Mutually exclusive events cannot occur simultaneously within the same set of alternatives. For such events, the probability of either event occurring equals the sum of their individual probabilities: P(A or B) = P(A) + P(B). section 2.2.2 section 2.5
Use the addition rule when:
- The alternatives cannot happen at the same time, such as rolling either a 4 or a 5 on one six-sided die. section 3.2
- A choice permits only one option, such as selecting one novel, one manual, or one travel route. section 2.2.2
- Do not substitute the multiplication rule: it applies to independent events occurring together or sequentially, not mutually exclusive alternatives. section 2.2.2 section 2.5
Rolling a 4 or 5
On one six-sided die, rolling a 4 and rolling a 5 are mutually exclusive. Each probability is 16.7%, so P(4 or 5) = 16.7% + 16.7% = 33%. section 3.2
