question_answer

If A and B are two events, then\[P\left( \frac{\overline{A}}{B} \right)\]is equal to

A)  \[1-P\left( \frac{A}{B} \right)\]

B)  \[\frac{1-P(AB)}{P(B)}\]

C)  \[\frac{1-P(A+B)}{P(\overline{B})}\]

D)  \[\frac{P(\overline{A})}{P(\overline{B})}\]

Correct Answer: C

Solution :

 \[P\left( \frac{\overline{A}}{B} \right)=\frac{P(\overline{A}\cap \overline{B})}{P(\overline{B})}\] \[=\frac{P(\overline{A\cup B})}{P(\overline{B})}\] \[=\frac{1-P(A\cup B)}{P(\overline{B})}\] \[=\frac{1-P(A+B)}{P(\overline{B})}\]