AMC12 2001 A

AMC12 2001 A · Q11

AMC12 2001 A · Q11. It mainly tests Probability (basic).

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?

一个盒子中正好有五个筹码，三个红色、两个白色。随机逐个无放回取出筹码，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。最后一个取出的筹码是白色的概率是多少？

(A) $\frac{3}{10}$ $\frac{3}{10}$

(B) $\frac{2}{5}$ $\frac{2}{5}$

(D) $\frac{3}{5}$ $\frac{3}{5}$

(E) $\frac{7}{10}$ $\frac{7}{10}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

Imagine that we draw all the chips in random order, i.e., we do not stop when the last chip of a color is drawn. To draw out all the white chips first, the last chip left must be red, and all previous chips can be drawn in any order. Since there are $3$ red chips, the probability that the last chip of the five is red (and so also the probability that the last chip drawn is white) is $\boxed{\textbf{(D) } \frac {3}{5}}$.

设想我们按随机顺序把所有筹码都取出，也就是说不在某种颜色的最后一个筹码被取出时停止。要使白色筹码先全部取完，则最后剩下的筹码必须是红色，而之前的筹码可以以任意顺序取出。由于有 $3$ 个红色筹码，五个筹码中最后一个是红色的概率（也就是最后取出的筹码是白色的概率）为 $\boxed{\textbf{(D) } \frac {3}{5}}$。

Topics

CP.006 Probability (basic)