Complement Probability Calculator

About this calculator

The complement rule is one of the most useful shortcuts in probability theory: the probability that an event does not happen is simply 1 minus the probability that it does, written P(A′) = 1 − P(A). It works because an event and its complement together cover every possible outcome, so their probabilities must add up to exactly 1.

This rule earns its keep on “at least one” problems, which are notoriously hard to compute directly but easy through the complement. Insurers and actuaries use it to find the probability of at least one claim across a policy pool by first computing the (much simpler) probability of zero claims and subtracting from 1. Quality-control engineers use the same trick to estimate the odds that at least one component in a batch fails, and gamblers and game designers use it to compute the odds of not rolling a particular number across several dice throws.

Enter the probability of the event happening, and this calculator returns the complementary probability that it does not — the two numbers you’d otherwise have to compute by hand and double-check add up to 1.