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In probability theory
Probability theory

Probability theory is the branch of mathematics concerned with analysis of Statistical randomness phenomena. The central objects of probability theory are random variables, stochastic processes, and event s: mathematical abstractions of determinism events or measured quantities that may either be single occurrences or evolve over time in an a...
, the sample space or universal sample space, often denoted S, O, or U (for "universe"), of an experiment
Experiment (probability theory)

An experiment is any procedure that can be infinitely repeated and has a well defined set of outcomes. Examples include tossing a coin or rolling a die....
 or random trial
Trial and error

Trial and error, or trial by error, is a general method of problem solving for obtaining knowledge, both propositional knowledge and know-how....
 is the set of all possible outcomes. For example, if the experiment is tossing a coin, the sample space is the set . For tossing a single six-sided die, the sample space is . For some kinds of experiments, there may be two or more plausible sample spaces available.






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In probability theory
Probability theory

Probability theory is the branch of mathematics concerned with analysis of Statistical randomness phenomena. The central objects of probability theory are random variables, stochastic processes, and event s: mathematical abstractions of determinism events or measured quantities that may either be single occurrences or evolve over time in an a...
, the sample space or universal sample space, often denoted S, O, or U (for "universe"), of an experiment
Experiment (probability theory)

An experiment is any procedure that can be infinitely repeated and has a well defined set of outcomes. Examples include tossing a coin or rolling a die....
 or random trial
Trial and error

Trial and error, or trial by error, is a general method of problem solving for obtaining knowledge, both propositional knowledge and know-how....
 is the set of all possible outcomes. For example, if the experiment is tossing a coin, the sample space is the set . For tossing a single six-sided die, the sample space is . For some kinds of experiments, there may be two or more plausible sample spaces available. For example, when drawing a card from a standard deck of 52 playing cards
Playing card

A playing card is a piece of specially prepared heavy paper, thin card, or thin plastic, figured with distinguishing motifs and used as one of a set for playing card games....
, one possibility for the sample space could be the rank (Ace through King), while another could be the suit
Suit (cards)

In playing cards, a suit is one of several categories into which the cards of a deck are divided. Most often, each card bears one of several symbols showing to which suit it belongs; the suit may alternatively or in addition be indicated by the color printed on the card....
 (clubs, diamonds, hearts, or spades). A complete description of outcomes, however, would specify both the denomination and the suit, and a sample space describing each individual card can be constructed as the Cartesian product
Cartesian product

In mathematics, the Cartesian product is a direct product of sets. The Cartesian product is named after Ren? Descartes, whose formulation of analytic geometry gave rise to this concept....
 of the two sample spaces noted above.

In an elementary approach to probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
, any subset of the sample space is usually called an event
Event (probability theory)

In probability theory, an event is a Set of outcomes to which a probability is assigned. Typically, when the sample space is finite, any subset of the sample space is an event ....
. However, this gives rise to problems when the sample space is infinite, so that a more precise definition of event is necessary. Under this definition only measurable
Measure (mathematics)

In mathematics, more specifically in measure theory, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset....
 subsets of the sample space, constituting a σ-algebra
Sigma-algebra

In mathematics, a s-algebra over a Set X is a nonempty collection S of subsets of X that is Closure under complement ation and countable union s of its members....
 over the sample space itself, are considered events. However, this has essentially only theoretical significance, since in general the σ-algebra can always be defined to include all subsets of interest in applications.

See also

Set
Set

A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics....
 Event (probability theory)
Event (probability theory)

In probability theory, an event is a Set of outcomes to which a probability is assigned. Typically, when the sample space is finite, any subset of the sample space is an event ....