Mutually Exclusive Events
If two events have no elements in common (Their intersection is the empty set.), the events are called mutually exclusive. Thus, . This means that the probability of event and event happening is zero. They cannot both happen.
A pair of dice is rolled. The events of rolling a
and rolling a double have NO outcomes in common so the two events are mutually exclusive.
A pair of dice is rolled. The events of rolling a and rolling a double have the outcome in common so the two events are not mutually exclusive.
From a group of freshmen and sophomores, students are to be selected at random to form a committee. What is the probability that at least freshmen are selected?The committee will have at least freshmen if either freshmen and sophomore are selected (event )or freshmen are selected (event ). Since the two events are mutually exclusive