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 $6P\left(F|E\right)$.

Answer 1

It is given that $P\left(E\right)=0.6,P\left(F\right)=0.3$ and $P(E\cap F)=0.2$
$\Rightarrow P\left(E|F\right)=\frac{P(E\cap F)}{P\left(F\right)}=\frac{0.2}{0.3}=\frac{2}{3}$
$\Rightarrow P\left(F|E\right)=\frac{P(E\cap F)}{P\left(E\right)}=\frac{0.2}{0.6}=\frac{1}{3}=0.33$