-07:00EJERCICIOS DE PROBABILIDAD<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixfjQS_jAKD4nAaLzcHZcI5dzRWPBUJPYLAxDHn87DJWI5WOEqvHWsPwN6DRuFHkQt-n27hf1G1zfd9WgZLob8WT_TM9stVtM2xuS-FA5mM-7Z1uZpwwTA5tL86awaJwACsmMKOeZ33hs/s1600/Diapositiva1.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixfjQS_jAKD4nAaLzcHZcI5dzRWPBUJPYLAxDHn87DJWI5WOEqvHWsPwN6DRuFHkQt-n27hf1G1zfd9WgZLob8WT_TM9stVtM2xuS-FA5mM-7Z1uZpwwTA5tL86awaJwACsmMKOeZ33hs/s320/Diapositiva1.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5657125607930338978" /></a><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_NYhfdy5wlKAr2Rviw1BRYdDUdSW6uVmdCXneUF-10KleyNy796xJzWj07eLfsaWhWiI1ZdQ9NXWgSCEZCCu8bLhKjb6UqqDapwEXwW0liuocZTLWBUgtBlw2rmH2bmLnpB_i5G74BDc/s1600/Diapositiva2.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img style="display:block; 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margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjmaVVfxyMMElJKPFnce84hJ3YnnaLjiEqds-qZUusI-E44XKX21RxUgvRCbqWWbNQW04bg1nyrla7oMgi_JRz5RIg3l_XEWO1BSh2vABlchv8YXUi_rB_-EdLwMJiL4ouYUHkXbT8_I0/s320/Diapositiva14.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5657124523637672274" /></a><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAKDK2kRugM2RfhEpXp9XaoVTXjZtOQAYkfL1qLVULdDImsGiFwIa0vnrJysG_7G28y1QpXv7c5PnKbTtPCGk6-7OJaNLMvIY06M53_-G2w6P2KfdRbRtjNCSzCXmyl4rO-aQoDNW_AzE/s1600/Diapositiva15.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAKDK2kRugM2RfhEpXp9XaoVTXjZtOQAYkfL1qLVULdDImsGiFwIa0vnrJysG_7G28y1QpXv7c5PnKbTtPCGk6-7OJaNLMvIY06M53_-G2w6P2KfdRbRtjNCSzCXmyl4rO-aQoDNW_AzE/s320/Diapositiva15.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5657124401155219986" /></a><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip3lHDHg9MxBKIt39eOAfCs7ofAKDWOFLVoZdiMPDcH6paOOdM7MFC9fQNLUYX5spKX0E27VC5sFTK5RRmGLEWIFIINuIBvX_bXWEAyB3IGEl_fMDiF4Ib9OOOHtEeCen84YZ9_qPrduU/s1600/Diapositiva16.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip3lHDHg9MxBKIt39eOAfCs7ofAKDWOFLVoZdiMPDcH6paOOdM7MFC9fQNLUYX5spKX0E27VC5sFTK5RRmGLEWIFIINuIBvX_bXWEAyB3IGEl_fMDiF4Ib9OOOHtEeCen84YZ9_qPrduU/s320/Diapositiva16.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5657124294586762434" /></a><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgb-WJix69OD6XG9uTxxf7gkfrfn40OQ1lBvSn_AAm2ATSGkrQxXLTMLUkn_Cz8S-y9dPjvy5aBouZoaj-Aej_2HuGY-wtnHtgoWBYKhmjmrDmST0Blqcoyzr5vbfERbo27Vim0JWRmxYo/s1600/Diapositiva17.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgb-WJix69OD6XG9uTxxf7gkfrfn40OQ1lBvSn_AAm2ATSGkrQxXLTMLUkn_Cz8S-y9dPjvy5aBouZoaj-Aej_2HuGY-wtnHtgoWBYKhmjmrDmST0Blqcoyzr5vbfERbo27Vim0JWRmxYo/s320/Diapositiva17.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5657124205848538642" /></a>Alexhttp://www.blogger.com/profile/05691170355315091916noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-2963384055452631462011-09-24T08:36:00.000-07:002011-09-24T08:37:21.503-07:00Probabilidad de una diferencia<strong>Introducción:</strong><br /><br />la probabilidad de una diferencia se aplica cuando se quiere obtener la probabilidad de que un suceso determinado ocurra y que simultaneamente otro suceso, también determinado, no ocurra.<br /><br /><strong>Desarrollo:</strong><br /><strong></strong><br /><br /><strong>Problema 25</strong><br /><br />En una urna hay pelotas rojas númeradas del 1 al 10 y pelotas azules numeradas del 1 al 5. ¿Cuál es la probabilidad de que al extraer al azar una pelota sea roja y no tenga el número 5?<br /><br />Solución:<br /><br />A: Se extrae pelota roja<br />B: Sale el número 5<br />El suceso que nos interesa es A - B. Aplicamos la relación:<br /><br />P(A - B) = P(A) - P(AnB)<br /><br />Con<br /><br />P(A)=10/15<br /><br />P(AnB)=1/15<br /><br />Porque sólo hay una pelota roja marcada con el número 5 del total de las 15 pelotas.<br />Por lo tanto:<br /><br />P(A - B)=10/15 - 1/15 = 9/15<br /><br />= 0.6 000<br /><br />=60%<br /><br /><br /><strong>Problema 26</strong><br /><br />La probabilidad de que Antonio gane un juego de tenis es de 2/5 y la probabilidad de que Juan gane es de 1/4. ¿Cuál es la probabilidad de que Antonio gane el torneo en que participa si en el juego final se enfrenta a Juan?