Question

If A and B are events such that P(A/B) = P(B/A) ≠ 0, 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) ≠ 0, then P(A) = P(B).

Explanation:

Given,

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

⇒ `(P(A cap B))/(P(B)) = (P(B cap A))/(P(A))`

⇒ `(P(A cap B))/(P(B)) = (P(A cap B))/(P(A))`

⇒ P(A) = P(B)