Visiting two girlfriends

Wacky · 2003-08-04, 15:06

A young man lives in New Orleans and uses the public trolley line for transportation. He has two girlfriends that he likes equally. One lives in town and the other in the surburbs. Wanting to avoid bias, he decides that he will go to the trolley stop each day and take the first one that arrives. He arrives at a completely random time, so his choice is not synchronized to the schedule.

After a while, the downtown girl complains that he isn't visiting her often enough. He thinks he has been "fair", but starts a log to verify things.

After a couple months, he reviews the data.

The trolleys are running exactly on schedule. There is one trolley in each direction every ten minutes. His arrival times are uniformly distributed.

But, it is true that he went to visit the surburban girlfriend 48 times and visited the downtown girfriend only 12 times.

Can you explain why?

trif · 2003-08-04, 16:17

Because the trolley arrival times are not evenly distributed. From the data, it appears likely that the trolley to the downtown girlfriend arrives two minutes after the trolley to the suburban girlfriend. He will visit her only if he arrives at the stop in the two minutes between the time that the suburban trolley leaves and the downtown trolley leaves. But he will visit the suburban girlfriend if he arrives in any of the 8 minutes between the time the downtown trolley leaves and the suburban trolley leaves
.

2003-08-04, 15:06	#1
Wacky Jun 2003 The Texas Hill Country 2101₈ Posts	Visiting two girlfriends A young man lives in New Orleans and uses the public trolley line for transportation. He has two girlfriends that he likes equally. One lives in town and the other in the surburbs. Wanting to avoid bias, he decides that he will go to the trolley stop each day and take the first one that arrives. He arrives at a completely random time, so his choice is not synchronized to the schedule. After a while, the downtown girl complains that he isn't visiting her often enough. He thinks he has been "fair", but starts a log to verify things. After a couple months, he reviews the data. The trolleys are running exactly on schedule. There is one trolley in each direction every ten minutes. His arrival times are uniformly distributed. But, it is true that he went to visit the surburban girlfriend 48 times and visited the downtown girfriend only 12 times. Can you explain why?

2003-08-04, 16:17	#2
trif Aug 2002 2×101 Posts	Because the trolley arrival times are not evenly distributed. From the data, it appears likely that the trolley to the downtown girlfriend arrives two minutes after the trolley to the suburban girlfriend. He will visit her only if he arrives at the stop in the two minutes between the time that the suburban trolley leaves and the downtown trolley leaves. But he will visit the suburban girlfriend if he arrives in any of the 8 minutes between the time the downtown trolley leaves and the suburban trolley leaves .