A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?
A. $\frac{3}{10}$
B. $\frac{2}{5}$
C. $\frac{1}{2}$
D. $\frac{3}{5}$
E. $\frac{7}{10}$

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Worked solution

1. 2016 AMC 8 官方解析

翻译：一顶帽子里有3个红色筹码和2个绿色筹码 . 不放回的随机抽取筹码，直到3个红色或者2个绿色筹码都被抽出，那么3个红色筹码被抽出的可能性是（）？

枚举法：所有取法如下：22；122；212；111；1121；1211；2111；1122；1212；2112共10种

（1代表红色筹码，2代表绿色筹码）其中4种方法拿出了3个红色筹码 .

Answer

B. $\frac{2}{5}$

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