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