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Example:List Outcomes of an Event

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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).(Our solved example in mathguru.com uses this concept)

However, this approach does not work well in cases where the sample space is uncountably infinite, most notably when the outcome is a real number. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events.


A simple example

If we assemble a deck of 52 playing cards 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. (Our solved example in mathguru.com uses this concept)

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 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.

1.  "Red and black at the same time without being a joker" (0 elements),

2.  "The 5 of Hearts" (1 element),

3.  "A King" (4 elements),

4.  "A Face card" (12 elements),

5.  "A Spade" (13 elements),

6.  "A Face card or a red suit" (32 elements),

7.  "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. Given that each outcome in the sample space Ω is equally likely, the probability of an event A is






The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.