Probability Calculator

Free probability calculator. Compute the probability of coin flips (binomial), dice rolls (exact, at least, at most), and drawing marbles without replacement (hypergeometric).

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This tool has a free JSON API. Copy a prompt or skill below to use it with ChatGPT, Claude, or any AI agent — no API key needed.

API docs
Choose a scenario above.

How probability calculator works

Probability measures how likely an outcome is, from 0 (impossible) to 1 (certain). This calculator handles three classic scenarios: coin flips (the binomial probability of exactly k heads in n flips), dice rolls (the chance of an exact, at-least, or at-most result on a die), and drawing without replacement (the hypergeometric probability of drawing k successes from a bag of N items containing K successes).

For coins it uses P(k heads in n) = C(n,k) / 2^n, where C(n,k) is the binomial coefficient. For dice it counts the favourable outcomes over the total sides — exactly one for an exact roll, (sides − target + 1) for "at least", and target for "at most". For marbles it uses the hypergeometric formula C(K,k) × C(N−K, n−k) / C(N,n).

Choose a scenario and enter the parameters. The tool returns the probability as a fraction, a decimal, a percentage, and odds (1 in N). Use it for homework, games, statistics, and any "what are the chances" question.

Frequently asked questions

How is the coin-flip probability computed?
With the binomial formula P(k heads in n flips) = C(n,k) / 2^n. For exactly 2 heads in 3 flips, C(3,2) = 3 and 2^3 = 8, so the probability is 3/8 = 37.5%.
What do the dice modes mean?
Exact is the chance of rolling exactly the target. At least is the chance of rolling the target or higher. At most is the chance of rolling the target or lower. Each counts favourable outcomes over the number of sides.
What is the marble scenario?
Drawing without replacement — the hypergeometric distribution. From a bag of N items with K successes, drawing n of them, P(exactly k successes) = C(K,k) × C(N−K, n−k) / C(N,n). The API supports it; the on-page panel demonstrates coin and dice.
What are the "odds" reported?
The reciprocal of the probability, written as "1 in N". A 25% probability has odds of 1 in 4, meaning you would expect it once in every four trials on average.