Mutually Exclusive Events

Two events A and B are said to be mutually exclusive or disjoint if the events cannot occur simultaneously. This means that A and B have no common outcomes, implying that the probability of A and B is zero.

By the Addition Rule of Probability, it can be concluded that the probability of A or B is equal to the sum of the individual probabilities.

Below, some examples of mutually exclusive events are presented.

• A given integer number is either even or odd.
• The outcome of tossing a coin is either heads or tails.

Three or more events are mutually exclusive if all pairs are mutually exclusive.

• In a soccer match, a team either wins, loses, or the result is a draw.
• The outcome of rolling a dice is either 1, 2, 3, 4, 5, or 6.

Events can be mutually exclusive without being the only possible outcomes.

• A given number is either negative or positive.
• A card randomly drawn from a deck of cards is hearts or clubs.