🎲Probability Calculator

About this tool

Choose two events or repeated trials. For two events, enter P(A) and P(B) as decimals, percentages or fractions and say whether they are independent, mutually exclusive or dependent; the table shows every combination with its formula. For repeated trials, enter the chance of success, the number of trials and a number of successes to get the chance of at least one, none, exactly k, at most k and at least k.

How to combine probabilities

Probabilities run from 0, impossible, to 1, certain. The chance an event doesn't happen is 1 minus the chance it does. For independent events, where one doesn't affect the other, the chance of both is the product: P(A and B) = P(A) × P(B). The chance of either is P(A) + P(B) − P(A and B), subtracting the overlap so it isn't counted twice. With P(A) = 0.5 and P(B) = 0.4, both happen with probability 0.2 and at least one with 0.7. Mutually exclusive events, such as rolling a 2 and a 5 on one die, can't happen together, so the overlap is zero. For dependent events, you need the conditional probability P(B | A), the chance of B once A has happened. Repeated independent trials follow the binomial distribution. The chance of at least one success in n tries is 1 − (1 − p)ⁿ, so rolling at least one six in ten rolls is 1 − (5/6)¹⁰ ≈ 83.85%, and exactly two sixes is about 29.07%. Honest limits: these rules assume you've correctly judged whether events are independent, and real-world events are often linked. Probabilities also describe long-run frequencies, not guarantees for a single try. The dice roller and the coin flipper let you test the odds, and the permutation and combination calculator counts outcomes. Dice probability explained: why 7 is the most common roll, and how to work out any odds and Is a coin flip really 50/50? go deeper.

Frequently asked questions