Probability Calculator

Probability measures uncertainty on a scale from zero to one. Zero represents an impossible event, one represents a certain event, and values between them describe different levels of chance. This calculator accepts the probabilities of two events and derives four commonly requested results: the complement of event A, the probability that both events occur, the probability that at least one occurs, and the probability that neither occurs. Results are also displayed as percentages for quick interpretation. The complement rule says that the probability of an event not occurring equals one minus its probability. For independent events, the multiplication rule gives the intersection: multiply P(A) by P(B) to find the chance that both occur. The addition rule finds the union. Add P(A) and P(B), then subtract their intersection so the shared outcome is not counted twice. The probability that neither event occurs is the product of both complements when events are independent. Independence is the key assumption behind these calculations. Two events are independent when learning that one occurred does not change the probability of the other. Separate fair coin tosses are a standard example. Weather and traffic delay may not be independent because rain can affect traffic. For dependent events, use a conditional probability such as P(B given A) when computing the intersection. The general multiplication rule is P(A and B) = P(A) times P(B given A), and the union still subtracts that intersection. Probabilities may come from equally likely outcomes, historical frequencies, a fitted statistical model, or informed judgment. Make sure both inputs use the same population and time frame. A probability is not a guarantee for one trial; it describes expected behavior across comparable repetitions. Rounded percentages can also hide small differences, so retain sufficient precision in formal work. This calculator is useful for classroom exercises, risk summaries, planning, and basic quality checks, but dependent events and complex sample spaces require a model that explicitly represents their relationship.