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)

Answer 1

Answer:

option (D) is correct

Step-by-step explanation:

Conceept:

conditional probabiity of B given A is

$P(B|A)=\frac{P(A\:intersection\:B)}{P(A)}$

Given:

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

$\frac{P(A\:intersection\:B)}{P(B)}=\frac{P(A\:intersection\:B)}{P(A)}\\\\\frac{1}{P(B)}=\frac{1}{P(A)}$

P(A)=P(B)