배반사건의 확률

${\mathrm{P}} \left( A ^{C} \right) = 1 - {\mathrm{P}} \left( A \right)$에서 $\displaystyle 1 - {\mathrm{P}} \left( A \right) = {\mathrm{P}} \left( A \right) + \frac{1}{2}$, $\displaystyle {\mathrm{P}} \left( A \right) = \frac{1}{4}$ 두 사건 $A$, $B$가 서로 배반사건이므로 $\displaystyle {\mathrm{P}} \left( A \cup B \right) = {\mathrm{P}} \left( A \right) + {\mathrm{P}} \left( B \right) = \frac{1}{4} + {\mathrm{P}} \left( B \right) = \frac{1}{3}$ 따라서 $\displaystyle {\mathrm{P}} \left( B \right) = \frac{1}{3} - \frac{1}{4} = \frac{1}{12}$