Question

King 初中的 $600$ 名学生午餐时被平均分成三组。每组在不同时间吃午餐。电脑随机把每名学生分到三组之一。三个朋友 Al、Bob 和 Carol 被分到同一午餐组的概率大约是

The $600$ students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of the three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately

$\dfrac{1}{27}$

$\dfrac19$

$\dfrac18$

$\dfrac16$

$\dfrac13$

答案：B

知识点：基本概率独立事件

难度评级：1120

解答：

不论 Al 在哪一组，Bob 进入同一组的概率约为 $\dfrac{199}{599}$ ，Carol 进入同一组的概率也约为 $\dfrac{198}{598}$ 。

所以三人在同一组的概率约为 $\dfrac{199}{599} \cdot \dfrac{198}{598} \approx 0.110$ 。 $\dfrac19$ 。

所以正确答案是 B。

Whatever group Al is in, Bob joins that same group with probability $\dfrac{199}{599}.$ If Bob does, Carol joins them with probability $\dfrac{198}{598}.$

Thus all three share a group with probability $\dfrac{199}{599} \cdot \dfrac{198}{598} \approx 0.110,$ closest to $\dfrac19.$

Thus, the correct answer is B .

1986 AMC 8 第 24 题

答案：B

难度评级：1120

解答：

其他年份的第 24 题