E E E:抓到娃娃
H H H:坐地铁
H ˉ \bar H Hˉ:坐公交
P ( E ) = P ( H ) P ( E ∣ H ) + P ( H ‾ ) P ( E ∣ H ‾ ) P({E}) = P({H}) P({E} \mid {H}) + {P}(\overline{{H}}) {P}({E} \mid \overline{{H}}) P(E)=P(H)P(E∣H)+P(H)P(E∣H)
P ( H ∣ E ) = P ( E ∣ H ) P ( H ) P ( E ) = 0.6 P({H} \mid {E}) = \dfrac{{P}({E} \mid {H}) {P}({H})}{{P}({E})} = 0.6 P(H∣E)=P(E)P(E∣H)P(H)=0.6
P ( H ‾ ∣ E ) = P ( E ∣ H ‾ ) P ( H ‾ ) P ( E ) = 0.4 P(\overline{{H}} \mid {E}) = \dfrac{{P}({E} \mid \overline{{H}}) {P}(\overline{{H}})}{{P}({E})} = 0.4 P(H∣E)=P(E)P(E∣H)P(H)=0.4
面积为1的概率空间,任何事件都对应概率空间的一个子集,事件发生的概率是子集的面积。