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Probability Theory with Pascal and Fermat
18
Transcript
Pascal and Fermat Discuss the Theory of Probability
The Problem of Points
Probability Theory with Pascal and Fermat
The Discussion between Pascal and Fermat
Suppose that two players with equal chances of winning are playing some game of chance for some amount of money. While playing this game, they are interrupted. Given the score of the game at this point, how should the money be divided between the players?
Pierre de Fermat (1601-1665)
- Born in Beaumont-de-Lomagne, France
- French lawyer at the Parlement de Toulouse
- Mathematician
Blaise Pascal (1623-1662)
- Born in Clermont-Ferrand, France
- Inventor, mathematician, physicist, and theologian
- In 1654, this problem was proposed to Pascal and Fermat by French nobleman and gambler, Chevalier de Mere.
- This led to a discussion between Pascal and Fermat through letters.
- This exchange of letters resulted in the development of the fundamental principles of probability theory.
Pascal Generalized the Problem
Sources
- http://homepages.wmich.edu/~mackey/Teaching/145/probHist.html
- http://www.york.ac.uk/depts/maths/histstat/pascal.pdf
- http://mathforum.org/isaac/problems/prob1.html
- http://www.biography.com/people/blaise-pascal-9434176
- The problem proposed dealt with the probability of rolling double sixes in 24 throws, using two standard dice.
- After Pascal's first attempted solution, Fermat responded, proposing a different argument to this specific scenario.
- Pascal agreed that he was initially wrong in his first attempt at a solution and proceeded to generalize the correct solution to the problem, using the famous Pascal's Triangle to do so.
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