Tuesday, May 12, 2015

Lewis Carroll's Fifth Pillow Problem

   Lewis Carroll is the pen name of Charles Dodgson (1832–1898). Dodgson was a mathematician, logician, and church deacon. He is most remembered as the author of Alice's Adventures in Wonderland and Through the Looking-Glass.
   He also wrote a book of problems called Pillow Problems. This project looks at one of those problems, a particularly tricky probability problem. Here it is.
The Fifth Pillow Problem
   A bag contains one counter, known to be either white or black. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?
   Most problem solvers quickly decide that the probability of drawing the white counter is one-half. This is wrong.
   You could of course Google Lewis Carroll’s Fifth Pillow Problem to find a derivation of the theoretical probability. Instead, examine the data from several runs of this project and form your conjecture as to the chances for drawing a white counter and then look at the theoretical solution.

   The project can be viewed and downloaded by clicking on this link.

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