Editing Event (probability theory) (section)

==A simple example==

If we assemble a deck of 52 [[playing card]]s with no jokers, and draw a single card from the deck, then the sample space is a 52-element set, as each card is a possible outcome.  An event, however, is any subset of the sample space, including any [[singleton set]] (an [[elementary event]]), the [[empty set]] (an impossible event, with probability zero) and the sample space itself (a certain event, with probability one).  Other events are [[proper subset]]s of the sample space that contain multiple elements.  So, for example, potential events include:  
[[Image:Venn A subset B.svg|thumb|150px|An [[Euler diagram]] of an event. <math>B</math> is the sample space and <math>A</math> is an event.<br>By the ratio of their areas, the probability of <math>A</math> 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 (for example, {1, 2, 3}), and represented graphically using [[Venn diagram]]s. In the situation where each outcome in the sample space Ω is equally likely, the probability <math>P</math> of an event <math>A</math> is the following {{visible anchor|formula}}:
<math display=block>\mathrm{P}(A) = \frac{|A|}{|\Omega|}\,\ \left( \text{alternatively:}\ \Pr(A) = \frac{|A|}{|\Omega|}\right)</math>
This rule can readily be applied to each of the example events above.