Q71 of 108 Page 271

Let A and B be two events such that P(A) = 3/8, P(B) = 5/8 and P(A ∪ B) = 3/4. Then P(A | B).P(A′ | B) is equal to

Given, P(A) = 3/8, P(B) = 5/8 and P(A ∪ B) = 3/4

Now, We know that, P(A ∪ B)=P(A)+P(B)- P(A ∩ B)


P(A ∩ B)=


P(A ∩ B)=


So, P(A|B) = , then


P(A|B) =


P(A|B)=2/5


Now, For, P(A’|B)




P(A’|B)=


P(A’|B)=


P(A’|B)= 3/5


Therefore, P(A | B).P(A′|B)=


Hence, P(A | B).P(A′|B)=6/25

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