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# Let E and F be events with $P (E) = \frac{3}{5} , P (F)= \frac{3}{10}$ and $P (E \cap F) = \frac{1}{5}$ . Are E and F independent?

Can you answer this question?

Toolbox:
• To check if 2 events E and F are independent, check if $\;P(E).P(F)=P(E\cap\;F)$
Given $\;P(E)=\large \frac{3}{5}$, $\;P(F)=\large \frac{3}{10}$ and $\;P(E\cap\;F)=\large \frac{1}{5}$

$\Rightarrow \;P(E).P(F)=\large \frac{3}{5}\times\frac{3}{10}$$=\large \frac{9}{50}$$\neq\;P(E\cap\;F)$
Therefore, E and F are NOT independent

answered Jun 19, 2013