조건부확률

$\displaystyle \mathrm{P} \mathit{\left( B | A \right)} = \frac{\mathrm{P} \mathit{\left( A \cap B \right)}}{\mathrm{P} \mathit{\left( A \right)}} = \frac{1}{4}$에서 $\displaystyle \mathrm{P} \mathit{\left( A \right)} = \frac{2}{5}$이므로 $\displaystyle \mathrm{P} \mathit{\left( A \cap B \right)} = \frac{1}{4} \times \frac{2}{5} = \frac{1}{10}$ 이때 $\mathrm{P} \mathit{\left( A \cup B \right)} = \mathrm{P} \mathit{\left( A \right)} + \mathrm{P} \mathit{\left( B \right)} - \mathrm{P} \mathit{\left( A \cap B \right)}$에서 $\displaystyle 1 = \frac{2}{5} + \mathrm{P} \mathit{\left( B \right)} - \frac{1}{10}$ $\therefore$ $\displaystyle \mathrm{P} \mathit{\left( B \right)} = \frac{7}{10}$