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Chapter 7: Probability
Definition: Compound Event
A compound event is an event that is defined by combining two or more
events.
To illustrate, consider the following example.
Example 7-11:
Let
A
be the event of a student owning an i-Phone. Let
B
be the event of a student owning an i-Pad2. Let
C
be the event of a student
owning both an i-Phone and an i-Pad2. Discuss the event
C
that is common
to both
A
and
B
.
Solution:
From the given information,
C
is the event that is common to
both
A
and
B
. Since the event
C
is obtained by combining
A
and
B
,
C
will
be a compound event.
Union of Events
Consider two events
A
and
B
. We may be interested in the event that is
obtained by considering the elements that are in
A
, or in
B
, or in both
A
and
B
. Such a compound event is called the
union of events
A
and
B
.
Definition: Union of Two Events
The union of two events A and B is the set of outcomes that are included in
A or in B or in both A and B.
Notation: The union of A and B will be denoted A
B.
Note:
Sometimes the union of
A
and
B
is written as “
A or B
”
. That is,
A
B
A or B
.
The diagram given in
Figure 7-8
, called a
Venn diagram
, depicts the union
of events
A
and
B
. The total shaded area within the two circles represents
the event of
A
B
or (
A
or
B
).