Probability

The word probability derives from the Latin probare (to prove, or to test).

Concepts

There is essentially one set of mathematical rules for manipulating probability; these rules are listed under "Formalization of probability" below.

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(There are other rules for quantifying uncertainty,

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such as the Dempster-Shafer theory and possibility theory,

Related Topics:
Dempster-Shafer theory - Possibility theory

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but those are essentially different and not compatible with the laws of probability as they are usually understood.)

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However, there is ongoing debate over what, exactly, the rules apply to; this is the topic of probability interpretations.

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The general idea of probability is often divided into two related concepts:

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• Aleatory probability, which represents the likelihood of future events whose occurrence is governed by some random physical phenomenon. This concept can be further divided into physical phenomena that are predictable, in principle, with sufficient information (see Determinism), and phenomena which are essentially unpredictable. Examples of the first kind include tossing dice or spinning a roulette wheel, and an example of the second kind is radioactive decay.
• Epistemic probability, which represents our uncertainty about propositions when one lacks complete knowledge of causative circumstances. Such propositions may be about past or future events, but need not be. Some examples of epistemic probability are to assign a probability to the proposition that a proposed law of physics is true, and to determine how "probable" it is that a suspect committed a crime, based on the evidence presented.

It is an open question whether aleatory probability is reducible to epistemic probability based on our inability to precisely predict every force that might affect the roll of a die, or whether such uncertainties exist in the nature of reality itself, particularly in quantum phenomena governed by Heisenberg's uncertainty principle. Although the same mathematical rules apply regardless of which interpretation is chosen, the choice has major implications for the way in which probability is used to model the real world.

Related Topics:
Quantum - Uncertainty principle

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