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Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.
In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the ...
Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
Probability theory is the part of mathematics that studies random situations. [1][2][3][4][5][6] Probability theory usually studies random events, random variables, stochastic processes, and non-deterministic events (events that do not follow a simple pattern).
The probability of a specified event is the chance or likelihood that it will occur. There are several ways of viewing probability. One would be experimental in nature, where we repeatedly conduct an experiment.
A probability is a number that represents the likelihood of an uncertain event. Probabilities are always between 0 and 1, inclusive. The larger the probability, the more likely the event is to happen.
In the Frequency Theory of Probability, probability is the limit of the relative frequency with which certain outcomes occur in repeated trials (note that the outcome of any single trial cannot depend on the outcome of other trials).
In probability theory, the basic, specific concept is that of independence of events, trials and random variables. Moreover, probability theory comprises a thorough study of subjects such as probability distributions, conditional mathematical expectations, etc.
The mathematical sense of the term is from 1718. In the 18th century, the term chance was also used in the mathematical sense of "probability" (and probability theory was called Doctrine of Chances). This word is ultimately from Latin cadentia, i.e. "a fall, case".