1986 AMC 8 第 24 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。
24.
金氏初中的 名学生午餐时被平均分成三组。每组在不同时间吃午餐。电脑随机把每名学生分到三组之一。三个朋友艾尔、鲍勃和卡罗尔被分到同一午餐组的概率大约是
The students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of the three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately
小提示：
固定艾尔的组；再求鲍勃也进同一组的概率
Fix Al’s group; then find the chance that Bob lands in that same group
大提示：
固定艾尔的组后，鲍勃进入该组的概率是 ，接着卡罗尔进入该组的概率是
After Al’s group is fixed, Bob’s chance is and then Carol’s is
解答：
不论艾尔在哪一组，鲍勃进入同一组的概率为 。如果鲍勃进入该组，卡罗尔也进入该组的概率为 。
所以三人在同一组的概率约为 ，最接近 。
所以正确答案是 B。
Whatever group Al is in, Bob joins that same group with probability If Bob does, Carol joins them with probability
Thus all three share a group with probability closest to
Thus, the correct answer is B .
其他年份的第 24 题
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