If A and B are events such that (P(A|B)=P(B|A)), then: | Mathematics | SolveeIt | Solveeit

Today, August 19

Question

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

A

$A⊂B$

B

$A=B$

C

$A∩B=ϕ$

D

$P(A)=P(B)$

Answer

$P(A)=P(B)$

Explanation

Solution

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

$⇒\frac {P(A∩B)}{P(B)} =\frac {P(B∩A)}{P(A)}$

$P(A)=P(B)$

$Therefore,\ option \ (D)\ is\ correct.$