1996 AMC 12 第 26 题
先试着解答 1996 AMC 12 第 26 题，然后核对你的答案与精心整理的解答，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 1996 AMC 12 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。
26.
一个罐子里有红、白、蓝、绿四种颜色的弹珠。不放回地抽取四颗弹珠时，下列事件的发生概率相同：
（a）抽到四颗红色弹珠；
（b）抽到一颗白色弹珠和三颗红色弹珠；
（c）抽到一颗白色、一颗蓝色和两颗红色弹珠；以及
（d）每种颜色各抽到一颗弹珠。
满足上述条件的弹珠总数最少是多少？
An urn contains marbles of four colors: red, white, blue, and green. When four marbles are drawn without replacement, the following events are equally likely:
(a) the selection of four red marbles;
(b) the selection of one white and three red marbles;
(c) the selection of one white, one blue, and two red marbles; and
(d) the selection of one marble of each color.
What is the smallest number of marbles satisfying the given condition?
大于
more than
答案：B
小提示：
设四种颜色的弹珠数分别为 ，令四个事件的组合数相等
Let the four color counts be and equate the combination counts for the four events
大提示：
逐次取比值，把 表示成 的函数，再求使三者都是整数的最小
Successive ratios determine in terms of ; then find the smallest making all three integers
解答：
相等的概率具有相同的总样本数，因此有利选法数满足 。逐次取比值得 、 和 。使三者均为正整数的最小 是 。此时 ，弹珠总数为 。所以正确答案是 B。
Equal probabilities have the same common denominator, so their favorable selection counts satisfy Successive ratios give and The least making all three positive integers is Then for marbles. Thus the correct answer is B.
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