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

What it is

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.

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.