History
As a mathematical subject, the theory of probability arose very late—as compared to geometry for example—despite the fact that we have prehistoric evidence of man playing with dice from cultures from all over the world. In fact we have the exact year when it was born; in the year 1654 Blaise Pascal had some correspondence with his father's friend Pierre de Fermat about two problems concerning games of chance he had heard from the Chevalier de Méré earlier the same year, whom Pascal happened to accompany during a trip.
One problem was the so called problem of points, a classic problem already then (treated by Luca Pacioli as early as 1494, and even earlier in an anonymous manuscript in 1400), dealing with the question how to split the money at stake in a fair way when the game at hand is interrupted half-way through. The other problem was one about a mathematical rule of thumb that seemed not to hold when extending a game of dice from using one die to two dice. This last problem, or paradox, was the discovery of Méré himself and showed, according to him, how dangerous it was to apply mathematics to reality. They discussed other mathematical-philosophical issues and paradoxes as well during the trip that Méré thought was strengthening his general philosophical view.
Pascal, in disagreement with Méré's view of mathematics as something beautiful and flawless but poorly connected to reality, determined to prove Méré wrong by solving these two problems within pure mathematics. When he learned that Fermat, already recognized as a distinguished mathematician, had reached the same conclusions, he was convinced they had solved the problems conclusively. This correspondence circulated among other scholars at the time, in particular, to Huygens, Roberval and indirectly Caramuel, and marks the starting point for when mathematicians in general began to study problems from games of chance.
This does not mean that Pascal and Fermat had a clear concept of probability, nor that they made the first correct calculations concerning games of chance. No clear distinction had yet been made between probabilities and expected values. The first person known to have seen the need for a clear definition of probability was Laplace. As late as 1814 he stated:
The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.
— Pierre-Simon Laplace, A Philosophical Essay on Probabilities
This description is what would ultimately provide the classical definition of probability.
Read more about this topic: Classical Definition Of Probability
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