Mutually exclusive events

Mutually exclusive events cannot both occur in the same trial, so P(A and B) = 0 and P(A or B) = P(A) + P(B). Business examples include a project succeeding or failing, or a customer choosing between two competing products.

ByHoang TruongUpdated July 2, 2026

FrameworkProbability theory

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A customer chooses either product A or product B in a single purchase, never both, so the two outcomes are mutually exclusive. With P(A) at 55% and P(B) at 45%, the probability of choosing one or the other is simply their sum, P(A or B) = P(A) + P(B), which here totals 100% because the two outcomes are also exhaustive.

Where it fits

TopicProbability & DistributionsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

P(A \cup B) = P(A) + P(B) \text{ when } P(A \cap B) = 0

Variables

$P (A)$: Probability of event A
$P (B)$: Probability of event B
$P (A an d B)$: Joint probability that both events occur in the same trial

The addition rule simplifies to a plain sum because the overlap is zero. For a set of mutually exclusive and exhaustive outcomes, probabilities must sum to 1.