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What is an event?

Module by: Arnold Mwesigye. E-mail the author

An event is a set of outcomes, a subset of the sample space, to which a probability is assigned. Typically, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are events), but when defining a probability space it is possible to exclude certain subsets of the sample space from being events.


If we assemble a deck of 52 playing cards and two jokers, and draw a single card from the deck, then the sample space is a 54-element set, as each individual card is a possible outcome. An event, however, is any subset of the sample space, including any single-element set (an elementary event, of which there are 54, representing the 54 possible cards drawn from the deck), the empty set (which is defined to have probability zero) and the entire set of 54 cards, the sample space itself (which is defined to have probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential events include:

"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" (54 elements).


Wikipedia. "Statistical Independence", Wikipedia Foundation Inc, "", Last accessed 17th February 2006.

Arnold Mwesigye

Petrina Mangala

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