Question:
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Solution:
It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2
$\Rightarrow \mathrm{P}(\mathrm{E} \mid \mathrm{F})=\frac{\mathrm{P}(\mathrm{E} \cap \mathrm{F})}{\mathrm{P}(\mathrm{F})}=\frac{0.2}{0.3}=\frac{2}{3}$
$\Rightarrow \mathrm{P}(\mathrm{F} \mid \mathrm{E})=\frac{\mathrm{P}(\mathrm{E} \cap \mathrm{F})}{\mathrm{P}(\mathrm{E})}=\frac{0.2}{0.6}=\frac{1}{3}$
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