AMC10 2001 A

AMC10 2001 A · Q23

AMC10 2001 A · Q23. It mainly tests Basic counting (rules of product/sum), 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?

一个盒子中恰好有五张筹码，三张红色，两张白色。随机依次无放回取出筹码，直到取出所有红色筹码或所有白色筹码。最后一張取出的筹码为白色的概率是多少？

(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: (E)

正确答案：（E）

Solution

(D) Think of continuing the drawing until all five chips are removed form the box. There are ten possible orderings of the colors: RRRWW, RRWRW, RWRRW, WRRRW, RRWWR, RWRWR, WRRWR, RWWRR, WRWRR, and WWRRR. The six orderings that end in R represent drawings that would have ended when the second white chip was drawn.

（D）设想继续抽取，直到盒子里的五个筹码都被取出。颜色共有十种可能的抽取顺序：RRRWW、RRWRW、RWRRW、WRRRW、RRWWR、RWRWR、WRRWR、RWWRR、WRWRR，以及 WWRRR。以 R 结尾的六种顺序表示：当第二个白色筹码被抽到时，抽取过程本应已经结束的那些情况。

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