Question

If two events $A$ and $B$ are such that $P\left(A^C\right)=0.3,P\left(B\right)=0.4$ and $P\left({AB}^C\right)=0.5$, then $P\left[B/(A\cup B^C)\right]$ is equal to

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

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

Given, $P\left(A^C\right)=0.3,P\left(B\right)=0.4$ and $P\left({AB}^C\right)=0.5$

Therefore, $P\left[B^C|(A\cup B^C)\right]=\frac{P\{B\cap (A\cup B^C)\}}{P(A\cup B^C)}$
$=\frac{P(A\cap B^C)}{P\left(A\right)+P\left(B\right)-P(A\cap B^C)}$

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