Question

在 Typico 高中， $60\%$ 的学生喜欢跳舞，其余学生不喜欢。在真正喜欢跳舞的人中， $80\%$ 说他们喜欢，剩下的人说他们不喜欢。在真正不喜欢跳舞的人中， $90\%$ 说他们不喜欢，剩下的人说他们喜欢。那些说自己不喜欢跳舞的学生中，实际喜欢跳舞的占多少比例？

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?

$10\%$

$12\%$

$20\%$

$25\%$

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

答案：D

知识点：条件概率百分数

难度评级：1370

解答：

真正喜欢跳舞的人占 $60\%$ ，其中只有 $80\%$ 说自己喜欢跳舞。因此全体学生中有 $48\%$ 说自己喜欢跳舞，而真正喜欢但说不喜欢的占 $60\%-48\% = 12\%$ 。

真正不喜欢跳舞的人占 $40\%$ ，其中 $90\%$ 说自己不喜欢，因而这部分占全体的 $36\%$ 。

所以说自己不喜欢跳舞的人共占 $12\%+36\% = 48\%.$

因此，说自己不喜欢、但实际上喜欢跳舞的人所占比例为 $\frac{12}{48} = \frac 14 = 25\% .$

所以正确答案是 D。

Observe that of the $60\%$ of people that actually like dancing, only $80\%$ say they like dancing. This suggests that $48\%$ of the students say that they like dancing, and as such, $60\%-48\% = 12\%$ of the students who like dancing say they don't like it.

Then, we know that $90\%$ of the $40\%$ of people who don't like dancing say they don't like it, which is $36\%$ of the total student population.

This means the total amount of people who say they don't like dancing is $12\%+36\% = 48\%.$

We know then that the fraction of people who say they dislike dancing but actually like it is equal to: $\frac{12}{48} = \frac 14 = 25\% .$

Thus, the correct answer is D .

2017 AMC 10B 第 11 题

答案：D

难度评级：1370

解答：

其他年份的第 11 题