Let $A$ and $B$ be two events with $P(A)=\frac{1}{7}$, $P\left(\frac{A}{B}\right)=\frac{2}{3}$ and…
Let $A$ and $B$ be two events with $P(A)=\frac{1}{7}$, $P\left(\frac{A}{B}\right)=\frac{2}{3}$ and $P(B)=\frac{2}{7}$. Then, the value $P\left(\frac{B}{A}\right)$ is
$\frac{1}{5}$
$\frac{5}{49}$
$\frac{4}{5}$
$\frac{3}{5}$
Solution
$\begin{aligned} P(B / A) & =\frac{P(A / B) P(B)}{P(A)} \\ & =\frac{(2 / 5)(2 / 7)}{(1 / 7)}=\frac{4}{5}\end{aligned}$