Two events and are said to be mutually exclusive events or disjoint, if the events cannot occur simultaneously. This means that and have no common outcomes, implying that the probability of and is zero.
Thanks to the Addition Rule of Probability, it can be concluded that the probability of or is equal to the individual probabilities added together.
Below, some examples of mutually exclusive events are presented.
Three or more events are mutually exclusive if all pairs are mutually exclusive.
Events can be mutually exclusive without being the only possible outcomes.
Compare this concept with the concept of collectively exhaustive events, where the events cover all possible outcomes.
|Events||Are these Mutually Exclusive Events?||Are these Collectively Exhaustive Events?|
|A given integer number is even or odd.||Yes||Yes|
|A given integer number is negative or positive.||Yes||No, it can also be zero.|
|A given integer number is greater than or less than .||No, is greater than and less than .||Yes|
|A given integer number is prime or even.||No, is both prime and even.||No, is neither prime nor even.|