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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]
A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often represented in notation by is the set of all possible outcomes of a random phenomenon being observed. The sample space may be any set: a set of real numbers, a set of descriptive labels, a set of vectors ...
The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same ...
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. Typically these axioms formalise probability in terms of a ...
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.
Probability theory. Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or ...
There are two broad categories [1] [2] of probability interpretations which can be called "physical" and "evidential" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms.
v. t. e. In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. [1] This particular method relies on event A occurring with some sort of relationship with another event B.