2014 AMC 8 第 18 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
18.
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?
个都是男孩
all are boys
个都是女孩
all are girls
个女孩和 个男孩
are girls and are boys
个是一种性别， 个是另一种性别
are of one gender and is of the
other gender
所有这些结果可能性相同
all of these outcomes are equally likely
小提示：
按男孩和女孩的人数分类列出结果
List outcomes by the number of boys and girls.
大提示：
最可能的类别是排列方式最多的类别
The most likely category is the one with the most arrangements.
解答：
四个孩子按出生顺序共有 个等可能结果。各类别数量为：全是男孩 种；全是女孩 种；两男两女 种；三人一种性别、一人另一种性别 种。
最大数量是 ，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 equally likely birth-order outcomes. The counts by category are: all boys, ; all girls, ; two boys and two girls, ; and three of one gender and one of the other, .
The largest count is , so the most likely outcome is three children of one gender and one of the other.
Thus, D is the correct answer.
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