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Inside probability theory, an event is a set of outcomes (the subset of the sample space) to which a probability is assigned. Generally, any subset of the sample space is an event (i.e. everthing elements of the power set of the sample space are cases), however after defining the probability space it is possible to exclude certain subsets of the sample space from either existence cases (view §2, in the image below).
A simple example
Whenever i assemble the deck of 52 playing cards & two jokers, and draw one card from either a deck, so a sample space occurs when 54-element placed, as apiece single card occurs as imaginable effect. An event, still, is any subset of the sample space, including any lone-element set (an elementary event, of which there are 54, representing a 54 conceivable cards drawn from either a deck), the empty set (which is defined to keep close at hand probability zero) & a entire placed of 54 cards, a sample space itself (which is defined to have probability a single). More cases come sets come proper subsets of the sample space that contain multiple elements. Thus, e.g., likely cases include:
"Red and black at the same time without being a joker" (Cipher elements),
"The 5 of Hearts" (Unity element),
"A King" (Quartet elements),
"A Face card" (Dozen elements),
"A Spade" (Baker's dozen elements),
"A Face card or a red suit" (32 elements),
"A card" (54 elements).
Since 100% cases come sets, it is unremarkably written when sets (e.g. ), & delineated graphically applying Venn diagrams. Venn diagrams come particularly utile for representing cases because a probability of a event may be identified by having a ratio of the region of the event & the metropolitan area of the sample space. (Indeed, every of the axioms of probability, and a definition of conditional probability can be represented in this fashion.)
of an event. B is the sample space & The is an event.
Per ratio of their areas, a probability of The is roughly Nought.Little joe.
Events in probability spaces
In the measure-theoretic description of probability spaces, an event may be defined as an element of the σ-algebra on the sample space. Note, still, that under this definition, any subset of the sample space that is non an element of the σ-algebra is non technically an event, & doesn't have a probability. Any confusion can exist as resolved by looking for any subset of a sample space to be an event, but only the elements of the σ-algebra to exist as cases of interest.
category:probability theory
de:Ereignis (Wahrscheinlichkeitstheorie)
fr:Événement (mathématiques)
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