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