Probability

In this chapter, the authors introduce the notion of a sample space, state Kolmogorov's axioms of probability and study some simple consequences of these axioms. The authors then focus on the computation of probability on finite sample spaces. The probabilities of events are computed on the assumption that no information was available about the experiment other than the sample space. In games of chance we usually deal with finite sample spaces where uniform probability is assigned to all simple events. The same is the case in sampling schemes. In such instances the computation of the probability of an event reduces to a combinatorial counting problem. The chapter therefore considers some rules of counting. It then deals conditional probability and Bayes's rule. Finally, the chapter examines the independence of events.