AMC10 2017 B

AMC10 2017 B · Q11

AMC10 2017 B · Q11. It mainly tests 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，其余说他们不喜欢。不喜欢跳舞的学生中，90%说他们不喜欢，其余说他们喜欢。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) $33\dfrac{1}{3}\%$ $33\dfrac{1}{3}\%$

Answer

Correct choice: (D)

正确答案：（D）

Solution

The students who like dancing but say they dislike it constitute 60% · (100% − 80%) = 12% of the students. Similarly, the students who dislike dancing and say they dislike it constitute (100% − 60%) · 90% = 36% of the students. Therefore the requested fraction is 12 / (12 + 36) = 1/4 = 25%.

喜欢跳舞但说不喜欢的学生占总学生的60% · (100% − 80%) = 12%。同样，不喜欢跳舞且说不喜欢的学生占(100% − 60%) · 90% = 36%。因此，所求分数是12 / (12 + 36) = 1/4 = 25%。

Topics

CP.007 Conditional probability (basic)