Probability Calculator
Work out the probability of single and multiple events, convert outcomes to odds, and run binomial repeated-trial calculations.
Two independent events A and B
- P(Aโฒ) โ A does not happen
- โ
- P(Bโฒ) โ B does not happen
- โ
- P(A โฉ B) โ both happen
- โ
- P(A โช B) โ at least one happens
- โ
- P(A ฮ B) โ exactly one happens
- โ
- P(Aโฒ โฉ Bโฒ) โ neither happens
- โ
Probability from favourable outcomes
- Probability
- โ
- Complement (does not happen)
- โ
- Odds in favour
- โ
- Odds against
- โ
Repeated trials (binomial)
- Never happens (0 successes)
- โ
- Happens at least once
- โ
- Exactly k successes
- โ
- At least k successes
- โ
- Expected successes (n ร p)
- โ
How it works
Three probability calculators on one page, all live: every probability box accepts a
decimal like 0.5 or a percentage like 50%, and the results
update as you type โ there is no calculate button. The first takes the probability of two
independent events and works out every combination from them: the complement of each event
(1 โ P), both happening (P(A) ร P(B)), at least one happening (P(A) + P(B) โ P(A) ร P(B)),
exactly one happening, and neither happening. The second turns a count of favourable
outcomes over total outcomes into a probability, its complement and the odds for and
against, reduced with the greatest common divisor โ 13 of 52 cards becomes 0.25, or odds of
1 : 3.
The third handles repeated independent trials with the binomial formula C(n, k) ร pk ร (1 โ p)n โ k: it shows the chance of never succeeding, of succeeding at least once, of exactly k successes, of k or more successes, and the expected number of successes. Type probabilities as decimals (0.5) or percentages (50%). All of the maths runs in JavaScript inside your browser โ nothing is uploaded, there is no sign-up and there are no ads. Copy any block, copy them all, or download the results as a plain text file.
Frequently asked questions
How do you calculate the probability of two events happening?
For two independent events, multiply their probabilities: P(A and B) = P(A) x P(B). With P(A) = 0.5 and P(B) = 0.2 that gives 0.1, or 10%. For at least one of them happening you add the probabilities and subtract the overlap: P(A or B) = P(A) + P(B) - P(A) x P(B), which is 0.6 here. The calculator shows both, plus the chance that exactly one or neither event happens.
How do I convert a probability into odds?
Odds compare favourable outcomes with unfavourable ones, while probability compares favourable outcomes with the total. Drawing a heart from a 52-card deck is 13 favourable and 39 unfavourable outcomes, so the probability is 13/52 = 0.25 and the odds in favour are 13:39, which reduce to 1:3 (odds against are 3:1). Enter the two counts and the tool reduces the ratio for you with the greatest common divisor.
What is the chance of something happening at least once in several tries?
Work out the chance it never happens and subtract that from 1: P(at least once) = 1 - (1 - p)^n. Flipping heads on a fair coin ten times has a never-chance of 0.5^10 = 0.0009765625, so heads appears at least once with probability 0.9990234375, about 99.9%. The repeated-trials section also gives the binomial probability of exactly k successes and of k or more.