If the occurrence of one event has no effect on the probability of another event, the two events are independent events .
Consider the experiment of tossing a coin twice. The sample space for the experiment is . Let be the event that a tail is obtained on the first toss and be the event that a head is obtained on the second toss.
and are not mutually exclusive because but they are independent because obtaining a tail on the first toss does not affect the outcome of the second toss.
Two events are independent if and only if .