We are defining probability as the likelihood of the occurrence of an event, usually expressed in the form of a proportion and interpreted as a percentage. Probabilities can range from .00, a zero percent likelihood of occurrence to 1.0, a 100 percent chance of occurrence. Probabilities are never expressed in negative numbers. In this primer, we are concerned with combining the probabilities of two different events.
Different formats are available to help visualize combining the probabilities of two events.
One is a tree format, but we are going to use the contingency table format. We shall also limit ourselves to situations in which each of the events has only two alternatives. The four cells that represent the intersection of those two variables are labeled a,b,c,and d, respectively. In the context of testing for the presence or absence of a condition or event, we can identify whether the test result was accurate or not. Table 2 provides the language of such tests.