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
  1. $\frac{1}{5}$
  2. $\frac{5}{49}$
  3. $\frac{4}{5}$
  4. $\frac{3}{5}$

Solution

$\begin{aligned} P(B / A) & =\frac{P(A / B) P(B)}{P(A)} \\ & =\frac{(2 / 5)(2 / 7)}{(1 / 7)}=\frac{4}{5}\end{aligned}$

Asked in: AP EAMCET 2021 (23 Aug Shift 1)

Practice more Probability questions on Aicharya