两趟地铁同频率却总有一趟先到：可能原因

the two trains running in opposite directions

专题: Probability / 概率
难度: L4
来源: QuantQuestion

题目详情

At your subway station, you notice that of the two trains running in opposite directions which are supposed to arrive with the same frequency, the train going in one direction comes first $80\%$ of the time, while the train going in the opposite direction comes first only $20\%$ of the time. What do you think could be happening?

解析

一种可能是两趟车实际发车频率不同。

即使频率相同，也可能因为“相位差”导致你观测到某一方向更常先到：例如两趟车都每 10 分钟一班，但 A 在整点（1:00,1:10,1:20, …）到站，B 在 1:12,1:22, … 到站。

若你到站时间在周期内均匀分布，那么你更可能遇到 A 先到（这里会是 80% vs 20%）。