2001 AMC 12 第 11 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。
11.
一个盒子里恰有五枚筹码，三枚红色、两枚白色。随机一次取出一枚且不放回，直到所有红筹码都被取出或所有白筹码都被取出为止。最后一枚被取出的筹码是白色的概率是多少？
A box contains exactly five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are drawn or all the white chips are drawn. What is the probability that the last chip drawn is white?
小提示：
想象把五枚筹码全部取完，并记录完整顺序
Imagine drawing all five chips and recording the full order
大提示：
抽取过程在第二枚白筹码处结束，恰好等价于完整顺序的最后一枚筹码是红色
The drawing ends on the second white exactly when the very last chip in the full order is red
解答：
想象继续取直到五枚筹码全部取出。实际过程停在白筹码上，恰好说明白筹码先于红筹码用完，也就是完整排列中的最后一枚筹码是红色。
五枚筹码中最后一枚等可能是任意一枚，因此它是红色的概率为 。
因此，正确答案是 D。
Imagine continuing until all five chips are removed. The process actually stops on a white chip exactly when the whites run out before the reds, i.e. when the last chip in the full ordering is red.
The last of the five chips is equally likely to be any chip, so it is red with probability
Thus, the correct answer is D.
其他年份的第 11 题
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