Probability is a mathematical framework for measuring uncertainty and quantifying the likelihood of events occurring. The sample space represents all possible outcomes of an experiment, while an event is any subset of these outcomes. For example, when flipping a coin, the sample space contains heads and tails, and getting heads is one possible event. The basic probability formula states that the probability of an event equals the number of favorable outcomes divided by the total number of possible outcomes.
Probability theory is built on three fundamental axioms. First, non-negativity states that probabilities are never negative. Second, normalization requires that the probability of the entire sample space equals one. Third, additivity means that for mutually exclusive events, the probability of their union equals the sum of their individual probabilities. The complement rule states that the probability of an event not occurring equals one minus the probability of it occurring. These rules form the mathematical foundation for all probability calculations.