Enter each probability in the chosen format. Events are assumed independent.
About this tool
The Probability Calculator combines two independent events A and B and reports the common derived probabilities as percentages. Enter P(A) and P(B) either as decimals from 0 to 1 or as percentages — pick the matching mode from the dropdown — and the results update live, all computed in your browser.
Assuming independence, it uses P(A and B) = P(A)·P(B); P(A or B) = P(A) + P(B) − P(A)·P(B); P(neither) = (1 − P(A))·(1 − P(B)); P(not A) = 1 − P(A); and P(exactly one) = P(A) + P(B) − 2·P(A)·P(B). If you enter a number of trials n, it also gives P(at least one A in n) = 1 − (1 − P(A))ⁿ.
Each probability is validated to fall between 0 and 1 (or 0 and 100 in percent mode); anything outside that range is flagged as invalid. Independence means the outcome of one event does not affect the other — the formulas above do not apply to mutually exclusive or dependent events.
Frequently asked questions
Does this assume the events are independent?
Yes. All formulas assume A and B are independent, so P(A and B) = P(A)·P(B). They do not hold for dependent events or ones that cannot both happen (mutually exclusive).
Can I enter percentages instead of decimals?
Yes. Switch the mode to Percent and type values like 50 and 30; the tool divides by 100 internally. In Decimal mode enter 0.5 and 0.3. Either way the result is shown as a percentage.
How is 'at least one in n trials' found?
By the complement rule: the chance of no A in n independent trials is (1 − P(A))ⁿ, so the chance of at least one is 1 − (1 − P(A))ⁿ. Leave the trials field blank to skip it.
What is P(exactly one)?
The probability that exactly one of A or B occurs (one but not both): P(A) + P(B) − 2·P(A)·P(B). It equals P(A or B) minus P(A and B).