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December 28, 2007

Strange But True!

Q. Math teacher asks half her class to flip a coin 100 times, the other half to just imagine doing so. Both record their H-T outcomes. Then she collects the unsigned papers and tries to distinguish the real flippers from the fakers. Any chance she could really do this?

A. In “The Canon: A Whirligig Tour of the Beautiful Basics of Science,” Natalie Angier reports on an elementary statistics prof who starts each semester in just this way. And the prof is almost always right in how she calls them, leaving the students aghast. The reason she can tell is that true randomness is more haphazard than most people think. Real coin tossing will generally include more strings than people are comfortable with, such as streaks of five heads in a row or seven tails in a row. True, 50-50 rules over the long haul, but not in the short run, and it's the short run where the surprises lie. When Angier tried the experiment herself a dozen times (12 100-flip trials), she always got at least one streak of six or seven heads or tails, often more than one six per set, plus many fives and fours. Once she even got nine in a row, which she felt queasy about including in a display of faux flipping.


 
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