Question

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

• A. $\frac{1}{4}$
• B. $\frac{1}{12}$
• C. $\frac{3}{16}$
• D. $\frac{3}{4}$

Answer 1

Answer: (A)

$P(A)=\frac{1}{2},P(B)=\frac{1}{3},P(A\cap B)=\frac{1}{4}\times \frac{1}{3}=\frac{1}{12}$
$P(A\cap B)=P(\overline{A\cup B})$
$P(A\cap B)=1-P(A\cup B)$
$P(A\cap B)=1-\left[\frac{1}{2}+\frac{1}{3}-\frac{1}{12}\right]$
$P(A\cap B)=1-\left[\frac{6+4-1}{12}\right]$
$P(A\cap B)=1-\frac{9}{12}$
$P(A\cap B)=\frac{1}{4}$