Question

一个聚会上只有单身女性和已婚男性及其妻子。随机选择一名女性，她是单身的概率为 $\dfrac{2}{5}$ 。房间里的人中，已婚男性占几分之几？

At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is $\dfrac{2}{5}.$ What fraction of the people in the room are married men?

$\dfrac{1}{3}$

$\dfrac{3}{8}$

$\dfrac{2}{5}$

$\dfrac{5}{12}$

$\dfrac{3}{5}$

答案：B

知识点：比与比例

难度评级：1450

解答：

不失一般性，设房间里有 $5$ 名女性。那么单身女性有 $5 \cdot \dfrac{2}{5} = 2$ 名。

因此已婚女性有 $5 - 2 = 3$ 名，也就是已婚男性的人数。

房间里共有 $5 + 3 = 8$ 人。已婚男性所占比例为 $\dfrac{3}{8}$ 。

所以正确答案是 B。

WLOG, let there be $5$ women in the room. Then there are $5 \cdot \dfrac{2}{5} = 2$ single women.

This means that there are $5 - 2 = 3$ married women, which is also the number of married men.

There are a total of $5 + 3 = 8$ people in the room. The fraction of married men is $\dfrac{3}{8}.$

Thus, B is the correct answer.

2004 AMC 8 第 22 题

答案：B

难度评级：1450

解答：

其他年份的第 22 题