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Ejemplo de probabilidad total

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Ejemplo de probabilidad total

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Un problema de cálculo de probabilidad total.

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Created by

Violeta Migallón
Violeta Migallón
Spain

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    Violeta Migallón
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    Sergio Molero García
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    65
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Ejemplo de probabilidad totalOnline version

Un problema de cálculo de probabilidad total.

by Violeta Migallón
1

E A 6 2 20 B C 75 Cb total 5 50 probabilidad 1 Cc Ca

Enunciado : Tres personas A B , y C , comparten una oficina con una única cuenta de correo electrónico . De los correos que llegan 2 / 5 son para A , 2 / 5 para B y 1 / 5 para C . El trabajo de estas personas les obliga a frecuentes salidas , de manera que A está fuera el 50 por ciento de su tiempo y B y C el 25 por ciento de su tiempo . Atendiendo a todo esto calcula la probabilidad de que esté la persona a la que le han mandado el correo .

Solución :
Atendiendo al enunciado del problema definimos los siguientes sucesos y calculamos sus probabilidades :

Ca = { correo para A } , P ( Ca ) = 2 / 5 ,
Cb = { correo para } , P ( Cb ) = / 5 ,
Cc = { correo para } , P ( Cc ) = /

Ea = { estar } , P ( Ea ) = 0 . ,
Eb = { estar B } , P ( Eb ) = 0 . 75 ,
Ec = { estar C } , P ( Ec ) = 0 .

A continuación definimos el suceso

E = { estar la persona a la que le han mandado el correo } y habrá que calcular la P ( ) .

Entonces , teniendo en cuenta el teorema de la :

P ( E ) = P ( E / } P ( Ca ) + P ( E / } P ( Cb ) + P ( E / } P ( Cc ) = 0 . 50 ? ( 2 / 5 ) + 0 . 75 ( 2 / 5 ) + 0 ? 75 ? ( 1 / 5 ) = 13 / = 0 . 65

Por lo que la probabilidad de que esté la persona a la que le han mandado el correo es igual a 0 .

 
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