How do we associate probabilities with events? Since events are subsets of S, let us employ a set function^{4} from the sample space to the unit interval [0,1]. Here P is a rule that can be ascribed to any event some number called its probability (Fig. 4.5). Note that if , then is the impossible event; and if then is the certain event. Thus probability is a number between 0 and 1 inclusive, where the larger is the more likely it is that event will occur.

What are the characteristics of ? To answer this question, we start ...

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