Probability Calculator

What this calculator does

This tool answers everyday probability questions in three modes. The single-event mode turns a count of favourable and total outcomes into a probability, percentage, odds, and complement. The two-event mode combines two independent events A and B, giving the chance that both happen, that at least one happens, and that neither happens. The at-least-one mode finds the probability of at least one success across a run of independent trials. Every result updates live as you type, and all of the arithmetic happens locally in your browser.

Why you might need it

Probability questions come up constantly once you start looking for them. What are the odds of drawing a heart from a deck? If a process has a 5% failure rate and you run it ten times, how likely is at least one failure? If two independent checks each catch a defect 80% of the time, how often does a defect slip past both? Students need a reliable check for statistics homework, and anyone making decisions under uncertainty — quality control, game design, risk estimation — benefits from quick, correct probability arithmetic. This calculator covers the three patterns those questions almost always reduce to.

How to use it

1. Choose a mode: single event, two events, or at least one.
2. Fill in the two input fields — their labels change with the mode, so they always tell you exactly what to enter.
3. Read the headline answer in the result card and the supporting figures in the grid below it.
4. Use the copy button to grab the headline result, and Reset to return to the example values.

How it’s calculated

Single event: the probability is the favourable outcomes divided by the total outcomes, P = f / t. The percentage is that value times 100, the complement is 1 − P, and the odds in favour are f to (t − f).

Two independent events: because A and B do not affect each other, the chance both occur is the product, P(A and B) = P(A) × P(B). The chance at least one occurs uses the addition rule, P(A or B) = P(A) + P(B) − P(A) × P(B), where the last term removes the double-counted overlap. The chance neither occurs is (1 − P(A)) × (1 − P(B)).

At least one of N trials: the complement trick is used. Each trial fails with probability 1 − p, all N fail with probability (1 − p)ᴺ, so the chance of at least one success is 1 − (1 − p)ᴺ.

Common pitfalls

The biggest mistake is assuming independence when it does not hold — drawing two cards without replacement is not independent, so the second draw’s probability changes. Another is adding probabilities for “and” instead of multiplying, or forgetting to subtract the overlap in the “or” formula, which can push a result above 1. People also confuse odds with probability: odds of 1:3 in favour means a probability of one in four, not one in three. Finally, a probability can never exceed 1 or fall below 0 — if your answer does, an input or a formula is wrong.

Tips and related calculations

The complement trick — find the chance something doesn’t happen and subtract from one — is the single most useful shortcut in probability, and it powers the at-least-one mode. For sequences of dependent events you would multiply conditional probabilities instead, which is a step beyond this calculator. When counting outcomes for the single-event mode, a permutations and combinations calculator can give you the favourable and total counts to plug in here. Because all the maths runs on your device, you can explore scenarios freely and nothing you enter ever leaves the browser.