<br /><br />Solución:<br /><br />Sucesos<br /><br />A: Gane Antonio<br />B: Gane Juan<br /><br />El suceso que nos interesa es que Antonio gane y simultáneamente que Juan pierda. por tanto. aplicamos la siguiente relación:<br /><br />P(A - B) = P(A) - P(A n B). con P(A) = 2/5, ahora es necesario calcular P(AnB)<br /><br />Como A y B son sucesos dependientes aplicamos la siguiente relación:<br /><br />P(A n B) = P(A y B) = P(A) . P(B)<br /><br />= 2/5 (1/4) = 2/20<br /><br />P(A - B) = P(A) - P(A n B)<br /><br />= 2/5 - 2/20 = 8-2/20 = 6/20 = .03<br /><br />= 30%<br /><br /><br /><strong>Conclusiones:</strong><br /><br />Al analizar estos problemas escritos y desarrollados mediante el procedimiento de probabilidad de una diferencia puedo concluir con esta nota que son de gran importancia los diferentes procedimientos aplicados en la práctica, ya que nos permite facilitar el trabajo de probabilidad cuando sea necesaria su aplicación.contador navahttp://www.blogger.com/profile/18119397243166467877noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-62449557559872166492011-09-24T07:59:00.000-07:002011-09-24T08:10:24.780-07:00Blog ArturoVisiten mi blog, por favor!!!<br /><br /><a href="http://contadornava.blogspot.com/">http://contadornava.blogspot.com/</a>contador navahttp://www.blogger.com/profile/18119397243166467877noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-40359999915316909532011-09-23T16:45:00.000-07:002011-09-24T05:58:28.601-07:00Ejemplo de $$\LaTeX$$$$f(x)=\begin{cases} \begin{matrix} 0 x 0 \\ x^2 x 0 \end{matrix} \end{cases}$$Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-66566971868453511802011-09-23T13:48:00.001-07:002011-09-23T13:48:49.286-07:00Intereses Bancarios R<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi07kVj4pUDBY4M-P1B6CaLLLf1PTvPey1cD50c_Yz0KfbE_EHMr1PyM8Rt1IA5ed2dCkxp7MLnloi1DoUEXr7LF7RhfJilOzRQIaB2X66S3muh2rSdCo_-4Jh5r6XGAu6Ptg6tU1Y8ve4/s1600/interestrate.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi07kVj4pUDBY4M-P1B6CaLLLf1PTvPey1cD50c_Yz0KfbE_EHMr1PyM8Rt1IA5ed2dCkxp7MLnloi1DoUEXr7LF7RhfJilOzRQIaB2X66S3muh2rSdCo_-4Jh5r6XGAu6Ptg6tU1Y8ve4/s640/interestrate.png" width="610" /></a></div>
<br />Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-23982294387993589062011-09-23T13:45:00.001-07:002011-09-23T13:45:21.229-07:00Correlación en R<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN4R1ETRYo0ZL94zPFHza_9V8yXPOY74UAPxnHjro1RbuhtZE1XZSJYIz5L42DG1Q3QdTvY5S-Lfof65ENHSjYGebBoKkymm1VLH6VYR054Wf2GB0ZUnLKNeDO-W5oGGXhMuc1uJT-OfU/s1600/ls.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="560" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN4R1ETRYo0ZL94zPFHza_9V8yXPOY74UAPxnHjro1RbuhtZE1XZSJYIz5L42DG1Q3QdTvY5S-Lfof65ENHSjYGebBoKkymm1VLH6VYR054Wf2GB0ZUnLKNeDO-W5oGGXhMuc1uJT-OfU/s640/ls.png" width="640" /></a></div>
<br />Eduardo Cantoralhttp://www.blogger.com/profile/10543097158450944601noreply@blogger.com0tag:blogger.com,1999:blog-8148792504959658820.post-81782418885852960132011-09-23T07:47:00.000-07:002011-09-23T07:47:39.498-07:00que estos dias de felicidad se prolonguen por mucho tiempo y que su alegria y ser, nos sigan enseñando, no solo a nosotros sino a muchas personas mas, mis mas sinceros saludos y una coordial felicitacion aunque tarde, pero de corazon.Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-79614906721286849032011-09-23T07:40:00.000-07:002011-09-23T07:40:35.156-07:00hola a tod@s yo realize el trabajo en mis cuadernillo de notas y solo voy a subir el resultado, espero estar en lo correcto:<br />
Conjunto potenancia: A= {1,2,3,4}<br />
