Question

Let A and B be two events such that $P\left(A\right)=\frac{1}{3},P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P\left(\frac{B}{A}\right)=\frac{2}{5}$
$P\left(\frac{\overline{A}}{B}\right)=$

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

Answer 1

The correct option is A $\frac{1}{2}$

$P\left(\frac{\overline{A}}{B}\right)=1-P\left(\frac{A}{B}\right)=\frac{1}{2}\frac{P(A\cap B)}{P\left(A\right)}=\frac{2}{5}\Rightarrow P(A\cap B)=\frac{2}{15}\Rightarrow P\left(B\right)=\frac{4}{15}P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=\frac{7}{15}$