圆桌相邻概率

Meeting at a Round Table

专题: Probability / 概率
难度: L2
来源: QuantQuestion

题目详情

12 位数学家（含 Alice 与 Bob）围坐圆桌。问：Alice 与 Bob 相邻的概率是多少？

Twelve mathematicians, including Alice and Bob, are to be seated at a round table for a conference discussion. What is the probability that Alice and Bob sit next to each other?

解析

固定 Alice 位置不失一般性。此时 Bob 有 11 个可选座位，其中与 Alice 相邻的座位有 2 个。

所以概率为

\frac{2}{11}.

Original Explanation

Fix Alice’s position without loss of generality. Once Alice’s position is fixed, there are 11 possible seats left for Bob. However, only 2 of these seats (one to Alice’s left and one to her right) will result in Bob sitting next to Alice.

So the number of favorable outcomes is 2, and the total number of possible positions for Bob is 11. Therefore, the probability that Bob sits next to Alice is:

\frac{2}{11}