선거 당선과 노선 개편

$\mathrm{P} ( \mathit{B} _{1} ) , \mathrm{P} ( \mathit{B} _{2} ) , \mathrm{P} ( \mathit{B} _{3} )$을 각각 갑, 을, 병이 당선될 확률이라 하면, $\mathrm{P} ( \mathit{B} _{1} ) = 0.3 , \mathrm{P} ( \mathit{B} _{2} ) = 0.5 , \mathrm{P} ( \mathit{B} _{3} ) = 0.2$가 된다. $P ( A )$를 버스노선이 개편 될 확률이라고 하면, $\mathrm{P} ( \mathit{A} | B _{1} ) = 0.8 , \mathrm{P} ( \mathit{A} | B _{2} ) = 0.1$$, \mathrm{P} ( \mathit{A} | B _{3} ) = 0.4$가 된다. 따라서, $\mathrm{P} ( \mathit{A} ) = \mathrm{P} ( \mathit{A} | B _{1} ) \mathrm{P} ( \mathit{B} _{1} ) + \mathrm{P} ( \mathit{A} | B _{2} ) \mathrm{P} ( \mathit{B} _{2} )$$+ \mathrm{P} ( \mathit{A} | B _{3} ) \mathrm{P} ( \mathit{B} _{3} )$$= 0.37$