Probability Calculator

Calculate probabilities for single events, two independent events (A and B, A or B, exactly one), the chance of something happening at least once in several tries, binomial “exactly k of n” questions, and exact combinations and permutations (nCr, nPr).

This tool runs entirely in your browser.

Loading tool…

How to use the Probability Calculator

1Choose the kind of question: one event, two events, at least once, k successes, or combinations.
2Enter the probabilities (in %) or counts.
3Read the probability, its decimal and percentage forms, and — for binomials with up to 200 tries — the full distribution table.

What is the Probability Calculator?

For independent events, P(A and B) = P(A) × P(B) and P(A or B) = P(A) + P(B) − P(A and B). The chance of at least one success in n tries is 1 − (1 − p)^n: with a 10 % chance each time, ten tries give about 65 %, not 100 %.

The binomial distribution gives the probability of exactly k successes in n independent tries: C(n, k) × p^k × (1 − p)^(n − k). Combinations count choices where order doesn’t matter — there are 2,598,960 five-card poker hands — and are computed exactly even for large numbers (very long results are shortened on screen).

Frequently asked questions

What is the difference between combinations and permutations?

Combinations ignore order (which 3 people get picked); permutations count each order separately (who comes first, second and third). P(n, k) = C(n, k) × k!.

Does a coin “owe” me heads after several tails?

No — independent tries have no memory. The chance stays 50 % each flip; that mistaken belief is the gambler’s fallacy.

Is the Probability Calculator free and private?

Yes. The Probability Calculator is free, needs no account, and runs entirely in your browser. What you type is never sent to a server or stored.

All calculators →