Question

Let $A$ and $B$ are two independent events such that $P\left(A\right)+P\left(B\right)=\frac{3}{4}$ and $P\left(\frac{\overline{A}}{B}\right)=\frac{2}{5}$, then $P(A\cap B)$ is -

• A. $\frac{9}{20}$
• B. $\frac{9}{100}$
• C. $\frac{5}{17}$
• D. $\frac{6}{20}$

Answer 1

The correct option is B $\frac{9}{100}$

$P\left(\frac{\overline{A}}{B}\right)=\frac{P\left(\overline{A}\right)P\left(B\right)}{P\left(B\right)}=\frac{2}{5}\Rightarrow P\left(A\right)=\frac{3}{5}$

$P(A\cap B)=P\left(A\right)P\left(B\right)$

$=\frac{3}{5}(\frac{3}{4}-\frac{3}{5})=\frac{9}{100}$