Answer
$p(F|E)=\frac{3}{5}$
Work Step by Step
In this problem, we seek to find $p(F|E)$, which is the probability of event $F$ if $E$ occurs. In order to do so, we use Bayes' theorem, or $p(F|E)=\frac{p(E|F)p(F)}{p(E)}=\frac{\frac{2}{5}\frac{1}{2}}{\frac{1}{3}}=\frac{3}{5}$.
