Chevalier de Méré's Problem
A 17^{th} century gambler, the Chevalier de Méré, made it to history by turning to Blaise Pascal for an explanation of his unexpectd losses. Pascal combined his efforts with his friend Pierre de Fermat and the two of them laid out mathematical foundations for the theory of probability.
Gamblers in the 17
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Copyright © 19962018 Alexander Bogomolny
Chevalier de Mere's Problem
Compare two problems:
What is the probability of having at least one 1 in four rolls of a dice?
What is the probability of having at least one double 1 in 24 rolls of two die?
Solution to Problem 1
Four rolls of a dice may have one of 6^{4} equiprobable outcomes. Of these, 5^{4} are unfavorable leaving

showing that the odds are in favor of the bettor.
Solution to Problem 2
One double roll has 36 equiprobable out comes of which 35 are unfavorable to the bet. In 24 rolls there are 36^{24} possible outcomes of which only

References
 J. Bewersdorff, Luck, Logic & White Lies, A K Peters, 2005
 R. Falk, Understanding Probability and Statistics, A K Peters, 1993
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Copyright © 19962018 Alexander Bogomolny