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Problem of the Week 958

A Chinese Dice Game

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There is a traditional Chinese dice game which is played during the New Year's celebration. In this game a player rolls six dice. It is our understanding that in the actual game a roll with two pairs beats a roll with one pair. What is the probability of each of these events? In other words find the probability of getting one pair in a roll of six dice, and the probability of getting two pairs in a roll of six dice.

SOURCE: the text "Elementary Probability Theory with Stochastic Processes" by Kai Lai Chung.
© Copyright 2002 Stan Wagon. Reproduced with permission.

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2 April 2002