Question

If two events A and B are such that $P\left(A^c\right)=0.3,P\left(B\right)=0.4$ and $P(A\cap B^c)=0.5$ then the value of $P\left(\frac{B}{A\cup B^c}\right)$ is

• A. $\frac{1}{8}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{1}{4}$

$P\left(\frac{B}{A\cup B^c}\right)=\frac{P(B\cap (A\cup B^c\left)\right)}{P(A\cup B^c)}$
$=\frac{P(A\cap B)}{P\left(A\right)+P\left(B^c\right)-P(A\cap B^c)}$
$=\frac{P\left(A\right)-P(A\cap B^c)}{P\left(A\right)+P\left(B^c\right)-P(A\cap B^c)}$
$=\frac{0.7-0.5}{0.8}=\frac{1}{4}$