Mutually Exclusive Events

When two events A and B cannot happen at the same time, they are said to be mutually exclusive (in other words, keep to themselves or don't mix with one another) and may be represented using a Venn diagram as follows.

Because the intersection of A and B is empty (meaning that they have no common outcomes), we may deduce that the probability of both happening at the same time is 0. That is,

P(A and B) = 0.

The Addition Law of Probability for mutually exclusive events A and B, which gives the probability of either one or the other of them happening, becomes:

P(A or B) = P(A) + P(B).

Examples

Example using the Rule of Addition

Example comparing mutually exclusive events and independent events

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Last Updated by SAS October 07, 2026, 16:00:54