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} )}

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}

🪴 Cyril