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Probability of A or B (Union) Calculator

Find P(A or B) with the addition rule — for independent, mutually exclusive or overlapping events with a known joint probability.

P(A)

P(B)

Relationship

P(A and B) (only for “overlapping”)

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How it works

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Adding P(A) and P(B) double-counts the outcomes where both happen, so the overlap is subtracted once. For mutually exclusive events the overlap is zero; for independent events it is the product of the two probabilities.

Worked example

P(A) = 0.3, P(B) = 0.5, independent → overlap 0.15 → P(A or B) = 0.3 + 0.5 − 0.15 = 0.65.

Frequently asked questions

Can P(A or B) ever exceed 1?

No. If your inputs give more than 1, the events must overlap more than you assumed — enter the actual joint probability.

Is “or” inclusive?

Yes, the union includes the case where both occur. “Exactly one” is shown separately.

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For education — check assumptions (sample size, distribution) before using statistics in real decisions.