Question

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

• A. $1/12$
• B. $5/12$
• C. $4/9$
• D. $1/3$

Answer 1

Answer: (B)

$5/12$

$P(\overline{A}\cap B)=P\left(\overline{A}\right)-(1-P(A\cup B\left)\right)$

$=\frac{2}{3}-\frac{1}{4}=\frac{5}{12}$