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They play on the following conditions: they are to draw blindfold, and the first who draws a white ball wins. A is to have the first turn, B the next, C the next; then A again, and so on. Determine the chances of the players. Bernoulli solved the problem under several interpretations—for example, drawing the balls with or without replacement.  75] for Huygens’ own solution of the division problem. Huygens’ book served as a text in probability—the only one available for the next fifty years, when it was incorporated, with commentary, as Part I of Jakob Bernoulli’s Ars Conjectandi [2].

Mon. : A History of Mathematics: An Introduction, 3rd edn. : Algebra, geometry, and algebraic geometry. Am. Math. Mon. : Mathematical Thought from Ancient to Modern Times. : The Mathematical Career of Pierre de Fermat, 2nd edn. Princeton University Press, Princeton (1994) Further Reading 13. : The Geometry of René Descartes, with a Facsimile of the First Edition. Dover, New York (1954) 14. : The Scientific Work of René Descartes (1596–1650). Taylor & Francis, New York (1952) 27 4 Probability: From Games of Chance to an Abstract Theory H.

Indeed, contemporary mathematicians recognized that Fermat and Pascal had done precisely that. Why was there no definition of probability, and why were there no theorems and proofs in the Pascal–Fermat correspondence—a work that initiated a new subject? First, such matters are not to be expected in a correspondence dealing with the solution of problems. Beyond that, it is almost always the case that the formal development of a subject comes at the end of an evolutionary process. Calculus is an excellent example of this phenomenon (see 7 Chapter 5).

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