Probability

Probability is a mathematical measure of uncertainty, assigning events values from 0 to 1. It supports reasoning about chance, evidence, and uncertain outcomes.

Sample space: The set of all possible outcomes of a random experiment. Events are subsets of this outcome set, which determines the probabilities being assigned.
Kolmogorov axioms: The three axioms that formalize probability measures on a sample space. They provide the mathematical rules that every probability assignment must satisfy.
Gambling: The staking of money or valuables on outcomes involving chance or uncertain judgment. Questions about fair wagers prompted early mathematical work on chance.
Bayesian probability: An interpretation of probability as a coherent degree of belief, updated using Bayes' theorem. It treats probabilities as rational uncertainty assessments rather than only long-run frequencies.
Event (probability theory): A set of outcomes of a random experiment to which a probability can be assigned. Probability measures the chance that outcomes in an event occur.
Addition rule for probability: A rule for finding the probability that at least one of two events occurs. It combines event probabilities while accounting for outcomes they share.
Blaise Pascal: A French mathematician, physicist, and philosopher who helped found probability theory. His correspondence with Pierre de Fermat analyzed how to divide stakes in an interrupted game.
Classical probability: An approach assigning equal probability to outcomes when a finite set of outcomes is considered symmetric. It gives a simple route to probabilities but depends on a defensible notion of equally likely outcomes.
Random variable: A function that assigns a numerical value to each outcome in a sample space. Random variables turn uncertain outcomes into quantities whose distributions can be studied.
Bayes' theorem: A theorem relating conditional probabilities in opposite directions. It revises probabilities for hypotheses after evidence is observed.

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