best-prize selection

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An optimization problem concerning the selection of one of n prizes. The prizes are presented one at a time and n is known. We either accept the prize presented or we decline it and ask to see the next prize. We cannot accept a prize once we have declined it. It may seem that it will be difficult to do well, but in fact there is a good strategy, i.e. Reject the first n/e prizes (See exponential) and then accept either the first subsequent prize that is better than all the previous ones, or the last prize. With this strategy the probability that the prize selected is the best of all the n prizes is about 1/e ≈ 0.368.

Subjects: Probability and Statistics.

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