Introduction to Combined Events (College Board AP® Statistics) : Study Guide
Intersections & unions
What is the intersection of events?
The intersection of two events
and
is the set of outcomes that are included in both
and
The intersection of events
and
is denoted
is identical to

The intersection of any number of events is the set of outcomes that are included in all of the events
What is the union of events?
The union of two events
and
is the set of outcomes that are included in
or
or both
The union of events
and
is denoted
is identical to

The union of any number of events is the set of outcomes that are included in at least one of the events
How are the intersection and union related?
For any two events,
and
, the following events contain the same outcomes:
the intersection of the complements of the events,
the outcomes that are not in
and not in
the complement of the union of the events,
the outcomes that are not in either
or
or both
Therefore
and
are complementary events

Examiner Tips and Tricks
The fact that and
are complementary events can be used to find probabilities.
If you are asked to find the probability that or
occurs, you can find the probability that neither
nor
occurs and subtract that from 1.
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