The word __probability__ is used in a variety of ways since it was first applied as a mathematical concept. Does probability measure the frequency to which something occurs or how strongly one believes it will occur, or both? the simple answer is both, which leads to much debate by professionals. However, riskmaticians apply both definitions in practice

**Fuentist probability** or **frequentism** is an __interpretation of probability__; it defines an event's __probability__ as the __limit__ of its relative __frequency__ in a large number of trials. This interpretation supports the statistical needs of experimental scientists and pollsters; probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). It does not support all needs; gamblers typically require estimates of the odds without experiments. The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the __classical interpretation__. In the classical interpretation, probability was defined in terms of the __principle of indifference__, based on the natural symmetry of a problem, so, *e.g.* the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. This classical interpretation stumbled at any statistical problem that has no natural symmetry for reasoning.

**Bayesian probability** is an __interpretation of the concept of probability__, in which, instead of __frequency__ or __propensity__ of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of __propositional logic__ that enables reasoning with hypotheses, i.e., the propositions whose __truth or falsity__ is uncertain. In the Bayesian view, a probability is assigned to a hypothesis, whereas under __frequentist inference__, a hypothesis is typically tested without being assigned a probability.

Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies some __prior probability__, which is then updated to a __posterior probability__ in the light of new, relevant __data__ (evidence).__[4]__ The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation. The term *Bayesian* derives from the 18th century mathematician and theologian __Thomas Bayes__, who provided the first mathematical treatment of a non-trivial problem of statistical __data analysis__ using what is now known as __Bayesian inference__.__[5]__:131 Mathematician __Pierre-Simon Laplace__ pioneered and popularised what is now called Bayesian probability.