If two events have no elements in common (Their intersection is the empty set.), the events are called mutually exclusive. Thus, P(A ∩ B) = 0. This means that the probability of event A and event B happening is zero. They cannot both happen.
A pair of dice is rolled. The events of rolling a 5 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 4 and rolling a double have the outcome (2, 2) in common so the two events are not mutually exclusive.
From a group of 6 freshmen and 5 sophomores, 3 students are to be selected at random to form a committee. What is the probability that at least 2 freshmen are selected?The committee will have at least 2 freshmen if either 2 freshmen and 1 sophomore are selected (event A)or 3 freshmen are selected (event B). Since the two events are mutually exclusive