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Math 123
Practice Exam I
Name:
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the number of outcomes as requested.
1) Two 6-sided dice are thrown. Determine the number of ways that a score of either 3 or 4 can be
obtained.
A) 2
B) 5
C) 3
D) 4
2) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not
allowed?
A) 23
B) 24
C) 2401
1)
2)
D) 720
Find the probability.
3) Two dice are rolled. Find the probability that the score on the dice is 8.
1
5
2
A)
B)
C)
4
36
9
3)
D)
7
36
4) Two dice are rolled. Find the probability that the score on the dice is either 12 or at most 4.
5
2
4
7
A)
B)
C)
D)
36
9
9
36
4)
5) When a single card is drawn from an ordinary 52-card deck, find the probability of getting a ten.
1
1
1
1
A)
B)
C)
D)
4
52
26
13
5)
6) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face
card or a 3?
48
2
4
A)
B)
C) 16
D)
52
13
13
6)
7) A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. What is the probability of
choosing a marble that is not blue?
1
3
2
A)
B) 8
C)
D)
3
2
3
7)
8) One digit from the number 8,676,446 is written on each of seven cards. What is the probability of
drawing a card that shows 4?
1
2
4
A)
B) 1
C)
D)
7
7
7
8)
1
Construct the requested tree diagram.
9) Construct a tree diagram that shows all possible 2-letter code words using only the letters x and y
with repetition allowed.
A)
/\
x y
/| |
x y x
B)
|
x
|
y
C)
/\
x y
/\ /\
x yx y
D)
/\
x y
| |
y x
10) Construct a tree diagram that shows all possible outcomes when three coins are tossed.
A)
B)
C)
D)
9)
10)
Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the
probability.
11) Both marbles are green.
1
A)
28
11)
1
B)
14
1
C)
16
1
D)
4
12) The first marble is blue and the second marble is red.
1
1
1
A)
B)
C)
28
7
56
2
D)
7
12)
Find the requested probability.
13) A box contains the eleven letters PROBABILITY. Four letters are drawn one by one with
replacement and recorded in order. What is the probability that the outcome is PAIL?
2051
1
5
2
A)
B)
C)
D)
3960
3960
11
14641
13)
14) Following are three sets of numbers. Draw one number from Set 1 and place it in Set 2. Then draw
one number from Set 2 and place it in Set 3. Finally, draw a number from Set 3. What is the
probability that the last number drawn is a 5?
14)
577
7
Set 1
11
A)
36
77
55
Set 2
Set 3
B)
25
36
C)
2
3
4
D)
1
4
Solve the problem.
15) What is the probability that the arrow will land on an odd number?
A) 1
B)
2
5
C) 0
15)
D)
3
5
16) What is the probability of a dart landing in the shaded region?
(Assume that the x's represent equal measures and that the dart is equally likely to land in any
region on the board.)
A)
3
8
B)
1
2
C)
5
8
D)
3
4
17) Suppose there is a 0.008 chance the main computer will fail in a given time period and a 0.009
chance the backup computer will fail while the main computer is being repaired. Assume that the
failures are independent. Find the probability of both computers being down.
A) 0.00008
18) A husband and wife have a
B) 0.00072
C) 0.00007
16)
17)
D) 0.00006
1
probability of passing on brown eyes to their children. If they have
4
18)
three children, what is the probability that the children will all have brown eyes?
3
1
63
1
A)
B)
C)
D)
64
4
64
64
19) During a department store sale, 20 shoppers bought only clothing, 10 shoppers bought only towels,
and 10 shoppers bought both clothing and towels. If 145 people shopped that day and a shopper is
chosen at random, what is the probability that the shopper has bought towels?
1
8
4
2
A)
B)
C)
D)
2
29
29
29
19)
20) A fair die is tossed. What are the odds in favor of the cube showing a 4?
20)
A) 1:4
B) 2:3
C) 1:5
3
D) 1:6
21) When a single card is drawn from an ordinary 52-card deck, find the odds in favor of getting the 7
of spades.
A) 4 : 12
B) 1 : 51
C) 13 : 51
D) 2 : 51
22) A football player with a field goal kicking percentage of 80% for kicks of 40 yards or less attempts a
final-minute field goal of 32 yards. What are the odds in favor of a successful kick?
A) 4 to 5
B) 5 to 4
C) 1 to 4
B) 1 to 11
C) 9 to 1
22)
D) 4 to 1
23) Tote boards at race tracks list the odds that a horse will lose the race. If the probability of a horse
2
winning the race is
, then what are the odds listed on the tote board?
11
A) 9 to 2
21)
23)
D) 2 to 9
24) A race track tote board has the odds for a horse listed as 8 to 1. Tote boards list the odds that a horse
will lose the race. If this is the case, then what is the probability of the horse winning the race?
8
1
1
A)
B)
C) 9
D)
9
8
9
24)
25) The odds in favor of an earthquake are 6 to 1. What is the probability that an earthquake will occur?
1
6
1
A) 6
B)
C)
D)
7
7
6
25)
26) In how many ways can 7 people line up for concert tickets?
26)
A) 5040
B) 823,543
C) 1
D) 7
27) How many ways can the letters ABCDE be arranged?
A) 24
B) 4
27)
C) 12
D) 120
28) In how many ways can 7 people be chosen and arranged in a straight line, if there are 12 people
from whom to choose?
