Branch of mathematics concerning chance and uncertainty
Not to be confused with probability theory, game theory, graph theory, or statistics.
For the mathematical field of probability specifically, see Probability theory. For other uses, see Probability (disambiguation).
Probability
Outline
Catalog of articles
Probabilists
Glossary
Notation
Journals
Category
Mathematics portal
v
t
e
Part of a series on statistics
Probability theory
Probability
Axioms
Determinism
System
Indeterminism
Randomness
Probability space
Sample space
Event
Collectively exhaustive events
Elementary event
Mutual exclusivity
Outcome
Singleton
Experiment
Bernoulli trial
Probability distribution
Bernoulli distribution
Binomial distribution
Exponential distribution
Normal distribution
Pareto distribution
Poisson distribution
Probability measure
Random variable
Bernoulli process
Continuous or discrete
Expected value
Variance
Markov chain
Observed value
Random walk
Stochastic process
Complementary event
Joint probability
Marginal probability
Conditional probability
Independence
Conditional independence
Law of total probability
Law of large numbers
Bayes' theorem
Boole's inequality
Venn diagram
Tree diagram
v
t
e
Part of a series on
Mathematics
History
Outline
Index
Areas
Number theory
Geometry
Algebra
Calculus and Analysis
Discrete mathematics
Logic and Set theory
Probability
Statistics and Decision theory
Relationship with sciences
Physics
Chemistry
Geosciences
Computation
Biology
Linguistics
Economics
Philosophy
Education
Mathematics Portal
v
t
e
The probabilities of rolling several numbers using two dice
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 two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.[3]
Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).
^"Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), ISBN 978-0-534-24312-8.
^William Feller, An Introduction to Probability Theory and Its Applications, vol. 1, 3rd ed., (1968), Wiley, ISBN 0-471-25708-7.
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...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different...
Bayesian probability (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is an interpretation of the concept of probability, in which, instead of frequency or...
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations...
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption...
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose...
the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands. Probability and...
A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence...
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number...
populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of...
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes...
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood...
In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the...
In Information theory, outage probability of a communication channel is the probability that a given information rate is not supported, because of variable...
Probability plot, a graphical technique for comparing two data sets, may refer to: P–P plot, "Probability-Probability" or "Percent-Percent" plot Q–Q plot...
In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable...
several articles: Probability Statistics Glossary of probability and statistics Notation in probability and statistics Timeline of probability and statistics...
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It...
In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square of the modulus of this quantity...
Probability function may refer to: Probability distribution Probability axioms, which define a probability function Probability measure, a real-valued...
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms...
In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct...
In probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number...
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure...
In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence...
stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event...
variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs...
In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing...
Global Information
Mathematics Portal