NAME ______________________________________________ DATE
____________ PERIOD _____
13-1 Skills Practice
Sampling and Bias
Identify each sample, suggest a population from which it was selected, and state
whether it is unbiased (random) or biased. If unbiased, classify the sample as simple,
stratified, or systematic. If biased, classify as convenience or voluntary response.
2. HEALTH A hospital’s administration is interested in opening a gym on the premises for
all its employees. They ask each member of the night-shift emergency room staff if he or
she would use the gym, and if so, what hours the employee would prefer to use it.
3. POLITICS A senator wants to know her approval rating among the constituents in her
state. She sends questionnaires to the households of 1000 registered voters in her party.
4. MANUFACTURING A company that produces motherboards for computers randomly
selects 25 boxed motherboards out of a shipment of 1500, and then tests each selected
motherboard to see that it meets specifications.
5. GOVERNMENT The first 100 people entering a county park on Thursday are asked
their opinions on a proposed county ordinance that would allow dogs in county parks to
go unleashed in certain designated areas.
6. MUSIC To determine the music preferences of their customers, the owners of a music
store ask 10 customers who have expressed interest to participate in an in-store
interview in which they listen to new CDs from artists in all music categories.
7. LIBRARIES A community library asks every tenth patron who enters the library to
name the type or genre of book he or she is most likely to borrow. They conduct the
interviews from opening to closing on three days of the week. They will use the data for
new acquisitions.
8. COMPUTERS To determine the number of students who use computers at home, the
high school office chooses 10 students at random from each grade, and then interviews
the students.
©
Glencoe/McGraw-Hill
783
Glencoe Algebra 1
Lesson 13-1
1. LANDSCAPING A homeowner is concerned about the quality of the topsoil in the back
yard. The back yard is divided into 5 equal sections, and then a 1-inch plug of topsoil is
randomly removed from each of the 5 sections. The soil is taken to a nursery and
analyzed for mineral content.
NAME ______________________________________________ DATE
____________ PERIOD _____
13-1 Practice
Sampling and Bias
Identify each sample, suggest a population from which it was selected, and state
whether it is unbiased (random) or biased. If unbiased, classify the sample as simple,
stratified, or systematic. If biased, classify as convenience or voluntary response.
1. GOVERNMENT At a town council meeting, the chair asks 5 citizens attending for their
opinions on whether to approve rezoning for a residential area.
2. BOTANY To determine the extent of leaf blight in the maple trees at a nature preserve,
a botanist divides the reserve into 10 sections, randomly selects a 200-foot by 200-foot
square in the section, and then examines all the maple trees in the section.
3. FINANCES To determine the popularity of online banking in the United States, a
polling company sends a mail-in survey to 5000 adults to see if they bank online, and if
they do, how many times they bank online each month.
4. SHOES A shoe manufacturer wants to check the quality of its shoes. Every twenty
minutes, 20 pairs of shoes are pulled off the assembly line for a thorough quality
inspection.
5. BUSINESS To learn which benefits employees at a large company think are most
important, the management has a computer select 50 employees at random. The
employees are then interviewed by the Human Relations department.
6. BUSINESS An insurance company checks every hundredth claim payment to ensure
that claims have been processed correctly.
7. ENVIRONMENT Suppose you want to know if a manufacturing plant is discharging
contaminants into a local river. Describe an unbiased way in which you could check the
river water for contaminants.
8. SCHOOL Suppose you want to know the issues most important to teachers at your
school. Describe an unbiased way in which you could conduct your survey.
©
Glencoe/McGraw-Hill
784
Glencoe Algebra 1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-1 Reading to Learn Mathematics
Sampling and Bias
Pre-Activity
Why is sampling important in manufacturing?
Read the introduction to Lesson 13-1 at the top of page 708 in your textbook.
Reading the Lesson
Suppose the principal at a school wants to use Saturdays as make-up days when
school is closed for inclement weather. The principal selects and then polls a group
of students to see if the student body supports the idea. Complete the sentences.
