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Counter Play

http://books.google.com/books?id=XKECAAAAYAAJ&printsec=toc&rview=1&source=gbs_navlinks_s

A puzzle by Lewis Carroll:

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?

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