Question

在 Typico 高中， $60\%$ 的学生喜欢跳舞，其余学生不喜欢。在喜欢跳舞的学生中， $80\%$ 说自己喜欢跳舞，其余说自己不喜欢。在不喜欢跳舞的学生中， $90\%$ 说自己不喜欢跳舞，其余说自己喜欢。在所有说自己不喜欢跳舞的学生中，实际喜欢跳舞的学生占多少比例？

At Typico High School, $60\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\%$ say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

$10\%$

$12\%$

$20\%$

$25\%$

$33\tfrac{1}{3}\%$

答案：D

知识点：条件概率贝叶斯定理

难度评级：1440

解答：

喜欢跳舞但说自己不喜欢的学生占全体学生的 $60\% \cdot 20\% = 12\%$ 。不喜欢跳舞且如实这么说的学生占 $40\% \cdot 90\% = 36\%$ 。在所有说自己不喜欢跳舞的人中，实际喜欢跳舞的比例为 $\frac{12}{12 + 36} = \frac{12}{48} = \frac{1}{4} = 25\%.$

所以正确答案是 D。

Students who like dancing but say they dislike it make up $60\% \cdot 20\% = 12\%$ of all students. Students who dislike dancing and say so make up $40\% \cdot 90\% = 36\%.$ Among everyone who says they dislike dancing, the fraction who actually like it is $\frac{12}{12 + 36} = \frac{12}{48} = \frac{1}{4} = 25\%.$

Thus, the correct answer is D.

2017 AMC 12B 第 10 题

答案：D

难度评级：1440

解答：

其他年份的第 10 题