동전 사건 독립

$X :$ 앞면이 나오는 개수 ㄱ. $\mathrm{P} ( A ) = \mathrm{P} ( X = 0 ) + \mathrm{P} ( X = 1 )$$\displaystyle = _{3} \mathrm{C} _{0} \left( \frac{1}{2} \right) ^{3} + _{3} \mathrm{C} _{1} \left( \frac{1}{2} \right) ^{3}$ $\displaystyle = \frac{4}{8} = \frac{1}{2} \cdots \cdots \text{참}$ ㄴ. $A \cap B$ : 앞면이 $0$개 $\displaystyle \mathrm{P} ( \mathit{A} \cap B ) = \mathrm{P} ( \mathit{X} = 0 ) = _{3} \mathrm{C} _{0} \left( \frac{1}{2} \right) ^{3} \frac{1}{8}$ …………참 ㄷ. $\mathrm{P} ( \mathit{B} ) = \mathrm{P} ( \mathit{X} = 0 ) + \mathrm{P} ( \mathit{X} = 3 )$ $\displaystyle = 2 \times _{3} \mathrm{C} _{0} \left( \frac{1}{2} \right) ^{3} = \frac{2}{8} = \frac{1}{4}$ $\displaystyle \mathrm{P} ( A \cap B ) = \frac{1}{8}$, $\displaystyle \mathrm{P} ( A ) \cdot \mathrm{P} ( B ) = \frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8}$ $\therefore A , B$는 독립…………참