Question

一个盒子里有 $2$ 个红弹珠、 $2$ 个绿弹珠和 $2$ 个黄弹珠。Carol 随机从盒中取出 $2$ 个弹珠；然后 Claudia 从剩下的弹珠中随机取出 $2$ 个；最后 Cheryl 拿走最后 $2$ 个弹珠。 Cheryl 得到 $2$ 个同色弹珠的概率是多少？

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?

$\dfrac{1}{10}$

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

答案：C

知识点：基本概率对称性

难度评级：1500

解答：

因为留给 Cheryl 的弹珠是随机决定的，她的两个弹珠等可能是任意一对。固定她的第一个弹珠，第二个弹珠等可能是剩下 $5$ 个弹珠中的任意一个。

这 $5$ 个中恰好有一个与第一个弹珠颜色相同，所以概率为 $\dfrac{1}{5}$ 。

因此，正确答案是 C。

Because the marbles left for Cheryl are determined at random, her two marbles are equally likely to be any pair. Fixing her first marble, the second is equally likely to be any of the $5$ remaining marbles.

Exactly one of those $5$ matches the first marble in color, so the probability is $\dfrac{1}{5}.$

Thus, the correct answer is C.

2015 AMC 12A 第 9 题

答案：C

难度评级：1500

解答：

其他年份的第 9 题