2011 AMC 8 第 12 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。
12.
Angie、Bridget、Carlos 和 Diego 随机坐在一张方桌四周，每边坐一个人。Angie 和 Carlos 坐在相对两边的概率是多少？
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
小提示：
Carlos 有三个可能座位，其中只有一个与 Angie 相对
Carlos has three possible seats, only one opposite Angie.
大提示：
利用对称性，先固定 Angie 的座位
Fix Angie in one seat by symmetry.
解答：
设 Angie 的座位已经确定。Carlos 等可能坐在另外 个座位中的任意一个，但其中只有一个座位与 Angie 相对。因此概率为 。
所以正确答案是 B。
Consider that Angie’s seat is chosen. Carlos has an equal probability of being in any of the other seats. Only one of them is opposite Angie, however. Therefore, the probability is
Thus, B is the correct answer.
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