조건부확률 계산

$\displaystyle {\mathrm{P}} ( B ) = 1 - {\mathrm{P}} ( B ^{c} ) = 1 - \frac{2}{3} = \frac{1}{3}$ $\displaystyle {\mathrm{P}} ( B | A ) = \frac{{\mathrm{P}} ( A \cap B )}{{\mathrm{P}} ( A )} = \frac{1}{6}$에서 $\displaystyle {\mathrm{P}} ( A \cap B ) = \frac{1}{6} {\mathrm{P}} ( A ) = \frac{1}{6} \cdot \frac{1}{2} = \frac{1}{12}$ ${\mathrm{P}} ( A \cap B ) + {\mathrm{P}} ( A ^{c} \cap B ) = {\mathrm{P}} ( B )$이므로 $\displaystyle {\mathrm{P}} ( A ^{c} \cap B ) = \frac{1}{3} - \frac{1}{12} = \frac{1}{4}$ ∴ $\displaystyle {\mathrm{P}} ( A ^{c} | B ) = \frac{{\mathrm{P}} ( A ^{c} \cap B )}{{\mathrm{P}} ( B )}$$\displaystyle = \frac{\frac{1}{4}}{\frac{1}{3}} = \frac{3}{4}$