Probability Calculator
Find a single event’s complement or combine two independent events using both, at-least-one, exactly-one and neither modes.
Event probability
Two-event modes assume independence, not mutual exclusivity. Outcome-count mode assumes equally likely outcomes. Percentages must be 0–100; favourable counts cannot exceed total counts.
Formula checked · NumberSwift · Review process
How this calculator works
For one event, use a probability percentage or divide favourable outcomes by the total when all outcomes are equally likely. Its complement is the chance that it does not occur. For two independent events, multiplication gives both, and adding their individual probabilities then subtracting the overlap gives either, including both. “Either” and “at least one” are the same inclusive event here; “exactly one” excludes the overlap.
Formula
P(not A) = 1−P(A). Under independence: P(A and B) = P(A)P(B); P(A or B) = P(A)+P(B)−P(A)P(B); P(exactly one) = P(A)(1−P(B))+P(B)(1−P(A)); P(neither) = (1−P(A))(1−P(B)).
Assumptions & limitations
Two-event modes assume independence, not mutual exclusivity. Outcome-count mode assumes equally likely outcomes. Percentages must be 0–100; favourable counts cannot exceed total counts.
Worked example
For independent A = 30% and B = 40%, both is 0.3 × 0.4 = 12%, at least one is 30% + 40% − 12% = 58%, exactly one is 46% and neither is 42%. A single event with 3 favourable outcomes out of 10 has probability 30% and complement 70%.
Our approach to calculations ↗Common questions
Are independent events the same as mutually exclusive events?
No. Independent events can both happen. Mutually exclusive events cannot happen together and need different overlap assumptions.
Does “either” mean exactly one here?
No. Either / at least one includes both. Choose Exactly one when you want to exclude the both-events outcome.
Can I count outcomes when they are not equally likely?
Not by dividing counts alone. Enter the actual event probability or use a model that accounts for outcome weights.