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Three pancakesThree pancake problem was discussed in the popular "Ask Marylin" question-and-answer column of the Parade magazine. Details can also be found in the "Power of Logical Thinking" by Marylin vos Savant, St. Martin's Press, 1996. Marylin received the following question:
Solutions are available below. Not all give the same result. Which one(s) is (are) incorrect? 
Copyright © 1996-2009 Alexander Bogomolny
Solution #1 The chance is two out of three. The pancake you withdraw had to be one of only two of them: the brown/brown one or the brown/golden one. And of the three brown sides you could be seeing, two of them also have brown on the other side. Solution #2Only two pancakes have brown sides, and one of them has brown on only one side. There is a 50% chance that you are looking at the one with brown on both sides. Solution #3Here's a solution that makes use of the Principle of Proportionality. At the outset, there are three likely events to extract a pancake: brown/brown, brown/golden, golden/golden. A pancake is taken out and shows a brown side. Relative to the three possibilities, the probabilities of this happening are 1, 1/2, and 0. Since the probabilities ought to add up to 1, the conditional probabilities become 2/3, 1/3, 0. Only in the first case the chosen pancake will have the second side brown. This will happen with the probability of 2/3.
Copyright © 1996-2009 Alexander Bogomolny |
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