2016 AMC 8 第 21 题
先试着解答 2016 AMC 8 第 21 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2016 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
21.
一个盒子里有 枚红色筹码和 枚绿色筹码。每次随机抽出一枚筹码且不放回，直到 枚红色筹码都被抽出，或直到两枚绿色筹码都被抽出。 枚红色筹码都被抽出的概率是多少？
A box contains red chips and green chips. Chips are drawn randomly, one at a time without replacement, until all of the reds are drawn or until both green chips are drawn. What is the probability that the reds are drawn?
小提示：
停止时的结果由完整排列中哪种颜色最后出现决定
The stopping result is determined by which color appears last in the full ordering of the chips.
大提示：
在五个筹码位置中统计两枚绿色筹码的位置
Count equally likely positions for the two green chips among the five total chip positions.
视频讲解：
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文字解答：
枚红色筹码先于两枚绿色筹码都被抽出，当且仅当完整抽取顺序中的最后一枚筹码是绿色。选择两枚绿色筹码位置的等可能方式共有 种，其中最后一个位置为绿色的有 种。
因此所求概率为
所以正确答案是 B。
The reds are drawn before both green chips exactly when a green chip is the last chip in the full ordering. There are equally likely ways to choose the two positions of the green chips, and of them have a green chip in the last position.
Therefore, the desired probability is
Thus, B is the correct answer.
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