Question

一个盒子里正好有五个筹码，其中三个红色、两个白色。每次随机取出一个且不放回，直到所有红色筹码都被取出或所有白色筹码都被取出为止。最后一次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?

$\dfrac{3}{10}$

$\dfrac25$

$\dfrac12$

$\dfrac35$

$\dfrac{7}{10}$

答案：D

知识点：无放回抽样基本概率对称性

难度评级：1690

解答：

想象先给五个筹码排一个随机顺序。游戏停在白色筹码上，恰好表示两个白色筹码都在所有三个红色筹码取完之前出现，也就是完整顺序中的最后一个筹码是红色。

最后一个筹码为红色的概率为 $\dfrac{3}{5}$ 。所以正确答案是 D。

Imagine drawing all five chips in a random order. The drawing stops on a white chip exactly when both white chips come out before all three reds, which happens precisely when the very last chip in the full ordering is red.

That probability is $\dfrac{3}{5}.$ Thus, the correct answer is D.

2001 AMC 10 第 23 题

答案：D

难度评级：1690

解答：

其他年份的第 23 题