Q. If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$,then $P(A|\overline{B})$ is equal to (Here, $\overline{B}$is the complement of the event $B$)
A) $\frac{1}{P(B)}$
B) $\frac{1}{1 - P(B)}$
C) $\frac{P(A)}{P(B)}$
D) $\frac{P(A)}{1 - P(B)}$
Explanation
(d)
Given $A$ and $B$ are mutually exclusive events
$\therefore P(A \cap B) = \phi$
Now, $P\left( A \middle| \overline{B} \right) = \frac{P(A \cap \overline{B})}{P(B)}$
$= \frac{P(A) - P(A \cap B)}{P(\overline{B})}$
$= \frac{P(A)}{1 - P(B)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.