Statistical Inference: A Short Course

4.3 Basic Probability Calculations

How do we associate probabilities with events? Since events are subsets of S, let us employ a set function⁴ 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.

Figure 4.5 P is a set function on

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