AMC12 2015 A

AMC12 2015 A · Q9

AMC12 2015 A · Q9. It mainly tests Probability (basic).

A box contains 2 red marbles, 2 green marbles, and 2 yellow marbles. Carol takes 2 marbles from the box at random; then Claudia takes 2 of the remaining marbles at random; and then Cheryl takes the last 2 marbles. What is the probability that Cheryl gets 2 marbles of the same color?

一个盒子里有2颗红 marble、2颗绿 marble 和2颗黄 marble。Carol 随机从盒子里取出2颗 marble；然后 Claudia 随机从剩余的 marble 中取出2颗；然后 Cheryl 取出最后2颗 marble。Cheryl 得到2颗相同颜色的 marble 的概率是多少？

(A) $\frac{1}{10}$ $\frac{1}{10}$

(B) $\frac{1}{6}$ $\frac{1}{6}$

(D) $\frac{1}{3}$ $\frac{1}{3}$

(E) $\frac{1}{2}$ $\frac{1}{2}$

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Because the marbles left for Cheryl are determined at random, the second of Cheryl’s marbles is equally likely to be any of the 5 marbles other than her first marble. One of those 5 marbles matches her first marble in color. Therefore the probability is $\frac{1}{5}$.

答案（C）：因为留给 Cheryl 的弹珠是随机决定的，所以 Cheryl 的第二颗弹珠在除去第一颗弹珠之外的另外 5 颗弹珠中等可能地是任意一颗。其中这 5 颗里有 1 颗与她第一颗弹珠颜色相同。因此概率是 $\frac{1}{5}$。

Topics

CP.006 Probability (basic)