Question

A and B are two events such that $P\left(\overline{A}\right)=0.3,P\left(\overline{B}\right)=0.25$ and $P(\overline{A}\cap \overline{B})=0.2$ then $P\left(\frac{A}{B}\right)$ is

• A. $\frac{12}{15}$
• B. $\frac{11}{15}$
• C. $\frac{14}{15}$
• D. $\frac{13}{15}$

Answer 1

The correct option is D $\frac{13}{15}$

$P\left(A\right)=0.7$ & $P\left(B\right)=0.75$
$P(\overline{A}\cap \overline{B})=0.2$
$P\left(\overline{A\cup B}\right)=0.2$
$P(A\cup B)=0.8=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$P(A\cap B)=0.7+0.75-0.8=0.65$
$\therefore P\left(\frac{A}{B}\right)=\frac{0.65}{0.75}=\frac{13}{15}$