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Probability is the branch of mathematics and statistics 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] This number is often expressed as a percentage (%), ranging from 0% to ...
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 .
A probability distribution can either be univariate or multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution ) gives the probabilities of a random vector —a set of two or more random variables—taking on ...
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
Probability and statistics are two closely related fields in mathematics that are sometimes combined for academic purposes. [1] They are covered in multiple articles and lists: Probability; Statistics; Glossary of probability and statistics; Notation in probability and statistics; Timeline of probability and statistics
In probability theory, an event is a subset 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]
When probability is expressed as a number between 0 and 1, the relationships between probability p and odds are as follows. Note that if probability is to be expressed as a percentage these probability values should be multiplied by 100%. " X in Y" means that the probability is p = X / Y. " X to Y in favor" means that the probability is p = X ...
The classical definition of probability assigns equal probabilities to events based on physical symmetry which is natural for coins, cards and dice. Some mathematicians object that the definition is circular. [11] The probability for a "fair" coin is... A "fair" coin is defined by a probability of... The definition is very limited.