贝叶斯公式

$$P(B_j|A)=\frac{P(B_j)P(A|b_j)}{{\sum }_{i=1}^{n}P(B_i)P(A|B_i)}$$

$$\begin{array}{rl}P(B_1|A)& =\frac{P(A{B}_1)}{P(A)}\\ & =\frac{P(B_1)P(A|B_1)}{P(B_1)P(A|B_1)+{\sum }_{i=2}^{4}P(B_i)P(A|B_i)}\\ & =\frac{0.3\times 1}{0.3\times 1+0.2\times 1+0.4\times 0.25+0.1\times 1}\\ & =\frac{3}{7}\end{array}$$