독립사건 확률

${\mathrm{P}} ( A )$$= {\mathrm{P}} ( A \cup B ) - {\mathrm{P}} ( A ^{C} \cap B )$ $\displaystyle = \frac{5}{6} - \frac{1}{3}$ $\displaystyle = \frac{1}{2}$ 두 사건 $A$, $B$가 서로 독립이므로 $\displaystyle {\mathrm{P}} ( A \cap B ) = {\mathrm{P}} ( A ) {\mathrm{P}} ( B ) = \frac{1}{2} {\mathrm{P}} ( B )$ ${\mathrm{P}} ( A \cup B )$$= {\mathrm{P}} ( A ) + {\mathrm{P}} ( B ) - {\mathrm{P}} ( A \cap B )$ $\displaystyle = \frac{1}{2} + {\mathrm{P}} ( B ) - \frac{1}{2} {\mathrm{P}} ( B )$ $\displaystyle = \frac{5}{6}$ ∴ $\displaystyle {\mathrm{P}} ( B ) = \frac{2}{3}$