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Chapter 7: Probability
Note:
If events
A
and
B
are
not independent
, then the events are said to
be
dependent
.
Example 7-23:
A part-time student is enrolled in a course in business (
B
)
and a course in music (
M
). The probabilities that the student will pass the
business, music, or both subjects are respectively,
P
(
B
) = 0.8,
P
(
M
) = 0.7,
and
P
(
B
M
) = 0.56.
(a) What is the probability that the student will pass business course given
that the student passes the course in music?
Solution:
We need to find
P
(
B
|
M
). Thus,
0.8
0.7
0.56
) P(
)
P(
) | (
M
MB
MBP
.
(b) Are the events
B
and
M
independent?
Solution:
From part (a)
P
(
B
|
M
) = 0.8, and also
P
(
B
) = 0.8. That is,
P
(
B
|
M
) =
P
(
B
). Thus, events
B
and
M
are independent.
Rule 10
(
multiplication rule for two independent events
):
If events
A
and
B
are independent, then
P
(
A
B
) =
P
(
A
)
P
(
B
).
Example 7-24:
For the information given in
Example 7-23
, use
Rule 10
to determine whether events
B
and
M
are independent.
Solution:
We need to show whether
P
(
B
M
) =
P
(
B
)
P
(
M
) in order for
events
B
and
M
to be independent. Given
P
(
B
M) = 0.56 and
P
(
B
)
P
(
M
) = 0.8
0.7 = 0.56 therefore
P
(
B
M
) =
P
(
B
)
P
(
M
). Thus one
can conclude that events
B
and
M
are independent.
Example 7-25:
A consumer group studied the service provided by cellular
phone stores in a given community. One of the things they looked at was
the relationship between the service they received at the stores and whether
the server had a college degree or not. The information is summarized in
Table 7-1
.