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Probability is a fundamental concept in mathematics that quantifies the likelihood of an event occurring. It is expressed as a number between 0 and 1, inclusive, where 0 indicates impossibility and 1 indicates certainty. A probability of 0.5 means an event has an equal chance of happening or not happening.

The study of probability has its roots in the analysis of games of chance, such as dice rolling and card games. It has since expanded to become an essential tool in numerous fields, including statistics, physics, engineering, economics, and computer science.

There are different approaches to defining and calculating probability. The classical definition applies when all outcomes are equally likely, such as in a fair coin toss. In this case, the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. The frequentist approach defines probability based on the observed frequency of an event in a large number of trials. A third perspective, the subjective approach, assigns probabilities based on personal belief or judgment.

Probability theory provides the framework for understanding and managing uncertainty. It is used to make predictions, assess risks, and draw conclusions from data. Key concepts within probability include random variables, probability distributions, and expected values.