The Calculus of Probability
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Many of the early problems in mathematical probability dealt with the determination of odds in various games of chance. A rather famous example of this sort is the problem posed by the French nobleman, Antoine Gombaud, Chevalier de Me´re´, to one of the outstanding mathematicians of his day, Blaise Pascal: which is the more likely outcome, obtaining at least one six in four rolls of a single die or obtaining at least one double six in twenty-four rolls of a pair of dice? The question itself, dating back to the mid-seventeenth century, seems unimportant today, but it mattered greatly to Gombaud, whose successful wagering depended on having a reliable answer. Through the analysis of questions such as this (which, at this point in time, aptly constitutes a rather straightforward problem at the end of this chapter), the tools of probability computation were discovered. The body of knowledge we refer to as the probability calculus covers the general rules and methods we employ in calculating probabilities of interest.