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This chapter defines the central concepts and terms used in probability theory including the random experiment, space, event, elementary event, combined experiment, Cartesian product, etc. This chapter presents the axiomatic formulation of probability theory based on three axioms and shows how set operations are used in probability theory. This chapter also discusses the conditional probability, the total probability theorem, the Bayes’ theorem, and the independence of random events. Examples of a reliability problem and a communications signal detection problem are discussed.