2008 AMC 8 第 19 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。
19.
如图，八个点以一个单位的间隔分布在一个 正方形的周围。从这 个点中随机选两个点。它们相距一个单位的概率是多少？
Eight points are spaced at intervals of one unit around a square, as shown. Two of the points are chosen at random. What is the probability that the points are one unit apart?
小提示：
先数无序的两点组合总数
Count the total number of unordered pairs of points.
大提示：
正方形周围恰好有 条相邻的单位线段
There are exactly adjacent unit segments around the square.
解答：
每个点都有 个点与它相距一个单位。
因此无论第一个点怎么选，其余 个点中有 个与它相距一个单位，所以概率为 。
所以正确答案是 B。
Each dot has dots that are one unit away from it.
Therefore, regardless of the choice of the first dot, of the other dots would be within one unit, so the probability is
Thus, the answer is B .
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