ABSTRACT

This chapter studies independent events, where the occurrence of one event is not influenced by the occurrence of the other. It also presents the notion of disjoint events, those that cannot possibly happen together. It turns out that a number of uncertain situations can be analyzed by decomposing them into independent and disjoint events. Appropriate generalizations of the Multiplication Rule and the Addition Rule are involved. However, in many situations we encounter dependent events (e.g., forecasting today’s weather having observed yesterday’s weather). In such circumstances, we require the more general concept of conditional probability. Understanding conditional probabilities can be aided by the use of decision trees, introduced in Chapter 12.