Question

Given that $E$ and $F$ are events such that $P\left(E\right)=0.6,P\left(F\right)=0.3$ and $P(E\cap F)=0.2,$ find $P\left(E|F\right)$ and $P\left(F|E\right)$

Answer 1

$F(E\cap F)=0.2,P\left(F\right)=0.3$
$\therefore P\left(E|F\right)=\frac{P(E\cap F)}{P\left(F\right)}=\frac{.2}{.3}=\frac{2}{3}$
$P\left(F|E\right)=\frac{E(E\cap F)}{P\left(E\right)}=\frac{.2}{.6}\frac{2}{6}=\frac{1}{3}$