贝叶斯算法

一：计算公式

二：推导过程

某一学校60%是男生，40%是女生，男生基本都穿长裤，女生有一半穿长裤一般啊穿裙子
问题：迎面走来一穿长裤的学生，请问是女生的概率是多少
假设学校总人数为S
男生穿长裤的概率 P(pants|boys)=S*P(boys)*P(pants|boys)
女生穿长裤的概率 P(pants|girls)=S*P(girls)*P(pants|girls)
穿长裤总数：W=
P(pants|boys)+P(pants|girls)=S*P(boys)*P(pants|boys)+S*P(girls)*P(pants|girls)
W=S(P(boys)*P(pants|boys)+P(girls)*P(pants|girls))
P(girls|pants)=S*P(girls)*P(pants|girls)/W
P(girls|pants)=S*P(girls)*P(pants|girls)/S(P(boys)*P(pants|boys)+P(girls)*P(pants|girls))
P(girls|pants)=P(girls)*P(pants|girls)/(P(boys)*P(pants|boys)+P(girls)*P(pants|girls))
P(girls|pants)=P(girls)*P(pants|girls)/P(pants)