## Discrete Mathematics and Its Applications, Seventh Edition

$\frac{45}{64}$
To find $p(E|F)$, or the probability that event $E$ occurs if the event $F$ occurs, we use Bayes' Theorem, which states that $p(E|F)=p(F|E)p(F)p(E)$. $p(E)=\frac{2}{3},p(F)=\frac{3}{4}$, and $p(F|E)=\frac{5}{8}$, so $p(E|F)=\frac{\frac{5}{8}\frac{3}{4}}{\frac{2}{3}}=\frac{45}{64}$. This fraction is already in its simplest form.