Pronunciation: /ɪˈvɛnt/ ?

In probability, an event is something that happens. We can measure, calculate, or estimate the probability of the outcomes of this event. An event is a subset of a sample space.

For example, when flipping two coins, there are four possible outcomes: Heads and heads (HH), heads and tails (HT), or tails and tails (TT). If the event is 'at least one tail', then two of the outcomes are included in the event.

A certain event is an event that will always happen. The probability of a certain event is P(e) = 1. An impossible event is an event that will never occur. The probability of an impossible event is P(e) = 0.

Complementary Events

In probability, complementary events are two or more events where the outcome must be exactly one of the events. For example, when flipping a coin, the outcome must be either heads or tails. Since you can get either a head or a tail but not both a head and a tail on the same flip, the events are complementary.

When rolling a dice, the events of rolling a 1 and rolling a 2 are not complementary. The events of rolling a 3, 4, 5, or 6 can occur, so rolling a 1 and 2 are not all of the events that can occur. For people, the events of hair color and gender (male or female) are not complementary. Males and females can both have any color hair, so the events male and blonde overlap.

Examples of Events
ExperimentSample SpaceEventNumber of Elements
Tossing three coins.HHH, HHT, HTT, TTTExactly two heads1: HHT
Drawing a card from a 52 card deck.A, 2, 3, 4, 5, 6, 7, 8, 9, J, Q, KDrawing a king.4: There are 4 kings in a 52 card deck.
Selecting 4 people at random.F=female, M=male; FFFF, FFFM, FFMM, FMMM, MMMMSelecting at least three males.2: FMMM, MMMM.
Table 1


  1. event. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=event&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Grinstead, Charles M. and Snell, J. Laurie. Introduction to Probability, pg 18. (Accessed: 2010-01-12). http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf.
  3. Goldberg, Samuel. Probability, An Introduction, pp 51-64. Prentice Hall, 1960. (Accessed: 2010-01-16). http://www.archive.org/stream/probailityanintr000991mbp#page/n62/modehttp://www.archive.org/stream/probailityanintr000991mbp#page/n68/mode/1up/1up.
  4. Ross, Sheldon. A First Course in Probability, 6th, Low Price edition, pg 25. Pearson Education, 2002.

More Information

  • McAdams, David. Probability subjects. lifeisastoryproblem.com. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.com/probability/index.html.

Printed Resources

Cite this article as:

Event. 2010-02-01. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/event.html.


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Revision History

2010-02-01: Added "References" (McAdams, David.)
2009-01-06: Added mathworld to 'More Information', expanded examples (McAdams, David.)
2009-01-04: Expanded 'More Information' (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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