독립인 사건

$\displaystyle \mathrm{P} \mathit{\left( A | B \right)} = \frac{\mathrm{P} \mathit{\left( A \cap B \right)}}{\mathrm{P} \mathit{\left( B \right)}} = \mathrm{P} \mathit{\left( A \right)} = \frac{1}{2}$ 에서 $\displaystyle \mathrm{P} \mathit{\left( A \cap B \right)} = \frac{1}{5}$이므로 $\displaystyle \mathrm{P} \mathit{\left( B \right)} = \frac{\frac{1}{5}}{\frac{1}{2}} = \frac{2}{5}$ $\therefore$ $\mathrm{P} \mathit{\left( A \cup B \right)}$$= \mathrm{P} \mathit{\left( A \right)} + \mathrm{P} \mathit{\left( B \right)} - \mathrm{P} \mathit{\left( A \cap B \right)}$ $\displaystyle = \frac{1}{2} + \frac{2}{5} - \frac{1}{5} = \frac{7}{10}$