| Favourable outcomes | 3 |
| Total equally likely outcomes | 36 |
| P(event) = favourable / total | 0.08333333 |
| As a percentage | 8.3333% |
| P(event does not happen) | 0.91666667 |
P = 3 / 36. Each outcome is assumed equally likely, as with a fair die or a shuffled deck.
Count the favourable outcomes and divide by the total only when every outcome is equally likely. Otherwise start from the probabilities you know. Use the complement when "not" is easier to count. Use the addition rule for "or" and subtract the overlap; the overlap is multiplied only when the events are independent, which means one does not change the chance of the other. Use the conditional formula when the question says "given that".
Event probability, complements, P(A or B) and conditional probability. A probability is a number from 0 to 1 that measures how likely an event is. This calculator covers the basic rules: the classical probability of an event when outcomes are equally likely, the complement, the addition rule for A or B with the overlap removed, and the conditional probability of A given B. Each formula is shown next to its numbers.
Most probability mistakes come from picking the wrong rule. Use the counting formula only when outcomes are equally likely, and multiply probabilities only when the events are independent. The addition rule removes the overlap so it is not counted twice. 100% free, no registration, and complete privacy — everything runs locally in your browser, so your data never touches a server.
P = favourable / total, for equally likely outcomes such as a fair die or a shuffled deck.
P(not A) = 1 − P(A), which is often easier than counting the other outcomes.
P(A or B) = P(A) + P(B) − P(A and B). The overlap is subtracted once.
P(A | B) = P(A and B) / P(B), for a question that starts with 'given that'.
Exact nPr, nCr, factorials and counts with repetition.
Exact and cumulative probabilities for k successes in n trials.
Roll two dice and compare the sums with the exact probabilities.
Z score, percentile and probabilities between two values.
A or B is true when at least one event happens, so P(A or B) can be larger than either probability. A and B needs both, so P(A and B) is never larger than either one. The addition rule links them: P(A or B) = P(A) + P(B) − P(A and B).
Multiply only when the events are independent, meaning knowing one happened does not change the chance of the other. Two fair coin flips are independent, so P(two heads) = 0.5 × 0.5 = 0.25. Two cards drawn without replacement are not.
It is the probability of A once you know B has happened, computed as P(A and B) divided by P(B). In general P(A given B) and P(B given A) are different, so the order of the events matters.
An event and its complement cover every possible outcome exactly once. Their probabilities therefore add to 1, which gives P(not A) = 1 − P(A) directly.
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