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complementary event
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complementary event

probability theory
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In probability theory, a complementary event refers to the outcomes of an experiment that are not in a specific event. If an event is denoted as A, its complementary event is Ac. The sum of the probabilities of an event and its complement always equals 1, meaning P(A) + P(Ac) = 1. This is a fundamental principle derived from the idea that an event either occurs or it does not. For example, if you are flipping a coin, the event of getting heads has a complementary event of not getting heads (which means getting tails). The probability of getting heads plus the probability of getting tails equals 1. This concept is crucial for calculating probabilities, especially when it's easier to find the probability of the complementary event.1

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2 Britannica Sources
  1. probability theory - The principle of additivity
  2. probability theory - Independence

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