A) 84
B) 190,080
C) 95,040
D) 3,991,680
29) There are 5 women running in a race. How many first, second, and third place possibilities can
occur?
A) 125
B) 15
C) 60
B) 20160
C) 5040
4
29)
D) 10
30) Find the number of ways to arrange the letters in BASEBALL.
A) 10080
28)
30)
D) 40320
31) If an automobile license plate contains 3 numbers followed by 3 letters, how many different license
plates are possible?
A) 17,576
B) 17,576,000
C) 18,576
D) 1,000
32) A bag contains 7 apples and 5 oranges. If you select 6 pieces of fruit without looking, how many
ways can you get 6 oranges?
A) 0
B) 12
C) 7
B) 56
C) 7
32)
D) 35
33) In how many ways can a group of 7 students be selected from 8 students?
A) 8
31)
33)
D) 1
34) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people
from town C. If the council consists of 5 people, find the probability that 2 are from town A, 2 are
from town B, and 1 is from town C.
19
245
9
19
A)
B)
C)
D)
250
1292
100
500
34)
35) In a two-card hand, what is the probability of holding two cards of the same suit?
4
59
1
41
A)
B)
C)
D)
17
500
5
250
35)
Use the figure to answer the question.
36) Marriage Licenses Issued
(Each circle represents 20,000 licenses)
36)
In which month are the most licenses issued and how many are issued?
A) August; 90,000
B) June; 120,000
C) June; 100,000
5
D) May; 80,000
37) The wages of the employees of a company are presented in this histogram. Assume that $6 is in the
interval $6-$8, not $4-$6, similarly for $8, $10, and $12.
37)
How many employees earn at least $12 and less than $14 an hour?
A) 20
B) 16
C) 46
D) 10
38) This double-bar graph shows the number of male (M) and female (F) athletes at a university over a
four-year period.
Which year had the greatest number of male athletes?
A) 1988
B) 1989
C) 1987
6
D) 1986
38)
39) The sales figures for the Big "D" Company area shown below in a line plot.
39)
Which month in 1990 had the highest sales?
A) Month 12
B) Month 6
C) Month 5
D) Month 3
Use the circle graph to solve the problem.
40) A survey of the 6012 vehicles on the campus of State University yielded the following circle graph.
Motorcycles
8%
Convertibles
17%
Hatchbacks
35%
Vans →
8%
Sedans→
3%
Pickups
29%
Find the number of hatchbacks. Round your result to the nearest whole number.
A) 2405
B) 3908
C) 35
7
D) 2104
40)
41) In a school survey, students showed these preferences for instructional materials.
41)
About how many students would you expect to prefer TV in a school of 1000 students?
A) About 12 students
B) About 120 students
C) About 200 students
D) About 180 students
Find the mean, median, and mode. Round to the nearest tenth when necessary.
42) Given these class sizes: 1, 4, 6, 15, 16
A) 6.5, 6, none
42)
B) 8.4, 6, 4
C) 8.4, 6, none
D) 7.4, 6, 6
Solve the problem.
43) Six college buddies bought each other Christmas gifts. They spent $218.35, $174.64, $291.15,
$273.87, $274.82, and $212.99. Find the mean amount spent for Christmas gifts.
A) $361.46
B) $289.16
C) $240.97
D) $277.16
44) In the first two weeks of school, Jill studied 28 hours and 16 hours, respectively. How many hours
must she study during the third week to give her an average of 20 hours per week?
A) 32 hours
B) 22 hours
C) 20 hours
45)
93 81 59 69 82 73 61 77 95 84 88 71
85 97 63 72 89 80 60 98 91 62 78 83
76 81 94 66 83 96
Find the 1st quartile, Q1 .
Find the 3rd quartile, Q3.
B) 71, 85
C) 75, 87
8
44)
D) 16 hours
45) The following scores on the midterm exam in Chemistry 102 were recorded:
A) 69, 87
43)
D) 71, 89
Match the given data with one of the box plots from the Table of Box Plots.
46) 470, 490, 520, 690, 780, 780, 850, 890,
1000, 900, 1040, 1090, 1130, 1120, 1100
A) II
46)
B) III
C) I
D) IV
Solve the problem.
47) The pH of a patient's blood was measured periodically during one week, and the measured values
were 7.37, 7.40, 7.45, 7.45, and 7.44. Find the standard deviation and variance for the data. Round
the results to the nearest thousandth.
A) s = 0.036, v = 0.001
B) s = 0.079, v = 0.006
C) s = 0.071, v = 0.005
D) s = 0.001, v = 0.000
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the abuse of statistics.
48) The graph shows the increases in a certain expenditure over a four-year period. What is
wrong with the graph?
9
48)
47)
Answer Key
Testname: MATH 123 PRACTICE EXAM I
1) B
2) D
3) B
4) D
5) D
6) D
7) D
8) C
9) C
10) C
11) A
12) A
13) D
14) B
15) D
16) A
17) C
18) D
19) C
20) C
21) B
22) D
23) A
24) D
25) C
26) A
27) D
28) D
29) C
30) C
31) B
32) A
33) A
34) B
35) A
36) B
37) B
38) B
39) A
40) D
41) B
42) C
43) C
44) D
45) D
46) B
47) A
48) The bars are not drawn in the correct proportions.
10