Question

Let $A$ and $B$ be two events such that $p(A)=\frac{3}{8},p(B)=\frac{5}{8}$ and $p(A\cup B)=\frac{3}{4}$ then $p(A/B)\cdot P\left(A^{\prime }/B\right)$ is equal to

• A. $\frac{2}{5}$
• B. $\frac{3}{8}$
• C. $\frac{3}{20}$
• D. $\frac{6}{25}$

Answer 1

Answer: (D)

$P(A)=\frac{3}{8}P(B)=\frac{5}{8}P(A\cup B)=\frac{3}{4}$
$cP(A\cap B)=P(A)+P(B)-P(A\cup B)$
$=\frac{3}{8}+\frac{5}{8}-\frac{3}{4}=\frac{2}{8}=1/4$
$P(A/B)=\frac{1/4}{5/8}=2/5$
$P\left(A^{{}^{\prime }}/B\right)=\frac{P(A)-P(A\cap B)}{P(B)}=\frac{5/8-\frac{1}{4}}{5/8}=\frac{3}{5}$
$P(A/B)\cdot P\left(A^1/B\right)=\frac{2}{5}\cdot \frac{3}{5}=\frac{6}{25}$