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

Question

Philoid · Accepted Answer

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)=

So, P(A|B) = , then

P(A|B) =

P(A|B)=2/5

Now, For, 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