Although there are many different situations involving randomness, it is convenient to use a general terminology that can cover them all.

Definition

Experiment
A phenomenon whose result is uncertain will be called an experiment.
Outcomes
An outcome is the result of an experiment that cannot be reduced to simpler results.
Events
An event is a collection of outcomes.
Sample space
The sample space is the collection of all possible outcomes.

Links to set theory

These definitions are closely associated with set theory. Although the ideas behind probability can be understood without it, a formal definition of probability and its rules uses set theory. The following table links probability notation with set theory:

Probability notation Set theory notation
Sample space, S Universal set
Outcome Element
Event, E Subset

Set operations

In set theory, unions and intersections of sets are basic operations. These operations also correspond to meaningful ways to define events from others. Consider two events A and B.

Probability notation Set theory notation Interpretation
A or B A ∪ B Either A or B (or both) occurs
A and B A ∩ B Both A and B occur
not A Ac Event A does not occur