2017 AMC 10B 第 11 题

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

小提示：

区分真实喜好和口头回答。

Separate actual preference from reported preference

大提示：

分母是所有说自己不喜欢跳舞的人。

The denominator is everyone who says they dislike dancing

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\%\text{。}

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

小提示：

大提示：

解答：

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