Question

If $P\left(A\right)=\frac{1}{4},P\left(\overline{B}\right)=\frac{1}{2}$ and $P(A\cup B)=\frac{5}{9}$, then $P\left(A/B\right)$ is

• A. $\frac{7}{36}$
• B. $\frac{7}{9}$
• C. $\frac{7}{18}$
• D. $\frac{7}{72}$

Answer 1

Answer: (C)

$\frac{7}{18}$

We have,
$P(A\cup B)=\frac{5}{9}$
$\Rightarrow P\left(A\right)+P\left(B\right)-P(A\cap B)=\frac{5}{9}$
$\Rightarrow \frac{1}{4}+\frac{1}{2}-P(A\cap B)=\frac{5}{9}$
$\Rightarrow P(A\cap B)=\frac{7}{36}$
$\Rightarrow P\left(B\right)P\left(A/B\right)=\frac{7}{36}$
$\Rightarrow \frac{1}{2}\times P\left(A/B\right)=\frac{7}{36}\Rightarrow P\left(A/B\right)=\frac{7}{18}$