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Chris Conradi
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Jul0504, 05:03 PM (EST) 

"Lewis Carroll's Pillow Problem"

Carroll's Pillow Problemsee the Probability problemssays that we know a bag contains one counter, and it is either black or white. The solution presumes that the bag is equally likely to contain a black counter or a white counter, although neither Carroll nor Bogomolny makes that clear. It would be helpful to make that point in the statement of the problem. Otherwise, the answer cannot be determined from the statement of the problem. This is just a particular instance of a more general problem. Suppose that the first counter is drawn at random from another bag containing d counters, n of which are white and dn of which are black. Without revealing its color, this first counter is placed in a second, empty bag. Then a white counter is added to this bag. Now you draw a counter from this second bag and it turns out to be white. What is the probability that the remaining counter is white? The general answer is 2n/(n+d). I.e., if n=1 and d=2, the answer is 2/3, as given. But we can also determine the probability if n=1 and d=4 (2/5); if n=3 and d=4 (6/7); or if n=5 and d=18 (10/23). 

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