독립사건의 확률

$A , B$가 서로 독립이면 $A ^{C} , B$도 서로 독립이므로 $\mathrm{P} ( \mathit{A} ^{C} \cap B ) = \mathrm{P} ( \mathit{A} ^{C} ) \cdot \mathrm{P} ( \mathit{B} )$$= \left\{ 1 - \mathrm{P} ( \mathit{A} ) \right\} \cdot \mathrm{P} ( \mathit{B} )$ $\displaystyle = \left\{ 1 - P ( A ) \right\} \cdot \frac{1}{2} = \frac{1}{5}$ $\displaystyle \therefore P ( A ) = \frac{3}{5}$ $A , B$가 서로 독립이므로 $\mathrm{P} ( \mathit{A} \cap B ) = \mathrm{P} ( \mathit{A} ) \cdot \mathrm{P} ( \mathit{B} )$ $\mathrm{P} ( \mathit{A} \cup B ) = \mathrm{P} ( \mathit{A} ) + \mathrm{P} ( \mathit{B} ) - \mathrm{P} ( \mathit{A} \cap B )$ $\displaystyle = \frac{3}{5} + \frac{1}{2} - \frac{3}{5} \cdot \frac{1}{2} = \frac{8}{10} = 0.8$