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 ProblemA 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.