Question

一个盒子里有 $3$ 枚红色筹码和 $2$ 枚绿色筹码。每次随机抽出一枚筹码且不放回，直到 $3$ 枚红色筹码都被抽出，或直到两枚绿色筹码都被抽出。 $3$ 枚红色筹码都被抽出的概率是多少？

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?

$\dfrac{3}{10}$

$\dfrac{2}{5}$

$\dfrac{1}{2}$

$\dfrac{3}{5}$

$\dfrac{2}{3}$

答案：B

知识点：基本概率对称性

难度评级：1490

视频讲解：

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文字解答：

$3$ 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。在这些位置安排中共有 $10$ 种，其中最后一个位置为绿色的有 $4$ 种。

因此所求概率为 $\dfrac{4}{10} = \dfrac{2}{5}.$

所以正确答案是 B。

The $3$ reds are drawn before both green chips exactly when a green chip is the last chip in the full ordering. There are $10$ equally likely ways to choose the two positions of the green chips, and $4$ of them have a green chip in the last position.

Therefore, the desired probability is $\dfrac{4}{10} = \dfrac{2}{5}.$

Thus, B is the correct answer.

2016 AMC 8 第 21 题

答案：B

难度评级：1490

视频讲解：

文字解答：

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