Definition
Two events are mutually exclusive (sometimes called disjoint) when they cannot both occur on the same trial. If one happens, the other is logically excluded. The classic example is a single coin toss: the outcome is either heads or tails, never both. Drawing a single card and getting both a heart and a spade is impossible — those two events share no outcomes in the sample space.
Formally, two events A and B are mutually exclusive when their intersection is empty: P(A and B) = 0. This is the structural condition that lets you simply add their probabilities instead of subtracting an overlap.
Why it matters
How it works
The general addition rule for any two events states that P(A or B) = P(A) + P(B) - P(A and B). The subtraction corrects for double-counting outcomes that belong to both events. When the events are mutually exclusive, that joint probability is zero, and the rule collapses to the simpler form: P(A or B) = P(A) + P(B). This is why introductory probability problems lean so heavily on exclusive events — the arithmetic is clean.
The same logic generalises to more than two events. If a list of events is pairwise mutually exclusive — no two of them can co-occur — then the probability of at least one happening equals the sum of their individual probabilities. When the list is also exhaustive, meaning every possible outcome falls into exactly one event, those probabilities must sum to 1. This pairing of exclusive and exhaustive is what underwrites every probability distribution: each outcome is counted once and only once. Confusing mutual exclusivity with independence is a common error — independent events can and usually do co-occur, while mutually exclusive events by definition cannot.