{{},{1},{2},{3},{4},{1,2},{2,3},{3,4},{4,1},{4,2},{4,3},{4,4},{1,2,3},{2,3,4},{1,2,4},{1,2,3,4}}Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-43846055653521989142011-09-22T23:56:00.000-07:002011-09-22T23:56:21.528-07:00Gráfico de estaturas Vania...<div style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcbZebJSGvXNzEEakfChGqx489lD13RGfCm_DaDUY-0N936cdR_ycN9GF4tXOoxDyqw75Rm-rg_JOAoOKb18-Kv9DAsVm1QmONobfSSmqPdqs9Aa_MBKubrLXCDl1Dk2a6PgEwjMCFqJkS/s320/Dibujo.JPG" width="320" /></div><br />
Es la tarea que corresponde al gráfico de estaturas, las personas que han visitado mi blog, veran que tiene un error la primera gráfica que presente<br />
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Se entiende que hay una persona que mide 156cm, cuatro 166cm, cinco 176cm y una con 186. Sin embargo evidentemente eso no es cierto.<br />
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Lo que queria indicar eran los intervalos, sin embargo en excel no encontre la forma de realizar el histograma, así que opte por ún dragrama de barras. <br />
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De cualquier forma dejo sin modificar la primera tarea, que repito se encuentra en mi blog.<br />
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A continuación muestro dos gráficos, el primero si tomamos los siguientes datos:<br />
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<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO7di2bWvEprWfeI9ATcqq28bOVYkXvHNtZkRmfNKj4KEPeNfFmRD6VmbqOic5KkOiP_EpRG9iPo3Vlef1lIGYLOVZ8MlCUDt6niF9Ayu0-aQZ1pa4mBPcfbEkurrncrR5r3KiTlZ4S0Q/s1600/Dibujo+1.JPG" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" hca="true" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO7di2bWvEprWfeI9ATcqq28bOVYkXvHNtZkRmfNKj4KEPeNfFmRD6VmbqOic5KkOiP_EpRG9iPo3Vlef1lIGYLOVZ8MlCUDt6niF9Ayu0-aQZ1pa4mBPcfbEkurrncrR5r3KiTlZ4S0Q/s320/Dibujo+1.JPG" width="320" /></a> </div><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 160px;"><colgroup><col span="2" style="width: 60pt;" width="80"></colgroup><tbody>
<tr height="20" style="height: 15pt;"><td height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt; width: 60pt;" width="80"><span style="font-family: Calibri;">Estatura</span></td><td style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; width: 60pt;" width="80"><span style="font-family: Calibri;">Frecuencia</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">156</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">157</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">158</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">2</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">160</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">165</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">3</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">168</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">169</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">170</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">172</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">174</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
<tr height="20" style="height: 15pt;"><td align="right" height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">180</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
</tbody></table><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br />
</div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br />
</div><br />
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El segundo gráfico es si tomamos intervalos:<br />
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<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 160px;"><colgroup><col span="2" style="width: 60pt;" width="80"></colgroup><tbody>
<tr height="20" style="height: 15pt;"><td height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt; width: 60pt;" width="80"><span style="font-family: Calibri;">Intervalos</span></td><td style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; width: 60pt;" width="80"><span style="font-family: Calibri;">Personas</span></td></tr>
<tr height="20" style="height: 15pt;"><td height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">156-166</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">8</span></td></tr>
