If P(B)=0.2,P(A | B)=0.7,P(B)=0.8, and P(A|B)=0.5, find P(B | A).

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If P(B)=0.2,P(A | B)=0.7,P(B)=0.8, and P(A|B)=0.5, find P(B | A).

math Statistics-And-Probability

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Answer 1

Answer #1

Answer:

Given P(B)=0.2,P(A|B)=0.7,P(B')=0.8, and P(A|B')=0.5
P(A)= P(A∩S)
= P[A∩(BUB')]
= P[(A∩B) U (A∩B')]
= P(A∩B) + P(A∩B')
= P(A|B)P(B) + P(A|B')P(B')
= (0.7)(0.2) + (0.5)(0.8)
= 0.54

P(B|A) = P(A∩B)/P(A)
= 0.7*0.2/0.54
=0.2592

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Answer 2

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