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In probability theory, the sample space or universal sample space, often denoted S, Ω or U (for "universe"), of an experiment or random trial is the set of all possible outcomes. For example, if the experiment is tossing a coin, the sample space is the set {head, tail}. For tossing a single six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. 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, one possibility for the sample space could be the rank (Ace through King), while another could be the suit (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 of the two sample spaces noted above. Probability theory is the branch of mathematics concerned with analysis of random phenomena. ...
In the scientific method, an experiment (Latin: ex- periri, of (or from) trying) is a set of observations performed in the context of solving a particular problem or question, to support or falsify a hypothesis or research concerning phenomena. ...
Trial and error is a method for obtaining knowledge, both propositional knowledge and know-how. ...
For the Russian group of artists, see Jack of Diamonds (artists). ...
In mathematics, the Cartesian product is a direct product of sets. ...
In an elementary approach to probability, any subset of the sample space is usually called 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 subsets of the sample space, constituting a σ-algebra 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 interests in applications. Probability is the likelihood that something is the case or will happen. ...
In probability theory, an event is a set of outcomes (a subset of the sample space) to which a probability is assigned. ...
In mathematics the concept of a measure generalizes notions such as length, area, and volume (but not all of its applications have to do with physical sizes). ...
In mathematics, a σ-algebra (or σ-field) X over a set S is a family of subsets of S which is closed under countable set operations; σ-algebras are mainly used in order to define measures on S. The concept is important in mathematical analysis and probability theory. ...
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