# Sample space

**event spacespacerepresented by pointssample spaces**

In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.wikipedia

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### Probability theory

**theory of probabilityprobabilityprobability theorist**

In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.

Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

### Experiment (probability theory)

**experimentrandom experimentrandom experiments**

In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.

In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space.

### Outcome (probability)

**outcomeoutcomesequally likely outcomes**

In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.

All of the possible outcomes of an experiment form the elements of a sample space.

### Event (probability theory)

**eventeventsrandom event**

A subset of the sample space is an event, denoted by E. Referring to the experiment of tossing the coin, the possible events include E={H} and E={T}. A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

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.

### Probability space

**probability measuresGaussian measureoutcomes**

A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

### Sigma-algebra

**σ-algebraσ-algebrasigma algebra**

A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

This means the sample space Ω must consist of all possible infinite sequences of H or T:

### Space (mathematics)

**spacemathematical spacespaces**

### Trial and error

**trial-and-errorgenerate and test trial and error principle**

### Set (mathematics)

**setsetsmathematical set**

### Set notation

**notational motivationsthe broader class of means of denoting sets**

A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set.

### Element (mathematics)

**elementelementsset membership**

A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set.

### Universe (mathematics)

**universeuniversal setdomain**

It is common to refer to a sample space by the labels S, Ω, or U (for "universal set").

### Dice

**dieDice rollingpolyhedral dice**

For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).

### Probability

**probabilisticprobabilitieschance**

A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

### Probability measure

**measureprobability distributionlaw**

### Abstraction

**abstractabstract thinkingabstractions**

### Playing card

**playing cardscardscard**

For example, when drawing a card from a standard deck of fifty-two playing cards, one possibility for the sample space could be the various ranks (Ace through King), while another could be the suits (clubs, diamonds, hearts, or spades).

### Playing card suit

**suitsuitscard suit**

For example, when drawing a card from a standard deck of fifty-two playing cards, one possibility for the sample space could be the various ranks (Ace through King), while another could be the suits (clubs, diamonds, hearts, or spades).

### Cartesian product

**productCartesian squareCartesian power**

A more complete description of outcomes, however, could specify both the denomination and the suit, and a sample space describing each individual card can be constructed as the Cartesian product of the two sample spaces noted above (this space would contain fifty-two equally likely outcomes).

### Drawing pin

**thumbtackthumbtacksthumb tack**

However, there are experiments that are not easily described by a sample space of equally likely outcomes—for example, if one were to toss a thumb tack many times and observe whether it landed with its point upward or downward, there is no symmetry to suggest that the two outcomes should be equally likely.

### Statistics

**statisticalstatistical analysisstatistician**

In statistics, inferences are made about characteristics of a population by studying a sample of that population's individuals.

### Statistical population

**populationsubpopulationsubpopulations**

In statistics, inferences are made about characteristics of a population by studying a sample of that population's individuals.

### Sample (statistics)

**samplesamplesstatistical sample**

In statistics, inferences are made about characteristics of a population by studying a sample of that population's individuals.

### Bias of an estimator

**unbiasedunbiased estimatorbias**

In order to arrive at a sample that presents an unbiased estimate of the true characteristics of the population, statisticians often seek to study a simple random sample—that is, a sample in which every individual in the population is equally likely to be included.