Answer
$\frac{3}{17}$
Work Step by Step
By using Baye's theorem, we get
$P(F_{1}|E)=\frac{P(F_{1})P(E|F_{1})}{P(F_{1})P(E|F_{1})+P(F_{2})P(E|F_{2})+P(F_{3})P(E|F_{3})}=\frac{\frac{1}{4}\times\frac{1}{8}}{\frac{1}{4}\times\frac{1}{8}+\frac{1}{4}\times\frac{1}{4}+\frac{1}{2}\times\frac{1}{6}}=\frac{3}{17}$
