两趟地铁同频率却总有一趟先到

the two trains running in opposite directions

专题: Probability / 概率
难度: L4
来源: QuantQuestion

个人笔记

题目详情

概率题：两趟地铁同频率却总有一趟先到：可能原因。

英文原题

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%）。

英文解析

One thing that could be happening is that the train that comes first $80\%$ of the time comes in fact more frequently than the other one. However, even if both

trains run with the same frequency, one train might comefirst $80\%$ of the time. For example, assuming that your arrival in the station is uniformly distributed, if both trains run every ten minutes, and train A comes into the station at 1:00,1:10,1:20,..., while train B comes at 1:12,1:22, 1:32,..., then train A will come first $80\%$ of the time.