Question

If $P\left(A\right)=\frac{1}{2}$, $P\left(B\right)=\frac{3}{8}$ and $P(A\cap B)=\frac{1}{5}$ then P(B|A) is equal tp:

• A. $\frac{2}{5}$
• B. $\frac{8}{15}$
• C. $\frac{1}{3}$
• D. $\frac{5}{8}$

Answer 1

Answer: (A)

$\frac{2}{5}$

Given:-

$P\left(A\right)=\frac{1}{2}$

$P\left(B\right)=\frac{3}{8}$

$P(A\cap B)=\frac{1}{5}$

As we know that,

$P\left(B|A\right)=\frac{P(B\cap A)}{P\left(A\right)}$

$\therefore P\left(B|A\right)=\frac{\left(\frac{1}{5}\right)}{\left(\frac{1}{2}\right)}$

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

Hence the correct answer is $\frac{2}{5}$.