251y0322
10/27/03
ECO251 QBA1
SECOND HOUR EXAM
March 21, 2003
Name: ____KEY_____________
Social Security Number: _____________________
Part I: (48 points) Do all the following: All questions are 2 points each except as marked. Exam is
normed on 50 points including takehome.
Please reread, ‘Things that You should never do on an
Exam or Anywhere Else, ‘
and especially recall that a probability cannot be above 1!
The following joint probability table shows the relation between two sets of events. Let event
A
be that
the individual is below 22 (
A
is over 21), and the event
0
B
be that the individual had no traffic
violations in the last 18 months, the event
1
B
be that the individual has one traffic violation in the last 18
months and the event
2
B
be that the individual has 2 traffic violations over the last 18 months. No
individuals in this pool of drivers has more than 2 violations.
01
.
18
.
41
.
06
.
12
.
22
.
2
1
0
A
A
B
B
B
Note, to do the problems below, at least total the rows and columns 
00
.
1
07
.
30
.
63
.
60
.
40
.
01
.
18
.
41
.
06
.
12
.
22
.
2
1
0
A
A
B
B
B
1.
The probability that someone who is over 21 has no traffic violations is (To 2 decimal places):
a)
.63
b)
.60.
c)
.41
d)
*.68
You have been asked for
(
29
(
29
(
29
683
.
60
.
41
.
0
0
=
=
∩
=
A
P
A
B
P
A
B
P
e)
None of the above.
2.
The probability that someone picked at random is over 21 and has no traffic violations is (To 2
decimal places):
a)
.63
b)
.60.
c)
*.41
Joint probabilities are what the table shows!
d)
.68
e)
None of the above.
3.
The probability that someone chosen at random is either under 22 or has 2 violations is:
a)
.40
b)
.06
c)
.46
d)
.47
e)
*.41
(
29
(
29
(
29
(
29
41
.
06
.
07
.
40
.
2
2
2
=

+
=
∩

+
=
∪
B
A
P
B
P
A
P
B
A
P
f)
None of the above
1
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00
.
1
07
.
30
.
63
.
60
.
40
.
01
.
18
.
41
.
06
.
12
.
22
.
2
1
0
A
A
B
B
B
4.
Which two events are independent?
a)
A
and
A
Note that ‘mutually exclusive’ and ‘independent are almost opposites.
b)
A
and
2
B
c)
*
A
and
1
B
.
The definition of independence is
(
29
(
29
A
P
B
A
P
=
1
. In this case
(
29
60
.
=
A
P
and
(
29
(
29
(
29
60
.
30
.
18
.
1
1
1
=
=
∩
=
B
P
B
A
P
B
A
P
. But a better way to do this is to note
that
(
29
(
29
(
29
(
29
18
.
30
.
60
.
1
1
=
=
=
∩
B
P
A
P
B
A
P
.
d)
A
and
0
B
e)
A
and
2
B
f)
None of these.
5.
Which two events are mutually exclusive?
a)
*
A
and
A
Complements are always mutually exclusive. None of the other pairs
have a joint probability of zero.
b)
A
and
2
B
c)
A
and
1
B
.
d)
A
and
0
B
e)
A
and
2
B
f)
None of these.
In questions 6 and 7 you need to know what
(
29
0
B
P
,
(
29
1
B
P
and
(
29
2
B
P
are to do the problems. Show
your work.
Solution:
We can use the following table.
(
29
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 Microeconomics, Probability, Standard Deviation, Household income in the United States, Social Security number, business majors

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