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# Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E $\cap$ F) = 0.2, find P (E|F) and P(F|E)

$\begin{array}{1 1}P(E/F) = 1/3, P(F/E) = 2/3 \\P(E/F) = 2/3, P(F/E) = 1/3 \\P(E/F) = 1/3, P(F/E) = 1/3 \\P(E/F) = 2/3, P(F/E) = 2/3 \end{array}$

Toolbox:
• $\;P(E/F)=\Large \frac{p(E\;\cap\;F)}{P(F)}$
• $\;P(F/E)=\Large \frac{p(E\;\cap\;F)}{P(E)}$
Given $P(E)=0.6\;P(F)=0.3\;P(E\cap\;F)=0.2$
$\Rightarrow$ $\;P(E/F)=\large \frac{0.2}{0.3}=\frac{2}{3}$
$\Rightarrow$ $\;P(F/E)=\large \frac{0.2}{0.6}=\frac{2}{6}=\frac{1}{3}$
edited Jun 18, 2013