Chapter 6 - Independence in Probability Theory

Abstract

The concept of conditional probability incorporates into the model the idea that two events may have some “informational connection,” so that knowledge of the occurrence of one may influence the credibility or probability assigned to the other. There are many situations in which events under study seem to be “independent,” in the sense that occurrence or nonoccurrence of one has no effect on the credibility or likelihood of occurrence of the other. This seems to be a reasonable assumption for cases in which there is physical independence—although it is difficult to define precisely what is meant by physical independence. For example, in the usual coin-tossing experiment, there is no physical reason to suppose that the outcome of one toss can have any effect on the outcome of a subsequent or previous toss. These results would be deemed by most observers to be physically independent. The distribution assigned or assumed, in any case, reflects knowledge about the conditions under which the trials are performed.