Event

Pronunciation: /ɪˈvɛnt/ Explain

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

Experiment	Sample Space	Event	Number of Elements
Tossing three coins.	HHH, HHT, HTT, TTT	Exactly two heads	1: HHT
Drawing a card from a 52 card deck.	A, 2, 3, 4, 5, 6, 7, 8, 9, J, Q, K	Drawing 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, MMMM	Selecting at least three males.	2: FMMM, MMMM.
Table 1

References

1. McAdams, David E.. All Math Words Dictionary, event. 2nd Classroom edition 20150108-4799968. pg 74. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Grinstead, Charles M. and Snell, J. Laurie. Introduction to Probability. pg 18. Last Accessed 7/9/2018. http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf. Buy the book
3. Goldberg, Samuel. Probability, An Introduction. pp 51-64. www.archive.org. Prentice Hall. 1960. Last Accessed 7/9/2018. http://www.archive.org/stream/probailityanintr000991mbp#page/n62/modehttp://www.archive.org/stream/probailityanintr000991mbp#page/n68/mode/1up/1up. Buy the book
4. Ross, Sheldon. A First Course in Probability. 6th edition. pg 25. Pearson Education. 2002. Last Accessed 7/9/2018. Buy the book

More Information

• McAdams, David E.. Probability subjects. lifeisastoryproblem.com. Life is a Story Problem LLC. 3/12/2009. http://www.lifeisastoryproblem.com/probability/index.html.

Cite this article as:

McAdams, David E. Event. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/event.html.

Revision History

4/20/2019: Updated expressions and equations to match new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/1/2010: Added "References". (McAdams, David E.)
1/6/2009: Added mathworld to 'More Information', expanded examples. (McAdams, David E.)
1/4/2009: Expanded 'More Information'. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)