Calculate unions, intersections, complements and conditional probabilities for two events.
P(A or B)
How to use this tool
Probabilities are numbers between 0 and 1 — for example 0.4 means a 40% chance.
If you know the chance of both happening, enter it; otherwise leave it blank and choose an assumption.
Independent means one does not affect the other; mutually exclusive means they cannot both happen.
Union, intersection, complement, conditional probability and odds are all shown together.
Formula & worked example
P(A) = 0.4 and P(B) = 0.5, independent: P(A and B) = 0.20, P(A or B) = 0.70, P(not A) = 0.60, P(A | B) = 0.40 (independence means conditioning on B changes nothing).
Limitations — read this before you rely on it
The independence and mutual-exclusivity options are assumptions, not facts about your events — real events are often neither fully independent nor mutually exclusive. P(A and B) can never exceed the smaller of P(A) and P(B). This calculator covers two events; for more events, use the inclusion–exclusion principle or a tree diagram.
Frequently asked questions
Union (A or B) is at least one happening; intersection (A and B) is both happening. Union = P(A) + P(B) − intersection, to avoid double-counting the overlap.
The probability of A given that B has happened. It equals P(A and B) ÷ P(B).
When one does not change the probability of the other — then P(A | B) = P(A) and P(A and B) = P(A) × P(B).
Another way to state a probability: odds of 1 to 3 mean one success for every three failures, which is a probability of 1 ÷ 4 = 0.25.
No. Probabilities run from 0 (impossible) to 1 (certain). Anything outside that range is an error.