Question

要从一个由男生和女生组成的班级中选一名学生代表班级。每名学生被选中的可能性相同，选中男生的概率是选中女生概率的 $\frac23$ 。男生人数与全班人数之比为

One student in a class of boys and girls is to be chosen to represent the class. Each student is equally likely to be chosen and the probability that a boy is chosen is $\frac23$ of the probability that a girl is chosen. The ratio of the number of boys to the total number of boys and girls is

$\frac13$

$\frac25$

$\frac12$

$\frac35$

$\frac23$

答案：B

知识点：基本概率比与比例

难度评级：1100

小提示：

每人被选中的可能性相同，所以选中各组的概率与该组人数成正比

Equal likelihood makes the selection probabilities proportional to the class counts

大提示：

男生与女生人数比为 $2:3$ ，全班共包含五个相等的份额

A boys-to-girls ratio of $2:3$ uses five equal parts in all

解答：

因为每名学生被选中的可能性相同，男生人数是女生人数的 $\frac{2}{3}$ 。所以男生与女生人数之比为 $2:3$ ，男生占全班的 $\frac{2}{2+3}=\frac{2}{5}$ 。

所以正确答案是 B。

Because every student is equally likely to be selected, the number of boys is $\frac{2}{3}$ of the number of girls. Thus the boys-to-girls ratio is $2:3,$ and boys make up $\frac{2}{2+3}=\frac{2}{5}$ of the class.

Thus the correct answer is B.

1985 AMC 12 第 6 题

答案：B

难度评级：1100

小提示：

大提示：

解答：

其他年份的第 6 题