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 1717 France were used to bet on the event of getting at least one 1 (ace) in four rolls of a dice. As a more trying variation, two die were rolled 24 times with a bet on having at least one double ace. According to the reasoning of Chevalier de Méré, two aces in two rolls are 1/6 as likely as 1 ace in one roll. (Which is correct.) To compensate, de Méré thought, the two die should be rolled 6 times. And to achieve the probability of 1 ace in four rolls, the number of the rolls should be increased four fold - to 24. Thus reasoned Chevalier de Méré who expected a couple of aces to turn up in 24 double rolls with the frequency of an ace in 4 single rolls. However, he lost consistently.

Explain

Copyright © 1996-2009 Alexander Bogomolny

1. J. Bewersdorff, Luck, Logic & White Lies, A K Peters, 2005
2. R. Falk, Understanding Probability and Statistics, A K Peters, 1993

• What Is Probability?
• Intuitive Probability
• Probability Problems
• Sample Spaces and Random Variables
• Probabilities
  • Bernoulli Trials
  • Binomial Distribution
  • Proofreading Example
  • Continuous Sample Spaces
    • Geometric Probabilities
• Conditional Probability
  • Bayes' Theorem
    • Principle of Proportionality
• Dependent and Independent Events
  • Conditional Probability and Independent Events
  • Independent Events and Independent Experiments
• Algebra of Random Variables
• Expectation

Copyright © 1996-2009 Alexander Bogomolny