1. The student body is the
from which a
of students
is selected to be polled. If all the students are polled, it is called a
.
2. If all students are requested to enter school through the administration building and
every twenty-fifth student is selected to be polled, then the sample is a
sample. If only those students who are in the four
classrooms closest to the principal’s office are selected for the poll, then the sample is a
sample. If the principal announces a poll and then
interviews the students who sign up to be interviewed, then the sample is a
sample.
3. Numbers can be assigned to all students and a computer can select 50 of the numbers
at random. The students assigned those numbers would be polled. This would be a
sample. If students are first divided according to grade and
then chosen at random from each group, then the sample is a
sample.
4. All
samples are unbiased since they are selected without preference
for one unit of the population over another. A
or parts of the population over other parts.
sample favors one part
Helping You Remember
5. To remember what a stratified random sample is, look up the word stratified in a
dictionary. What everyday meaning do you find that seems closest to the mathematical
meaning presented in this lesson?
©
Glencoe/McGraw-Hill
785
Glencoe Algebra 1
Lesson 13-1
From what group are the CDs picked at random and then checked for
defects?
NAME ______________________________________________ DATE______________ PERIOD _____
13-2 Skills Practice
Introduction to Matrices
State the dimensions of each matrix. Then, identify the position of the circled
element in each matrix.
27 3
2.  0 9
 11 8
4 by 1;
second row,
first column
 2 3 24 
1
3
5.  1
 0 21 2 
3 by 3;
third row,
third column
 12
19 

37
218

4.  15
38 
27
96 
3 1 0 7
3. 6
0 0 1 4 3
3 by 2;
second row,
second column
3 27 
6. 6
2
2 by 5;
first row,
second column
1 0 2 1
8. 0 1 0 2
0 0 1 5
7. [228 42]
2 by 2;
second row,
first column
4 by 2;
third row,
first column
1 by 2;
first row,
second column
3 by 4;
second row,
third column
 5 2 27 
 2 9 23 
24 2 
 37 22 
4
7 , C 5  9
7  , and D 5 25 12  ,
If A 5 21 0 13  , B 5  12
 3 8 6
26 22 5 
 15 33 
 11 0 
find each sum, difference, or product. If the sum or difference does not exist,
write impossible.
9. A 1 B
 7
 11
23
11 210 
4
20 
6
11 
12. D 2 B
impossible
15. 2D
 74
 210
 22
©
11. C 1 D
13. A 2 B
14. D 2 C
impossible
 3 27 24 
 213 24
6
 9 10
1
16. 4B
44 
24 
0
18. 3C
 212
 27
 45
10. B 1 C
6
21 
99 
Glencoe/McGraw-Hill
 8 36 212 
 48 16
28 
 224 28
20 
19. 2C 1 B
impossible
789
33 24
 4 19
26 33
 41
20 
 214
5
 24 233 
17. 23A
 215 26
21 
 3
0 239 
 29 224 218 
20. 2B 1 A
 9
 23
29
20 213 
8
27 
4
16 
Glencoe Algebra 1
Lesson 13-2
 2
7
1. 21

 3
NAME ______________________________________________ DATE
____________ PERIOD _____
13-2 Practice
Introduction to Matrices
24 1 6 
 12 29 5 
 225 67 
 48 29 
9  , B 5  215 20
8  , C 5  86 49  , and D 5  7 52  ,
If A 5  7 25
 8 2 23 
 11 0 14 
 73 50 
 238 35 
find each sum, difference, or product. If the sum or difference does not exist,
write impossible.
1. A 1 B
2. C 1 D
3. D 2 C
5. 4A
6. 23D
7. C 2 2D
8. 3B 1 5A
4. B 2 C
9. What is the size of matrix C above?
10. In matrix A above, what is the location of the number 2?
11. Identify the element in row 2, column 3 in matrix B above.
SCHOOL For Exercises 12–15, use the following table that describes the percent of
high school students participating in organized physical activities at school.
