#### Question

If A and B are events such that P (A|B) = P(B|A), then

(A) A ⊂ B but A ≠ B

(B) A = B

(C) A ∩ B = Φ

(D) P(A) = P(B)

#### Solution

It is given that, P(A|B) = P(B|A)

`=> (P (A ∩ B))/(P(B)) = (P (A ∩ B))/(P(A))`

⇒ P (A) = P (B)

Thus, the correct answer is D.

Is there an error in this question or solution?

Solution If a and B Are Events Such that P (A|B) = P(B|A), Then Concept: Properties of Conditional Probability.