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## Two Girlfriends

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #1365 Fun: (2.37) Difficulty: (2.27) Category: Probability Submitted By: Rado Corrected By: cnmne

A man has two girlfriends. Each lives at the opposite final stop of the same train. The man gets up every day at a random time. He goes to a train stop and takes the first train to come regardless of the direction and goes to the final stop to see the girlfriend which lives there. Surprisingly he sees one of the girlfriends 4 times more often than the other one. How can this be?

The trains go in 10-minute intervals. One direction, it is every hour at 0, 10, 20, 30, 40, and 50 minutes and the other direction it is every hour at 2, 12, 22, 32, 42, and 52 minutes. When the man comes to the train stop at a random time, he will take the first train if he comes within the first two minutes in any of the 10-minute intervals, i.e. with probability of 20%. The ratio of visiting girlfriends is then 20%:80% or 1:4.
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