<tr height="20" style="height: 15pt;"><td height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">166-176</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">5</span></td></tr>
<tr height="20" style="height: 15pt;"><td height="20" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8; height: 15pt;"><span style="font-family: Calibri;">176-186</span></td><td align="right" style="background-color: transparent; border-bottom: #ece9d8; border-left: #ece9d8; border-right: #ece9d8; border-top: #ece9d8;"><span style="font-family: Calibri;">1</span></td></tr>
</tbody></table><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijk7wmlXE393ygezWwrO3RCVnqnwVOMUFFPLf3Ziloq7xqHhK2goJ9j1KUuMlX-3fctfR5adzLZBgDFBgycLHlQWsPs4TJWCtgaD3X3a5EO8EPFxnsLvse-6C2qHocP81IArPJQjq9F2I/s1600/Dibujo+1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" hca="true" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijk7wmlXE393ygezWwrO3RCVnqnwVOMUFFPLf3Ziloq7xqHhK2goJ9j1KUuMlX-3fctfR5adzLZBgDFBgycLHlQWsPs4TJWCtgaD3X3a5EO8EPFxnsLvse-6C2qHocP81IArPJQjq9F2I/s320/Dibujo+1.JPG" width="320" /></a></div><br />
Espero sean más claros.<br />
<img height="57" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO7di2bWvEprWfeI9ATcqq28bOVYkXvHNtZkRmfNKj4KEPeNfFmRD6VmbqOic5KkOiP_EpRG9iPo3Vlef1lIGYLOVZ8MlCUDt6niF9Ayu0-aQZ1pa4mBPcfbEkurrncrR5r3KiTlZ4S0Q/s320/Dibujo+1.JPG" style="filter: alpha(opacity=30); left: 494px; mozopacity: 0.3; opacity: 0.3; position: absolute; top: 592px; visibility: hidden;" width="96" />VANIAhttp://www.blogger.com/profile/04667486621993817950noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-33284047384400489052011-09-22T08:44:00.000-07:002011-09-23T16:32:42.661-07:00Tarea Conjunto Potencia VaniaElabora el conjunto potencia del siguiente conjunto {1, 2, 3, 4}<br />
<br />
Este problema lo resolví usando matrices<br />
<br />
El conjunto potencia de cuatro elementos tendra $$2^n$$ elementos, es decir<br />
<br />
$$2^4=2\times2\times2\times2=16$$<br />
<br />
<br />
1 2 3 4<br />
1 ----- 1, 2 1, 3 1, 4<br />
<br />
2 1, 2 ----- 2, 3 2, 4<br />
<br />
3 1, 3 2, 3 ---- 3, 4<br />
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4 1, 4 2, 4 3, 4 ----<br />
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De está combinación obtenemos los siguientes conjuntos: {1,2}, {1,3}, {1,4}{2,3}, {2,4}, {3,4}<br />
<br />
Tomamos los conjuntos anteriores y hacemos una nueva matriz:<br />
<br />
1,2 1,3 1,4 2,3 2,4 3,4<br />
1 ---- ---- ---- 1,2,3 1,2,4 1,3,4<br />
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2 ---- 1,2,3 1,2,4 ----- ----- 2,3,4,<br />
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3 1,2,3 ----- 1,3,4 ----- 2,3,4 -----<br />
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4 1,2,4 1,3,4 ----- 2,3,4, ----- -----<br />
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Obtenemos los conjuntos: {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}<br />
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Por finalizar todo conjunto es subconjunto de si mismo, por lo tanto agremos el conjunto {1,2,3,4} y el conjunto vacio {} es subconjunto de todo conjunto.<br />
<br />
Así la respuesta al conjunto potencia es<br />
<br />
{ {}, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4} }VANIAhttp://www.blogger.com/profile/04667486621993817950noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-20090667472664772011-09-21T21:10:00.000-07:002011-09-21T21:26:24.276-07:00Conjunto PotenciaTarea 2. Conjunto Potencia<br />Sea el conjunto [1,2,3,4]<br />¿Cual es el numero de elementos del conjunto potencia?<br />P(S)=2^n<br />S=[1,2,3,4]<br />P[1,2,3,4]=2^n<br />n=# de elementos = 4<br />P[1,2,3,4]=2^4<br />P[1,2,3,4]=16<br />[ ]<br />[1],[2],[3],[4]<br />[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]<br />[1,2,3],[1,2,4],[1,3,4],[2,3,4]<br />[1,2,3,4]<br />Otro ejemplo:<br />Sea el conjunto [a,b,c]<br />¿Cual es el numero de elementos del conjunto potencia?