Question

A fair die is rolled. Consider the events $E=\{1,3,5\}$ and $F=\{2,3\}$, find $P\left(E|F\right)$.

Answer 1

$E=\{1,3,5\};F=\{2,3\}$

$E\cap F=\left\{3\right\}$

Total no. of possible outcomes = 6

$P(E\cap F)=\frac{1}{6}$

$P\left(F\right)=\frac{2}{6}=\frac{1}{3}$

$P\left(E/F\right)=\frac{P(E\cap F)}{P\left(F\right)}$

$=\frac{1/6}{1/3}$

$=\frac{1}{2}$

$\therefore P\left(E/F\right)=\frac{1}{2}$