AMC8 2004

AMC8 2004 · Q22

AMC8 2004 · Q22. It mainly tests Ratios & proportions, Probability (basic).

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

在一个派对上，只有单身女性和带着妻子的已婚男性。随机选择的女性是单身的概率为 $\frac{2}{5}$。房间里的人中有多少分数是已婚男性？

(A) \frac{1}{3} \frac{1}{3}

(B) \frac{3}{8} \frac{3}{8}

(D) \frac{5}{12} \frac{5}{12}

(E) \frac{3}{5} \frac{3}{5}

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) Because $\frac{2}{5}$ of all the women in the room are single, there are two single women for every three married women in the room. There are also two single women for every three married men in the room. So out of every $2 + 3 + 3 = 8$ people, 3 are men. The fraction of the people who are married men is $\frac{3}{8}$.

（B）因为房间里所有女性中有$\frac{2}{5}$是单身，所以房间里每三位已婚女性对应两位单身女性。并且，房间里每三位已婚男性也对应两位单身女性。因此，在每$2 + 3 + 3 = 8$个人中，有3个人是男性。已婚男性占所有人的比例是$\frac{3}{8}$。

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