배반사건의 확률

두 사건 $A$, $B$는 서로 배반사건이므로 $\mathrm{P} \mathit{\left( A \cap B \right)} = 0$ $\displaystyle \mathrm{P} \mathit{\left( A ^{C} \right)} = \frac{5}{6}$이므로 $\displaystyle \mathrm{P} \mathit{\left( A \right)} = 1 - \frac{5}{6} = \frac{1}{6}$ $\mathrm{P} \mathit{\left( A \cup B \right)} = \mathrm{P} \mathit{\left( A \right)} + \mathrm{P} \mathit{\left( B \right)}$에서 $\displaystyle \frac{3}{4} = \frac{1}{6} + \mathrm{P} \mathit{\left( B \right)}$ $\displaystyle \mathrm{P} \mathit{\left( B \right)} = \frac{7}{12}$ $\therefore$ $\displaystyle \mathrm{P} \mathit{\left( B ^{C} \right)} = 1 - \frac{7}{12} = \frac{5}{12}$