Question

If A and B are events such that $P\left(A\right)=\frac{1}{2}$, $P\left(B\right)=\frac{1}{3}$ and $P(A\cap B)=\frac{1}{4}$, then find $P\left(B/A\right)$.

Answer 1

This is conditional probability, $P(A\bigcap B)=P\left(A\right)P\left(\frac{B}{A}\right)$

$\Rightarrow P\left(\frac{B}{A}\right)=\frac{P(A\bigcap B)}{P\left(A\right)}=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{2}{4}=\frac{1}{2}$