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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?

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  • 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 by balaji.thirumalai

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