Probability Calculator
Calculate the probability of two events, combined with AND/OR logic.
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25%
About this calculator
How This Probability Calculator Works
Enter the probability of two independent events, and the calculator returns the probability that both happen, and the probability that at least one happens.
Worked Example
Two independent events each with a 50% probability (like two coin flips both landing heads): the probability both happen is 25%, and the probability at least one happens is 75%.
The Formulas
P(A and B) = P(A) × P(B) — for independent events, multiply the probabilities. P(A or B) = P(A) + P(B) − P(A and B) — add the probabilities, then subtract the overlap (the "and" case) to avoid double-counting it.
The Independence Assumption
This calculator assumes A and B are independent — that one event happening doesn't change the probability of the other. Two coin flips are independent; drawing two cards from a deck without replacement is not (the first draw changes what's left for the second). For dependent events, these formulas need to be adjusted using conditional probability, which this calculator doesn't cover.
Worked example
Two independent coin flips, each with a 50% chance of heads: P(both heads) = 0.5 × 0.5 = 25%. P(at least one heads) = 0.5 + 0.5 − 0.25 = 75%.
Frequently asked questions
Does this assume A and B are independent?
Yes — the "P(A and B) = P(A) × P(B)" formula only holds when the two events don't influence each other, like separate coin flips or dice rolls. For dependent events, the true joint probability can differ.
What does "P(A or B)" actually include?
It's the probability that at least one of the two events happens — A alone, B alone, or both together — which is why the overlap (P(A and B)) is subtracted once to avoid double-counting it.
Can probabilities be entered as fractions instead of percentages?
Enter them as a percentage (e.g., 1/6 as 16.67%) — the calculator works in percentage terms throughout.