Enrolled in Phys. Ed. Class
Grade
Played on a Sports Team
9
10
11
12
9
10
11
12
Male
82.3
65.3
44.6
43.8
63.9
62.3
58.8
60.7
Female
75.6
56.6
36.8
29.4
53.4
50.9
45.8
42.3
Source: Centers for Disease Control and Prevention, 2000
65.3 44.6 43.8
12. If M 5 82.3
63.9 62.3 58.8 60.7 is a matrix
representing male participation in physical
education classes in row 1, and on a sports team
in row 2, create a similar matrix F for females.
13. Calculate D 5 M 2 F.
14. What does matrix D represent?
15. What is indicated by the element in row 1, column 3 of matrix D?
©
Glencoe/McGraw-Hill
790
Glencoe Algebra 1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-2 Reading to Learn Mathematics
Introduction to Matrices
Pre-Activity
How are matrices used to organize data?
Read the introduction to Lesson 13-2 at the top of page 715 in your textbook.
• The second row of the table gives data on which aircraft?
• According to the table, which aircraft uses the greatest amount of fuel
per hour?
Reading the Lesson
1. Give the dimensions of each matrix.
2 28
5 11
a. 19
7 16
1
 12 11 
28
1
b. 228
17 
 3 7
 13 22
c.  25 28
27 40
0
61 
54 
3. To perform scalar multiplication on a matrix, you
Lesson 13-2
2. How can you tell whether it is possible to add or subtract two matrices?
each
of the given matrix by a constant.
Tell whether each statement is true or false. If you say that a statement is false,
explain how you know it is false.
4. If two matrices contain the same number of elements, then they can be added.
5. If two matrices contain exactly the same numbers as elements, then they are equal
matrices.
Helping You Remember
6. Many students have difficulty remembering whether to give the number of rows or the
number of columns first when stating the dimensions of a matrix. Describe an easy
method for remembering that you should always give the number of rows first and then
the number of columns.
©
Glencoe/McGraw-Hill
791
Glencoe Algebra 1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-3 Skills Practice
Histograms
For each histogram, answer the following.
• In what measurement class does the median occur?
• Describe the distribution of the data.
2.
State Gas Tax
Frequency
Frequency
Highest Elevations in 50 States
20
16
12
8
4
0
0–3
3–6
6–9
20
16
12
8
4
0
5–10 10–15 15–20 20–25 25–30 30–35
9–12 12–15 15–18 18–21
Tax (cents/gallon)
Height (feet in thousands)
Source: Federal Highway Administration
Source: U.S. Geological Survey
3. For the pair of histograms, answer the following.
• Compare the medians of the two data sets.
• Compare and describe the overall shape of each
distribution of data.
Frequency
U.S. Monthly Births for 2000
6
5
4
3
2
1
0
315– 325– 335– 345– 355–
325 335 345 355 365
Births (thousands)
Frequency
U.S. Monthly Deaths for 2000
4
3
2
1
0
180– 190– 200– 210– 220– 230–
190 200 210 220 230 240
Deaths (thousands)
Source: Centers for Disease Control
Create a histogram to represent the data set.
Frequency
4. The number of absences at a high school the first two
months of the school year:
17, 11, 12, 6, 7, 18, 13, 19, 23, 17, 4, 9, 13, 8, 19, 11, 9,
21, 28, 12, 4, 0, 9, 18, 28, 29, 12, 16, 19, 9, 21, 3, 8, 11, 17
School Absences
12
10
8
6
4
2
0
0–5
5–10 10–15 15–20 20–25 25–30
Number of Absences
©
Glencoe/McGraw-Hill
795
Glencoe Algebra 1
Lesson 13-3
1.
NAME ______________________________________________ DATE
____________ PERIOD _____
13-3 Practice
Histograms
WEATHER For the histogram at the right, answer
U.S. Tornadoes in 2000
Number of
Months
the following.
