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2.2.1 Joint, Marginal, and Conditional Probabilities

We now consider an experiment that consists of two parts, and each part leads to the occurrence of specified events. Let us define events arising from the first part of the experiment by with probability and events from the second part by with probability . The combination of events and may be called a composite event, denoted by the ordered pair . We wish to generalize the definition of probability to apply to the composite event . The joint probability is defined to be the probability that the first part of the experiment led to event and the second part of the experiment led to event . Thus, the joint probability is the probability that the composite event occurred (i.e., the probability that both events and occur).