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Question

For two events A and B, if
P(A)=P(A | B) =1/4 and P(B | A) =1/2, then


A

(a) A and B are independent

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B

(b) A and B are mutually exclusive

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C

(c) P(A' | B ') =3/4

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D

(d) P(B' | A') =1/2

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Solution

The correct option is D

(d) P(B' | A') =1/2


We have,
P(A) =P(A|B) =P(AB)P(B)P(AB)=P(A)P(B)
Therefore, A and B are independent.
Since
P(AB)=P(A)P(B|A)=(1/4)(1/2)=1/80
A and B cannot be mutually exclusive.
As A and B are independent
P(A|B)=P(A)=1P(A)=11/4=3/4
Since A and B are independent,
P(B)=P(B|A)=1/2P(B|A)=P(B)=1P(B)=1/2



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