\[ \begin{align*} P(\text{恰好2人获胜}) &= P(A\text{胜且}B\text{胜且}C\text{败} \cup B\text{胜且}C\text{胜且}A\text{败} \cup A\text{胜且}C\text{胜且}B\text{败}) \\ &= P(A\text{胜且}B\text{胜且}C\text{败}) + P(B\text{胜且}C\text{胜且}A\text{败}) + P(A\text{胜且}C\text{胜且}B\text{败}) \end{align*} \] #### 分别计算各项概率 1. 计算\(P(A\text{胜且}B\text{胜且}C\text{败})\) \[ \begin{align*} P(A\text{胜且}B\text{胜且}C\text{败}) &= P(A\text{胜}) \times P(B\text{胜}) \times P(C\text{败}) \\ &= \frac{1}{5} \times \frac{3}{8} \times \frac{5}{7} \\ &= \frac{15}{280} \end{align*} \] 2. 计算\(P(B\text{胜且}C\text{胜且}A\text{败})\) \[ \begin{align*} P(B\text{胜且}C\text{胜且}A\text{败}) &= P(B\text{胜}) \times P(C\text{胜}) \times P(A\text{败}) \\ &= \frac{3}{8} \times \frac{2}{7} \times \frac{4}{5} \\ &= \frac{24}{280} \end{align*} \] 3. 计算\(P(A\text{胜且}C\text{胜且}B\text{败})\) \[ \begin{align*} P(A\text{胜且}C\text{胜且}B\text{败}) &= P(A\text{胜}) \times P(C\text{胜}) \times P(B\text{败}) \\ &= \frac{1}{5} \times \frac{2}{7} \times \frac{5}{8} \\ &= \frac{10}{280} \end{align*} \] #### 汇总计算最终概率 \[ \begin{align*} P(\text{恰好2人获胜}) &= \frac{15}{280} + \frac{24}{280} + \frac{10}{280} \\ &= \frac{49}{280} \\ &= \frac{7}{40} \end{align*} \] **答案**：\(\boldsymbol{E}\)