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Sample space

Any discussion of the probabilities of events begins with a precise definition of all the possible events. This is called the sample space, often denoted S or U (for "universe") of an experiment. It is the set of all possible outcomes of a single experimental trial. For example, if the experiment is tossing a coin, the sample space is the set {head, tail}. For tossing a single die, the sample space is {1, 2, 3, 4, 5, 6}.

Each element in the sample space is called an elementary event, while every subset of the sample space is called simply an event.

For some kinds of experiments, there may be two or more independent sample spaces available. For example, when drawing a card from a standard deck of 52 playing cards, one sample space could be the rank (Ace through King) and another could be the suit (clubs, diamonds, hearts, or spades). A complete description of an event would specify both the denomination and the suit. Such a sample space can be constructed as the Cartesian product of the two independent sample spaces.

Although the sample spaces are independent, some assignments of probabilities to points may lead to a circumstance in which the random variables thus defined are not describable as independent. Similarly, it is possible (but rare) that two events defined on the same sample space might be classified as independent.

See also : Probability

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