Question:
If A and B are events such that P (A|B) = P(B|A), then
(A) $A \subset B$ but $A \neq
B$ (B) $A=B$
(C) $A \cap B=\Phi$
(D) $P(A)=P(B)$
Solution:
It is given that, P(A|B) = P(B|A)
$\Rightarrow \frac{P(A \cap B)}{P(B)}=\frac{P(A \cap B)}{P(A)}$
$\Rightarrow P(A)=P(B)$
Thus, the correct answer is D.