Question

If A and B are events such that $P\left(A\right)=\frac{3}{8},$ $P\left(B\right)=\frac{5}{8}$ and $P(A\cup B)=\frac{3}{4},$ then $P\left(\frac{A}{B}\right)=$

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

Answer 1

The correct option is B $\frac{2}{5}$

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

$P\left(B\right)=\frac{5}{8}$

$P(A\cup B)=\frac{3}{4}$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$\frac{3}{4}=\frac{3}{8}+\frac{5}{8}-P(A\cap B)$

$\Rightarrow P(A\cap B)=1-\frac{3}{4}=\frac{1}{4}$

Now, $P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{1/4}{5/8}=\frac{2}{5}$.