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event: Definition, Synonyms and Much More from Answers.com

️Wed Jul 01 2015

A change or happening. The central debate in the philosophy of events is whether they are to be thought of as individuals, like objects, capable of date and place and capable of being described in different ways, or whether they are more like propositions or facts, whose identity depends essentially on the concepts in which they are framed. On the former model it may prove easier to understand how events can cause things, and how one event (e.g. a commotion in the brain) may be identical with another (e.g. being struck by a thought). The latter model assimilates events to facts, so that just as it can be a fact that the admiral did not arrive, his non-arrival can be a significant event (not at all a non-event) which may have its own causes and effects. Similarly there can exist disjunctive events (John's going to India or China) or quantificational events (Mary's finding a job, i.e. there being some job-finding by Mary).

Wikipedia: event (probability theory)

In probability theory, an event is a set of outcomes (a subset of the sample space) to which a probability is assigned. Typically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is infinite, most notably when the outcome is a real-valued random variable. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events (see §2, below).

A simple example

If we assemble a deck of 52 playing cards and no jokers, and draw a single card from the deck, then the sample space is a 52-element set, as each individual card is a possible outcome. An event, however, is any subset of the sample space, including any single-element set (an elementary event, of which there are 52, representing the 52 possible cards drawn from the deck), the empty set (which is defined to have probability zero) and the entire set of 52 cards, the sample space itself (which is defined to have probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential events include:

A Venn diagram of an event. B is the sample space and A is an event.
By the ratio of their areas, the probability of A is approximately 0.4.

"Red and black at the same time without being a joker" (0 elements),
"The 5 of Hearts" (1 element),
"A King" (4 elements),
"A Face card" (12 elements),
"A Spade" (13 elements),
"A Face card or a red suit" (32 elements),
"A card" (52 elements).

Since all events are sets, they are usually written as sets (e.g. {1, 2, 3}), and represented graphically using Venn diagrams. Venn diagrams are particularly useful for representing events because the probability of the event can be identified with the ratio of the area of the event and the area of the sample space. (Indeed, each of the axioms of probability, and the definition of conditional probability can be represented in this im so hot

Events in probability spaces

Defining all subsets of the sample space as events works well when there are only finitely many outcomes, but gives rise to problems when the sample space is infinite. For many standard probability distributions, such as the normal distribution the sample space is the set of real numbers or some subset of the real numbers. Attempts to define probabilities for all subsets of the real numbers run into difficulties when one considers 'badly-behaved' sets, such as those which are nonmeasurable. Hence, it is necessary to restrict attention to a more limited family of subsets. For the standard tools of probability theory, such as joint and conditional probabilities, to work, it is necessary to use a σ-algebra, that is, a family closed under countable unions and intersections. The most natural choice is the Borel measurable set derived from unions and intersections of intervals. However, the larger class of Lebesgue measurable sets proves more useful in practice.

In the general measure-theoretic description of probability spaces, an event may be defined as an element of a selected σ-algebra of subsets of the sample space. Under this definition, any subset of the sample space that is not an element of the σ-algebra is not an event, and does not have a probability. With a reasonable specification of the probability space, however, all events of interest will be elements of the σ-algebra.

event: Definition, Synonyms and Much More from Answers.com

A simple example

Events in probability spaces

See also