Question

If $A$ and $B$ are two events such that $P(\bar{A})=0.3,P(B)=0.4$ and $P(A\bar{B})=0.5$, then $P\left(\frac{B}{A\cup \bar{B}}\right)$ is equal to

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

Answer 1

Answer: (C)

$\Theta P(\bar{A})=1-P(A)=0.3\Rightarrow P(A)=0.7$
$P(A\bar{B})=P(A)-P(A\cap B)=0.5\Rightarrow P(A)-P(A\cap B)=0.2$
$\therefore P\left(\frac{B}{A\cup \bar{B}}\right)=\frac{P(B\cap (A\cup \bar{B}))}{P(A\cup \bar{B})}=\frac{P(A\cap B)}{1-(P(B)-P(A\cap B))}=\frac{0.2}{0.8}=\frac{1}{4}$