# probability

- The mathematics of probability is well understood. Probability is a non-negative, additive set function whose maximum value is unity. What is harder to understand is the application of the formal notion to the actual world. One point of application is statistical: when kinds of event or trials (such as the tossing of a coin) can be described, and the frequency of occurrence of particular outcomes (such as the coin falling heads) is measurable, then we can begin to think of the probability of that kind of outcome in that kind of trial. One account of probability is therefore the frequency theory, associated with Venn and Richard von Mises (1883–1953), that identifies the probability of an event with such a frequency of occurrence. A second point of application is the description of an hypothesis as probable when the evidence bears a favoured relationship to it. If this relation is conceived of as purely logical in nature, as in the work of Keynes and Carnap, probability statements are not empirical measures of frequencies, but represent something like ‘partial entailments’ or measures of possibilities left open by the evidence and by the hypothesis. Formal confirmation theories and range theories of probability are developments of this idea. The third point of application is in the use probability judgements have in regulating the confidence with which we hold various expectations. The approach sometimes called subjectivism, but more commonly known as personalism, associated with de Finetti and Ramsey, sees probability judgements as expressions of a subject's degree of confidence in an event or kind of event, and attempts to describe constraints on the way we should have degrees of confidence in different judgements that explain those judgements having the mathematical form of judgements of probability (see Dutch book, exchangeability, representation theorem ). For personalism, probability or chance is not an objective or real factor in the world, but rather a reflection of our own states of mind. However, those states of mind need to be governed by empirical frequencies, so personalism is not an invitation to licentious thinking.

*Philosophy dictionary.
Academic.
2011.*

**Synonyms**:

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**Probability**— is the likelihood or chance that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the… … Wikipedia**probability**— ► NOUN (pl. probabilities) 1) the extent to which something is probable. 2) a probable or most probable event. ● in all probability Cf. ↑in all probability … English terms dictionary**Probability**— Prob a*bil i*ty, n.; pl. {Probabilities}. [L. probabilitas: cf. F. probabilit[ e].] [1913 Webster] 1. The quality or state of being probable; appearance of reality or truth; reasonable ground of presumption; likelihood. [1913 Webster] Probability … The Collaborative International Dictionary of English**probability**— probability, probability distribution See distribution (statistical or frequency)}} ; sampling ; significance tests ; … Dictionary of sociology**probability**— [präb΄ə bil′ə tē] n. pl. probabilities [MFr probabilité < L probabilitas] 1. the quality or state of being probable; likelihood 2. something probable 3. Math. the ratio of the number of times something will probably occur to the total number… … English World dictionary**probability**— I noun anticipation, appearance of truth, believability, chance, conceivability, credibility, credibleness, expectation, fair chance, fair expectation, favorable chance, liability, liableness, likelihood, likeliness, odds, ostensibility,… … Law dictionary**Probability**— [engl.], Wahrscheinlichkeit … Universal-Lexikon**probability**— (n.) mid 15c., quality of being probable, from O.Fr. probabilite (14c.) and directly from L. probabilitatem (nom. probabilitas), from probabilis (see PROBABLE (Cf. probable)). Meaning вЂњsomething likely to be trueвЂќ is from 1570s; mathematical… … Etymology dictionary**probability**— [n] likelihood of something happening anticipation, chance, chances, conceivability, contingency, credibility, expectation, feasibility, hazard, liability, likeliness, odds, outside chance*, plausibility, possibility, practicability, prayer,… … New thesaurus**probability**— noun ADJECTIVE ▪ high, real, strong ▪ There is a high probability that it will snow tonight. ▪ greater, increased ▪ low … Collocations dictionary