全概率公式:

$$P(B)=P\left(A_1\right)P(B\mid A_1)+P\left(A_2\right)P(B\mid A_2)+\dots +P\left(A_n\right)P(B\mid A_n)$$

贝叶斯公式:

$$P(A_i\mid B)=\frac{P\left(A_i\right)P(B\mid A_i)}{\sum _{j=1}^{n}P\left(A_j\right)P(B\mid A_j)}=\frac{P\left(A_i\right)P(B\mid A_i)}{P\left(A_1\right)P(B\mid A_1)+\dots +P\left(A_n\right)P(B\mid A_n)}$$