Question

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

Options

• A ⊂ B but A ≠ B

• A = B

• A ∩ B = Φ

• P(A) = P(B)

Answer 1

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

Explanation:

P(A|B) = P(B|A)

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

⇒ P(A) = P(B)