1. In what measurement class does the median occur?
2. Describe the distribution of the data.
5
4
3
2
1
0
0–
50
50– 100– 150– 200–
100 150 200 250
Number of Tornadoes
Source: National Oceanic and
Atmospheric Adminsitration
Heights of Active Volcanoes
in North Amerca
Frequency
3. VOLCANOES For the pair of histograms, answer
the following.
• Compare the medians of the two data sets.
• Compare and describe the overall shape of each
distribution of data.
10
8
6
4
2
0
0–4
4–8
8–12 12–16 16–20
Height (feet in thousands)
Frequency
Heights of Active Volcanoes
in South Amerca
10
8
6
4
2
0
0–4
4–8
8–12 12–16 16–20 16–20
Height (feet in thousands)
Source: World Almanac 2001, data for 2000
FOOD For Exercises 4–6, use the following table.
Average Price of Trout in Selected States in 2000 (dollars per pound)
State
Price
State
Price
State
Price
State
Price
California
2.03
Michigan
2.65
Oregon
4.80
Virginia
2.90
Colorado
2.67
New York
4.53
Pennsylvania
3.30
West Virginia
2.17
Maine
5.80
North Carolina
1.30
Utah
2.02
Wisconsin
2.71
Source: U.S. Department of Agriculture
4. Create a histogram to represent the data.
6. Describe the distribution of the data.
Frequency
5. In what measurement class does the median occur?
Trout Prices
7
6
5
4
3
2
1
0
1.00– 2.00– 3.00– 4.00– 5.00–
2.00 3.00 4.00 5.00 6.00
Prices (dollars per pound)
©
Glencoe/McGraw-Hill
796
Glencoe Algebra 1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-3 Reading to Learn Mathematics
Histograms
Pre-Activity
How are histograms used to display data?
Read the introduction to Lesson 13-3 at the top of page 722 in your textbook.
The
score intervals in the frequency table are displayed on
the
axis of the graph. The width of each interval is
points.
Reading the Lesson
1. Use the histogram to complete the sentences on
interpreting histograms.
, each with a width
of
.
Frequency
a. From the histogram, you can see there are six
Job Applicants, Fox Music
30
25
20
15
10
5
0
1–2
3–4
5–6
7–8 9–10 11–12
Months
b. To determine the median, add the
to find the number of
. Then
locate the measurement class in which the median lies. If the median in the
.
c. Another way to interpret histograms is to describe the
The data in the histogram is skewed to the
of the data.
(left/right).
Complete each sentence.
2. When creating a histogram, identify the greatest and
values in the
data set so that you can create measurement classes of
3. Use measurement classes to determine the
.
for the
axis. Use frequency values from the frequency table to determine the
for the
axis.
Helping You Remember
4. At first glance, a histogram looks like a typical bar graph. What are some key features of
histograms that can help you to remember how histograms are different from other types
of bar graphs?
©
Glencoe/McGraw-Hill
797
Glencoe Algebra 1
Lesson 13-3
histogram is 53, it occurs in the measurement class
NAME ______________________________________________ DATE
____________ PERIOD _____
13-4 Skills Practice
Measures of Variation
Find the range, median, lower quartile, upper quartile, and interquartile range of
each set of data. Identify any outliers.
1. 13, 15, 25, 22, 18, 19, 15,
32, 57, 32, 12, 23, 38
2. 23, 38, 46, 57, 88, 23, 33,
23, 56, 77, 15, 86, 41
3. 107, 57, 47, 40, 34, 20, 25,
37, 46, 57, 69
4. 82, 71, 78, 89, 80, 81, 73,
78, 76, 77, 82, 75, 86
5. 120, 100, 90, 95, 105, 96,
110, 92, 95, 110
6. 200, 250, 230, 180, 160, 140,
210, 190, 170, 220
7. Stem | Leaf
8. Stem | Leaf
2
3
4
5
6
1
2
3
4
5
|001
|46
|233
|789
|1223
9. Stem | Leaf
10. Stem | Leaf
4
5
6
7
8
6
7
8
9
10
|16
|007
|779
|12245
| 8 67 5 67
|2458
|334
|22
|1
|224
11. Stem | Leaf
12. Stem | Leaf
7
8
9
10
11
8
9
10
11
12
©
|025
|00
|359
|1146
|6778
Glencoe/McGraw-Hill
116 5 116
801
26 5 26
Lesson 13-4
|01
|246
|3389
|224
| 3 6 43 5 43
104 5 104
|19
|236
|19
|2489
| 3 7 123 5 123
Glencoe Algebra 1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-4 Practice
Measures of Variation
Find the range, median, lower quartile, upper quartile, and interquartile range of
each set of data. Identify any outliers.