<br />P[a,b,c]=2^3<br />P[a,b,c]=8<br />[ ]<br />[a],[b],[c]<br />[a,b],[a,c],[b,c]<br />[a,b,c]dinora_achttp://www.blogger.com/profile/14320656125408134523noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-31280605095012798442011-09-21T18:57:00.003-07:002011-09-24T08:34:05.318-07:00Probabilidad e histograma<strong>Introducción. </strong><br /><br /><strong><br /></strong>La probabilidad es el estudio del azar, mide la frecuencia con la que se obtiene un resultado o conjuntos de resultados al llevar a cabo un experimento.<br />La probabilidad es un estudio sistemático que permite incrementar el grado de confianza para decidir, porque no hay precisión.<br /><br /><strong>Desarrollo.</strong><br /><br /><br />probabilidad S = Número de veces que el suceso ocurrió/Total de sucesos realizados = h/n<br /><br />¿Cuál es la probabilidad de que una persona de 25 años, de edad llegue hasta los 40 años, si de acuerdo con una tabla de mortalidad, de cada 93 745 personas de 25 años de edad sólo 87 426 llegan a los 40 años?<br /><br />probabilidad = 87 426/93 745 = 0.9325<br /><br /><br /><br /><strong>NOTA:</strong> La probabilidad de que una persona de 25 años llegue a los 40 años es de 0.9325<br /><br /><br />Relación de estaturas de 14 alumnos de la licenciatura en matemática educativa que toman clases los fines de semanas. " Histogramas de los alumnos del curso"<br />Estatura:<br />1.70<br />1.80<br />1.60<br />1.65<br />1.56<br />1.58<br />1.69<br />1.57<br />1.74<br />1.65<br />1.62<br />1.72<br />1.58<br />1.68<br /><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6EFbdKrMSLFFUyrqEjjJG5OI25oyh-7qQPXAyHHAxZnrC06FAOFoZkXpdiTJzymrCZH1WZsOuPKKvQJClkubjnTeB8WP9H6rsa8cYlf_jzQWc18AULX6GzPK0nPFw7iRQsH5iNeQNOt8/s1600/graficos+de+estaturas.jpg"><img style="WIDTH: 679px; HEIGHT: 275px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5655207413694580850" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6EFbdKrMSLFFUyrqEjjJG5OI25oyh-7qQPXAyHHAxZnrC06FAOFoZkXpdiTJzymrCZH1WZsOuPKKvQJClkubjnTeB8WP9H6rsa8cYlf_jzQWc18AULX6GzPK0nPFw7iRQsH5iNeQNOt8/s320/graficos+de+estaturas.jpg" /></a><br /><br /><br />n = 14, sumaxi =21.52, sumaxi^2 =35.6908, ó n - 1 =0.074678799, x =1.655384615<br /><br />NOTA: El símbolo matemático de suma lo sustitui por la palabra suma debido a que no pude aplicarlo por el desconocimiento de la opción del programa.<br /><br /><strong>Conclusiones:</strong><br /><strong></strong><br /><strong></strong>De acuerdo a la tarea realizada, se puede observar con claridad, el comportamiento que tienen los valores en cuanto a las estaturas de cada uno de los compañeros y se ven reflejados en la gráfica de histogramas y los intervalos de diez en diez centímetros.contador navahttp://www.blogger.com/profile/18119397243166467877noreply@blogger.com1tag:blogger.com,1999:blog-8148792504959658820.post-65402482126086651812011-09-21T18:57:00.001-07:002011-09-23T08:51:47.970-07:00Conjunto potenciaIntroducción<br /><br />El conjunto potencia nos permite simplificar un grupo o subgrupos de datos o elementos de manera muy precisa y en la probabilidad y estadística es de mucha relevancia hacer uso del conjunto potencia como el siguiente grupo de valores.<br /><br />Desarrollo:<br /><br />Conjunto potencia de (1,2,3,4)<br />2^n elementos es decir, 2^4 = 2*2*2*2 = 16<br /><br />( ( ) )<br />(1), (2), (3), (4)<br />(1,2), (1,3), (1,4)<br />(1,2,3), (1,2,4), (1,3,4)<br />(1,2,3,4)<br />(2,3), (2,4)<br />(2,3,4)<br />(3,4)<br /><br />Conclusiones:<br /><br /><br />Después de haber realizado la tarea y haber aplicado el conjunto potencia puedo concluir en que un grupo de datos, en este caso que fue de 4 elementos y agruparlos en pequeños subgrupos es semejante a la aplicación del conjunto potencia. es decir, al elevar cualquier valor a la n potencia, es igual que tomar los valores y agruparlos en subgrupos.contador navahttp://www.blogger.com/profile/18119397243166467877noreply@blogger.com6