question_answer

\[P(A\cup B)=\frac{1}{2},P(\bar{A})=\frac{2}{3},\] find \[P(\bar{A}\cap B)\]

A)  \[\frac{1}{3}\]

B)  \[1\]

C)  \[\frac{1}{5}\]

D)  \[\frac{1}{6}\]

Correct Answer: D

Solution :

Given,  \[P(A\cup B)=\frac{1}{2}\] and \[P(\bar{A})=\frac{2}{3}\] \[\therefore \] \[P(A)=1-\frac{2}{3}=\frac{1}{3}\] Now.\[P(\bar{A}\cap B)=P(A\cup B)-P(A)=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}\]