Question

If $P\left(A/B\right)=P\left(B/A\right)$. $A$ and $B$ are two non-mutually exclusive events then

• A. $A$ and $B$ are necessarily same events
• B. $P\left(A\right)=P\left(B\right)$
• C. $P(A\cap B)=P\left(A\right)P\left(B\right)$
• D. all the above

Answer 1

The correct option is B $P\left(A\right)=P\left(B\right)$

Given $p\left(\frac{A}{B}\right)=P\left(\frac{B}{A}\right)\Rightarrow \frac{P(A\cap B)}{P\left(B\right)}=\frac{P(A\cap B)}{P\left(A\right)}$

$P\left(A\right)=P\left(B\right)$ [$P(A\cap B)\ne P\left(A\right).P\left(B\right)$ as they not independent]

$\therefore$ Option $B$ is correct.