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).