Addition rule of probability

The addition rule gives P(A or B) = P(A) + P(B) − P(A and B), the probability that at least one of two events occurs, subtracting the overlap so it isn't counted twice.

ByHoang TruongUpdated July 5, 2026

See it move

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Among 200 job applicants, 120 hold a business degree and 50 have worked abroad, with 30 holding both. Adding 120/200 and 50/200 double-counts those 30, so the overlap is subtracted once: P(degree or abroad) = 120/200 + 50/200 − 30/200 = 140/200, or 70 per cent.

Where it fits

TopicProbability & DistributionsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

P(A \cup B) = P(A) + P(B) - P(A \cap B)

Variables

$P (A)$: Probability that event A occurs
$P (B)$: Probability that event B occurs
$P (A an d B)$: Probability that both A and B occur in the same trial

General addition rule for the probability that at least one of two events occurs; the overlap P(A and B) is subtracted once to avoid double-counting.

Check yourself

PracticeCORE

Among 150 weekly transactions at a retail store, 90 include a discount coupon, 45 are paid with a loyalty card, and 20 transactions use both. What is the probability that a randomly chosen transaction uses a coupon or a loyalty card?

Select an answer to check your understanding.