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 $P\left(A/B\right)$.

Answer 1

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

$P\left(A/B\right)=\frac{P(A\cap B)}{P\left(B\right)}$

$P\left(A/B\right)=\frac{1/4}{1/3}=\frac{3}{4}$.