Question

$A$ and $B$ are events such that $p(A\cup B)=3/4,P(A\cap B)=\frac{1}{4},P\left(\overline{A}\right)=\frac{2}{3}$, then $P\left(\right(\overline{A}\cap B)$ equals

• A. $\frac{5}{12}$
• B. $\frac{3}{8}$
• C. $\frac{4}{5}$
• D. $\frac{5}{4}$

Answer 1

The correct option is A $\frac{5}{12}$

Given $P(A\cup B)=3/4$

$P(A\cap B)=1/4$ $P\left(\overline{A}\right)=2/3\therefore P\left(B\right)=\frac{2}{3}$

By using $P\left(B\right)=P(A\cup B)+P(A\cap B)-P\left(A\right)$

$\therefore P(\overline{A}\cap B)=\frac{2}{3}-\frac{1}{4}=\frac{5}{12}$