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MoiLeiva
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Joined: 06 Mar 2015
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PostPosted: Fri Mar 06, 2015 8:11 am  Post subject:  Problema probabilidad. Reply with quoteBottom of PageBack to top

Sean A y B dos sucesos equiprobables. Se sabe que P(A ∩ B) = 0,2 y
P( A`∩ B`) = 0,1. Calcule P(A) y P(B).

Alguien me ayuda por favor. Gracias


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Granada
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PostPosted: Fri Mar 06, 2015 8:29 am  Post subject:  (No subject) Reply with quoteBottom of PageBack to top

P(A ∩ B) = P(A).P(B)
No se que significa P( A`∩ B`), pero seguro te quedan 2 ecuaciones con 2 incognitas.

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SMA
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PostPosted: Fri Mar 06, 2015 1:39 pm  Post subject:  (No subject) Reply with quoteBottom of PageBack to top

debe ser : A complemento y B complemento.

P(no A ) = 1 - P(A)
P(no B) = 1- P(B)


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Davydenko
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Joined: 16 Aug 2013
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PostPosted: Fri Mar 06, 2015 10:11 pm  Post subject:  (No subject) Reply with quoteBottom of PageBack to top

- Sean A y B dos sucesos equiprobables
P(A) = P(B)

- P(A ∩ B) = 0,2
Sabiendo que
P(A U B) = P(A) + P(B) - P(A ∩ B) sigue
P(A ∩ B) = P(A) + P(B) - P(A U B)

P( A`∩ B`) = 0,1
lo mismo
P(A` ∩ B`) = P(A`) + P(B`) - P(A` U B`) = 0,1

Y, por complemento
P(A`) = 1 - P(A)

Paso lo que hay, reemplazando P(A) = P(B)
P(A`) + P(A`) - P(A` U B`) = 0,1
y con P(A`) = 1 - P(A) :
1 - P(A) + 1 - P(A) - P(A` U B`) = 0,1

lo ultimo, con un diagramita de venn sacas info sobre P(A` U B`)
fijate que es (clave):
P(A` U B`) = 1 - P(A ∩ B)
P(A` U B`) = 1 - 0,2 = 0,8

queda
1 - P(A) + 1 - P(A) - 0,8 = 0,1 => 1,2 - 2*P(A) = 0,1

2*P(A) = 1,3
P(A) = P(B) = 0,75
P(A U B) = 1,1

La idea del ejercicio es hacer diagramas de Venn.


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Floyd
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PostPosted: Sat Mar 07, 2015 6:49 am  Post subject:  (No subject) Reply with quoteBottom of PageBack to top

P(A U B) = 1,1 ???????


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SMA
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Joined: 23 Jul 2012
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PostPosted: Sat Mar 07, 2015 3:42 pm  Post subject:  (No subject) Reply with quoteBottom of PageBack to top

jajajajaj, posta. 1,1?????


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Davydenko
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Joined: 16 Aug 2013
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PostPosted: Sat Mar 07, 2015 8:24 pm  Post subject:  (No subject) Reply with quoteBottom of PageBack to top

jaja, estaba viendo si estabas atento.
Fijate el ultimo paso

1 - P(A) + 1 - P(A) - 0,8 = 0,1
1,2 - 2*P(A) = 0,1
1,2 - 0,1 = 2*P(A)

2*P(A) = 1,1
P(A) = P(B) = 0,65
P(A U B) = 0,9


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Davydenko
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Joined: 16 Aug 2013
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PostPosted: Sat Mar 07, 2015 8:26 pm  Post subject:  (No subject) Reply with quoteBottom of PageBack to top

Una resolución más simple

P(A) = P(B)
P(A ∩ B) = 0,2
P( A`∩ B`) = 0,1

Sabiendo que
P(A U B) = P(A) + P(B) - P(A ∩ B) sigue
P(A ∩ B) = 2*P(A) - P(A U B) = 0,2


lo ultimo, con un diagramita de venn sacas info sobre P(A` U B`)
fijate que es (clave):
P( A`∩ B`) = 1 - P(A U B)
0,1 =1 - P(A U B)

Entonces
P(A U B) = 0,9

Y usando la primer ecuación, P(A) = P(B) = 0,65


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