Q. If $A$ and $B$ are two events such that $P(A) > 0$ and $P(B) \neq 1,$then $P(\overline{A}|\overline{B})$ is equal to
A) $1 - P(A|\overline{B})$
B) $1 - P(\overline{A}|B)$
C) $\frac{1 - P(A \cap B)}{P(B)}$
D) $\frac{P(\overline{A})}{P(\overline{B})}$
Explanation
(a)
We know that, $P(A|\overline{B}) + P(\overline{A}|\overline{B}) = 1$
$\Rightarrow P\left( \overline{A} \middle| \overline{B} \right) = 1 - P(A|\overline{B})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.