AMC8 2016

AMC8 2016 · Q21

AMC8 2016 · Q21. It mainly tests Basic counting (rules of product/sum), Probability (basic).

A box 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?

一个盒子里有3个红筹码和2个绿筹码。从盒子里随机抽取筹码，一次抽一个，不放回，直到抽到所有3个红筹码或抽到两个绿筹码为止。抽到3个红筹码的概率是多少？

(A) $3/10$ $3/10$

(B) $2/5$ $2/5$

(D) $3/5$ $3/5$

(E) $2/3$ $2/3$

Answer

Correct choice: (B)

正确答案：（B）

Solution

Consider drawing all five chips and listing the 10 possible outcomes: RRRGG, RRGRG, RGRRG, GRRRG, GGRRR, GRGRR, RGGRR, GRRGR, RGRGR, RRGGR. All 10 of these outcomes are equally likely. The outcomes that end in G correspond to the outcomes where the 3 reds are drawn and the outcomes that end in R correspond to the outcomes where the 2 greens are drawn. The probability that the 3 reds are drawn is $\frac{4}{10}=\frac{2}{5}$.

考虑把五个筹码全部抽完，并列出10种可能的结果：RRRGG、RRGRG、RGRRG、GRRRG、GGRRR、GRGRR、RGGRR、GRRGR、RGRGR、RRGGR。这10种结果等可能。以 G 结尾的结果对应于抽到3个红筹的情形，而以 R 结尾的结果对应于抽到2个绿筹的情形。抽到3个红筹的概率是 $\frac{4}{10}=\frac{2}{5}$。

Topics