Probability - Concepts

The word probability derives from the Latin probare (to prove, or to test). Informally, probable is one of several words applied to uncertain events or knowledge, being more or less interchangeable with likely, risky, hazardous, uncertain, and doubtful, depending on the context. Chance, odds, and bet are other words expressing similar notions. As with the theory of mechanics which assigns precise definitions to such everyday terms as work and force< ...

Including:

• Probability - Historical remarks
• Probability - Concepts
• Probability - Formalization of probability
• Probability - Representation and interpretation of probability values
• Probability - Distributions
• Probability - Probability in mathematics
• Probability - Remarks on probability calculations
• Probability - Applications of probability theory to everyday life
• Probability - Quotations

Read more here: » Probability: Encyclopedia - Probability

There is essentially one set of mathematical rules for manipulating probability; these rules are listed under "Formalization of probability" below. (There are other rules for quantifying uncertainty, such as the Dempster-Shafer theory and possibility theory, but those are essentially different and not compatible with the laws of probability as they are usually understood.) However, there is ongoing debate over what, exactly, the rules apply to; this is t ...

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Probability, Probability - Historical remarks, Probability - Concepts, Probability - Formalization of probability, Probability - Representation and interpretation of probability values, Probability - Distributions, Probability - Probability in mathematics, Probability - Remarks on probability calculations, Probability - Applications of probability theory to everyday life, Probability - Quotations

Read more here: » Probability: Encyclopedia II - Probability - Concepts

The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions of use in those problems only arose much later. The doctrine of probabilities dates to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaan Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's Doctrine of Chances (171 ...

See also:

Probability, Probability - Historical remarks, Probability - Concepts, Probability - Formalization of probability, Probability - Representation and interpretation of probability values, Probability - Distributions, Probability - Probability in mathematics, Probability - Remarks on probability calculations, Probability - Applications of probability theory to everyday life, Probability - Quotations

Read more here: » Probability: Encyclopedia II - Probability - Historical remarks

Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms—that is, in terms that can be considered separately from their meaning. These formal terms are manipulated by the rules of mathematics and logic, and any results are then interpreted or translated back into the problem domain. There have been at least two successful attempts to formalize probability, namely the Kolmogorov formulation and the Cox formulation. In Kolmogorov's formulation, sets are interpreted as events and prob ...

See also:

Probability, Probability - Historical remarks, Probability - Concepts, Probability - Formalization of probability, Probability - Representation and interpretation of probability values, Probability - Distributions, Probability - Probability in mathematics, Probability - Remarks on probability calculations, Probability - Applications of probability theory to everyday life, Probability - Quotations

Read more here: » Probability: Encyclopedia II - Probability - Formalization of probability

Two major applications of probability theory in everyday life are in risk assessment and in trade on commodity markets. Governments typically apply probability methods in environmental regulation where it is called "pathway analysis", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on statistical analyses of their probable effect on the population as a whole. It is not correct to say that statistics are involved in the modelling itself, as typically the assessments of r ...

See also:

Probability, Probability - Historical remarks, Probability - Concepts, Probability - Formalization of probability, Probability - Representation and interpretation of probability values, Probability - Distributions, Probability - Probability in mathematics, Probability - Remarks on probability calculations, Probability - Applications of probability theory to everyday life, Probability - Quotations

Read more here: » Probability: Encyclopedia II - Probability - Applications of probability theory to everyday life

Probability axioms form the basis for mathematical probability theory. Calculation of probabilities can often be determined using combinatorics or by applying the axioms directly. Probability applications include even more than statistics, which is usually based on the idea of probability distributions and the central limit theorem. To give a mathematical meaning to probability, consider flipping a "fair" coin. Intuitively, the probability that heads will come up on any given coin toss is "obviously" 50%; but this statement alone lack ...

See also:

Probability, Probability - Historical remarks, Probability - Concepts, Probability - Formalization of probability, Probability - Representation and interpretation of probability values, Probability - Distributions, Probability - Probability in mathematics, Probability - Remarks on probability calculations, Probability - Applications of probability theory to everyday life, Probability - Quotations

Read more here: » Probability: Encyclopedia II - Probability - Probability in mathematics

Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms -- that is, in terms that can be considered separately from their meaning. These formal terms are manipulated by the rules of mathematics and logic, and any results are then interpreted or translated back into the problem domain. There have been at least two successful attempts to formalize probability, namely the Kolmogorov formulation and the Cox formulation. In Kolmogorov's formulation, sets are interpreted as events and pro ...

See also:

Probability, Probability - Historical remarks, Probability - Concepts, Probability - Formalization of probability, Probability - Representation and interpretation of probability values, Probability - Distributions, Probability - Probability in mathematics, Probability - Remarks on probability calculations, Probability - Applications of probability theory to everyday life, Probability - Quotations

Read more here: » Probability: Encyclopedia II - Probability - Formalization of probability

A major effect of probability theory on everyday life is in risk assessment and in trade on commodity markets. Governments typically apply probability methods in environment regulation where it is called "pathway analysis", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on their perceived probable effect on the population as a whole, statistically. It is not correct to say that statistics are involved in the modelling itself, as typically the assessments of risk are on ...

See also:

Probability, Probability - Historical remarks, Probability - Concepts, Probability - Formalization of probability, Probability - Representation and interpretation of probability values, Probability - Distributions, Probability - Probability in mathematics, Probability - Remarks on probability calculations, Probability - Applications of probability theory to everyday life, Probability - Quotations

Read more here: » Probability: Encyclopedia II - Probability - Applications of probability theory to everyday life