A short history of probability(Northern Illinois University,Alan M. Polansky).pdf

A short history of probability(Northern Illinois University,Alan M. Polansky).pdf

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A short history of probability(Northern Illinois University,Alan M. Polansky)

A Short History of Probability Dr. Alan M. Polansky Division of Statistics Northern Illinois University History of Probability 2 French Society in the 1650’s ! Gambling was popular and fashionable ! Not restricted by law ! As the games became more complicated and the stakes became larger there was a need for mathematical methods for computing chances. History of Probability 3 Enter the Mathematicians ! A well-known gambler, the chevalier De Mere consulted Blaise Pascal in Paris about a some questions about some games of chance. ! Pascal began to correspond with his friend Pierre Fermat about these problems. History of Probability 4 Classical Probability ! The correspondence between Pascal and Fermat is the origin of the mathematical study of probability. ! The method they developed is now called the classical approach to computing probabilities. ! The method: Suppose a game has n equally likely outcomes, of which m outcomes correspond to winning. Then the probability of winning is m/n. History of Probability 5 Problems with the Classical Method ! The classical method requires a game to be broken down into equally likely outcomes. ! It is not always possible to do this. ! It is not always clear when possibilities are equally likely. History of Probability 6 Experience ! Another method, known as the frequency method had also been used for some time. ! This method consists of repeating a game a large number of times under the same conditions. The probability of winning is then approximately equal to the proportion of wins in the repeats. ! This method was used by Pascal and Fermat to verify results obtained by the classical method. History of Probability 7 Early Generalizations ! James Bernoulli proved that the frequency method and the classical method are consistent with one another in his book Ars Conjectandi in 1713. History of Probability 8 Early Generalizations ! Abraham De Moivre provided many tools to make the classical metho

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