Tip of the Week #37                     Tip Index

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"Repealing the Law of Averages"

Mathematical Recreations column by Ian Stewart, Scientific American, April 1998, pp. 102-104.

This month's discussion focuses on coin flips. Stewart discusses the law of large numbers that says the frequencies observed should in the long run be very close to their probabilities.  Some interesting remarks:

He notes another counter-intuitive situation.  In a large, predetermined number of trials, what is the proportion of time that the number of heads is larger than the number of tails?  Many persons suppose that either coin face would lead about half of the time.  Actually, this would be extremely rare.  Almost always, one coin side will lead most of the time.  The most likely outcome is that one side leads all of the time!

—John Schuyler, March 1998.

Copyright 1998 by John R. Schuyler. All rights reserved. Permission to copy with reproduction of this notice.