Lies, Damned Lies, and Statistics     Sampling Subtlies: Kevin and the Mysterious Trains

 

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THE STRANGE CASE OF KEVIN
SIGMA AND THE MYSTERIOUS TRAINS


Kevin Sigma was young and hot.  He had a girlfriend
up in the Bronx and another one out in Brooklyn.  Kevin lived
in Manhattan, and was equally attracted (or indifferent) to each of them.  Since the subway
ran north to the Bronx and also south to Brooklyn every twenty minutes throughout the
morning and afternoon, Kevin decided that he would leave his apartment at a random time
each day, run down to the platform, then let the subway decide who he would visit, taking
the train that showed up first.  In this way, he figured
chance would randomly assign him to each girl 50% of
the time, keeping both of them happy.

After a while, Kevin's Brooklyn girl, who was really hot on him, began to complain that he was showing up to be with her for only about one-fourth of his dates, while his Bronx friend, who was beginning to cool on him, complained that he was showing up for three-fourths of his dates with her.  Finally, statistical curiosity got the better of Kevin (or maybe he just got tired of the nagging).  He timed the trains with a stopwatch, and tallied the number of his dates with each girl, and, sure enough, the trains DID run almost exactly twenty minutes apart, just like the schedule said, he DID leave his aprtment at random times, yet he really WAS going to Brooklyn three times as often as to the Bronx (just like his girlfriends said). Can you figure out what was wrong with Kevin's random girlfriend-sampling plan?  What was causing the bias?

What!!   You're giving up already??   You wimp!!   Alright, Alright.....   click  for the answer.

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