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Probability is the subdiscipline of mathematics that focuses on a systematic study of randomness and uncertainty. In any situation in which one of a number of possible outcomes may occur, the theory of probability provides methods for quantifying the chances, or likelihoods, associated with the various outcomes. The language of probability is constantly used in an informal manner in both written and spoken contexts. Examples include such statements as “It is likely that the Dow Jones Industrial Average will increase by the end of the year,” “There is a 50–50 chance that the incumbent will seek reelection,” “There will probably be at least one section of that course offered next year,” “The odds favor a quick settlement of the strike,” and “It is expected that at least 20,000 concert tickets will be sold.” In this chapter, we introduce some elementary probability concepts, indicate how probabilities can be interpreted, and show how the rules of probability can be applied to compute the chances of many interesting events. The methodology of probability will then permit us to express in precise language such informal statements as those given above.
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However, the multiplication property is satisfied if P( B) = 0, yet P( A| B) is not defined in this case. To make the multiplication property completely equivalent to the definition of independence, we should append to that definition that A and B are also independent if either P( A) = 0 or P( B) = 0.
In the language of Chap. 3, the numbers produced by an RNG follow essentially a uniform distribution on the interval [0, 1).
Matthew A. Carlton
Jay L. Devore
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