AMC12 2017 B

AMC12 2017 B · Q10

AMC12 2017 B · Q10. It mainly tests Probability (basic), Conditional probability (basic).

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?

在 Typico 高中，60% 的学生喜欢跳舞，其余的不喜欢。喜欢跳舞的学生中，80% 说他们喜欢，其余说不喜欢。不喜欢跳舞的学生中，90% 说他们不喜欢，其余说喜欢。说不喜欢跳舞的学生中，实际喜欢跳舞的学生分数是多少？

(A) 10% 10%

(B) 12% 12%

(D) 25% 25%

(E) 33 $\frac{1}{3}$% 33 $\frac{1}{3}$%

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The students who like dancing but say they dislike it constitute $60\%\cdot(100\%-80\%)=12\%$ of the students. Similarly, the students who dislike dancing and say they dislike it constitute $(100\%-60\%)\cdot90\%=36\%$ of the students. Therefore the requested fraction is $\dfrac{12}{12+36}=\dfrac{1}{4}=25\%$.

答案（D）：喜欢跳舞但却说自己不喜欢的学生占全体学生的 $60\%\cdot(100\%-80\%)=12\%$。同样地，不喜欢跳舞且说自己不喜欢的学生占 $(100\%-60\%)\cdot90\%=36\%$。因此所求的比例为 $\dfrac{12}{12+36}=\dfrac{1}{4}=25\%$。

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