1.1 Sample Spaces, Events, and Probabilities

A sample space, S, is defined as the set of all possible outcomes of an experiment. If the outcomes in S are equally likely, we call S an equally probable sample space. Any subset of S is called an event. For example, if a box contains three chips numbered 1,2,3 and we draw one chip from the box in such a way that each of the three chips are equally likely to be selected, then {1,2,3} is an equally probable sample space and (empty set), {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} are events. For this experiment {odd, even} is also a sample space but it is not an equally probable sample space since an odd outcome is twice as likely as an even outcome.

Let P( A) denote the probability that event A will occur. If S is an equally probable sample space, then

Example 1.1. Box I contains chips numbered 1,2,3 and box II contains chips numbered 2,3,4. One chip is selected at random from each box. When we say at random we mean equally likely or in this example an equally likely selection.

where the first number in each ordered pair denotes the number on the chip drawn from box I and the second number in each ordered pair denotes the number on the chip drawn from box II. This is the set of all...