Question

昨天 City Hospital 有四个孩子出生。假设每个孩子是男孩或女孩的可能性相同。下列哪种结果最可能发生？

Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely?

$4$ 个都是男孩

all $4$ are boys

$4$ 个都是女孩

all $4$ are girls

$2$ 个女孩和 $2$ 个男孩

$2$ are girls and $2$ are boys

$3$ 个是一种性别， $1$ 个是另一种性别

$3$ are of one gender and $1$ is of the other gender

所有这些结果可能性相同

all of these outcomes are equally likely

答案：D

知识点：二项概率组合

难度评级：1170

解答：

四个孩子按出生顺序共有 $2^4=16$ 个等可能结果。各类别数量为：全是男孩 $1$ 种；全是女孩 $1$ 种；两男两女 $\binom{4}{2}=6$ 种；三人一种性别、一人另一种性别 $2\binom{4}{1}=8$ 种。

最大数量是 $8$ ，所以最可能的结果是三个孩子是一种性别，一个孩子是另一种性别。

所以正确答案是 D。

There are $2^4=16$ equally likely birth-order outcomes. The counts by category are: all boys, $1$ ; all girls, $1$ ; two boys and two girls, $\binom{4}{2}=6$ ; and three of one gender and one of the other, $2\binom{4}{1}=8$ .

The largest count is $8$ , so the most likely outcome is three children of one gender and one of the other.

Thus, D is the correct answer.

2014 AMC 8 第 18 题

答案：D

难度评级：1170

解答：

其他年份的第 18 题