# Are the terms “event” and “outcome” synonymous?

An outcome is a result of a random experiment and an event is a single result of an experiment.

Are the terms "event" and "outcome" synonymous?

Outcome and event are not synonymous.

Yes, an outcome is the result of a random experiment, like a rolling a die has six possible outcomes (say). However, an "event" is a set of outcomes to which a probability is assigned. One possible event is "rolling a number less than 3". See the Wikipedia page for probability theory and probability space for better descriptions.

• Hello @NeilG, is it correct to say that the term outcome is synonymous of sample point? – Gennaro Arguzzi Jul 21 '19 at 10:18

I would say that an outcome is an elementary event (atomic event or simple event). A set of outcomes or elementary events is an event.

• An outcome is not an event in some sigma-algebras. For example, with $\Omega = \{1,2,3,4\}$, consider the sigma-algebra $$\big\{\emptyset, \{1,2\}, \{3,4\}, \Omega\big\}$$ in which individual outcomes are not events. – Dilip Sarwate Mar 26 '15 at 13:38
• I wrote that outcomes are elementary events. – stochazesthai Mar 26 '15 at 13:39
• Yes, but even that statement implies that an outcome is an event, that is, a member of the sigma-algebra; which it is not. – Dilip Sarwate Mar 26 '15 at 13:41
• But still elementary event is established terminology, maybe unfortunate, since your examples shows that an elementary event is not always an event! Still, this is terminology mainly used in elementary courses, where no problems are caused by it. – kjetil b halvorsen Sep 27 '16 at 10:04
• Even an elementary event is a set, a singleton, not an outcome. The referenced Wikipedia article is careful to maintain this distinction. – Scortchi - Reinstate Monica May 23 '17 at 11:25

I would like to cite a section from the Wikipedia article on Outcome, which I think well summarises the relation between these terms

Since individual outcomes may be of little practical interest, or because there may be prohibitively (even infinitely) many of them, outcomes are grouped into sets of outcomes that satisfy some condition, which are called "events". The collection of all such events is a sigma-algebra.

An event containing exactly one outcome is called an elementary event. The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events.

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). However, this approach does not work well in cases where the sample space is uncountably infinite (most notably when the outcome must be some 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.

Event is a subset of Outcomes in the Sample Space.
Possibly, a single result of an experiment too. Lets say,

• Experiment : Rolling a Die

• Outcomes : S = {1,2,3,4,5,6}

• Event : All positive numbered faces e = {2,4,6}
• I think this is fine as an elementary exposition - definitely for high school level students, this is a good way to explain it. Much beyond that and one needs to start talking about sigma algebras etc. I think I might suggest you rephrase the answer slightly: you should probably make it clear that in the "Outcomes" bullet point, each of the 1, 2, 3 ... etc is an outcome, whereas in the "Event" bullet point, it is the set {2, 4, 6} which is the event. At the moment this distinction is not clear. – Silverfish Sep 27 '16 at 10:13