question_answer

\[P\left( \frac{\overline{A}}{A\cup B} \right)\]is equal to

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

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

C)  \[\frac{P(\overline{A}\cap B)}{P(A\cup B)}\]

D)  \[\frac{P(A)}{P(A\cup B)}\]

Correct Answer: C

Solution :

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