ABSTRACT

In this chapter, the authors describe some properties that any reasonable measure of uncertainty should satisfy; then they define probability as any measure that satisfies those properties. The nice thing about this way of defining probability is that not only does it avoid the problem of vagueness, but it also means that we can have more than one measure of probability. In particular, the authors see that both the frequentist and subjective approaches satisfy the axioms, and hence both are valid ways of defining probability. They introduce the basic machinery of probability calculations in the form of the axioms and theorems that are central to probability theory and the crucial notion of probability distributions. The authors aim to use the axioms to define the crucial issue of independence of events. They describe an especially important probability distribution—the Binomial distribution—which is based on the idea of independent events.