# Probability

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**Probability** is a subtle concept that is typically defined in terms of the relative frequency of occurrence of an event, or the degree of belief that the event will occur (or that a statement is true, etc.).

- Elementary probability
- Sometimes introduced in primary school mathematics classes, the first serious study of the subject is usually undertaken in secondary school or university level courses
- Probability theory
- Formal, axiomatic study at the university level, based on real analysis and especially measure theory.

## Major topics

Probability |
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- Interpretations of probability
- Frequentist approach (based on aleatory probability, empirical probability)
- Bayesian approach (based on epistemic probabilty)

- Definitions of probability
- Probability (relative frequency)
- Axioms of probability (or Probability axioms, a.k.a. Kolmogorov axioms)
- Cox's theorem
- Confidence and certainty

- Odds, expected value and outcome, fair and unfair games
- Properties of probability
- Discrete probability versus continuous probability
- Combinatorics and advanced counting
- Sets, set theory and cardinality
- Combination and permutation

- Weighted probability
- Probability distribution functions
- Probability density functions
- Cumulative distribution functions
- Conditional probability and mutually exclusive events
- Classical probability and statistics
- Probability and statistics

See Wikipedia:Probability for more information.