1. 73, 39, 58, 42, 71, 84, 27, 23, 36, 57, 70, 52, 35, 51, 29, 38
2. 42.1, 37.3, 20.0, 45.1, 39.3, 32.0, 38.1, 33.2
3. Stem | Leaf
4. Stem | Leaf
8
9
10
11
12
13
14
0
1
2
3
4
5
6
|016
|35
|0
|11589
|34
|
| 1 4 7 144 5 144
|45
|137
|07
|
|1459
|223
| 0 1 04 5 0.4
FARMING For Exercises 5–9, use the table below.
Hired Farm Workers October 8–14, 2000 (thousands)
Region
Number
Region
Number
Region
Number
Northeast I
50
Lake
71
Mountain I
34
Northeast II
45
Cornbelt I
56
Mountain II
24
Appalachian I
40
Cornbelt II
31
Mountain III
21
Appalachian II
33
Delta
42
Pacific
78
Southeast
33
Northern Plains
33
California
24
Florida
50
Southern Plains
61
Hawaii
8
Source: USDA-NASS Agricultural Statistics
5. What is the range in the number of workers hired?
6. What is the median number of workers hired?
7. What are the lower quartile and the upper quartile
of the data?
8. What is the interquartile range of the data?
9. Name any outliers.
ASTRONOMY For Exercises 10–14, use the stem-and-leaf plot
that gives the absolute magnitudes of notable comets.
10. What is the range in magnitudes?
11. What is the median magnitude?
12. What are the lower quartile and the upper
quartile of the data?
13. What is the interquartile range of the data?
Source: NASA
Stem
5
6
7
8
9
10
11
12
13
| Leaf
|5
|5
|
|5
|00008
|6
|79
|0015
| 5 85 5 8.5
14. Name any outliers.
©
Glencoe/McGraw-Hill
802
Glencoe Algebra 1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-4 Reading to Learn Mathematics
Measures of Variation
Pre-Activity
How is variation used in weather?
Read the introduction to Lesson 13-4 at the top of page 731 in your textbook.
Which city shows the least change in average monthly high temperatures?
Reading the Lesson
Complete each sentence or equation.
1. To find the range of a set of data, you need to know the least data value and the
data value.
2. To find the lower quartile of a set of data, you need to find the
lower half of the data set.
3. The upper quartile is the
of the
of the
half of the data set.
4. If Q1, Q2, and Q3 are the three quartiles for a set of data, then you can find the
interquartile range by calculating
2
.
5. Values that are less than Q1 2 1.5(interquartile range) or greater than
Q3 1 1.5(interquartile range) are called
.
6. Use the data diagram below to answer the questions.
Q2
10 11
14 15 16
a. IQR 5
Q3
18
20 21
2
38
40
b. 1.5IQR 5
c. Since Q3 1 1.5IQR 5 36, the data elements
and
are outliers.
Helping You Remember
7. Describe an easy way to remember the basic meaning of the term outlier.
©
Glencoe/McGraw-Hill
803
Glencoe Algebra 1
Lesson 13-4
7
Q1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-5 Skills Practice
Box-and-Whisker Plots
For Exercises 1–4, use the box-and-whisker plot at the right.
1. What are the extremes of the data?
30 31 32 33 34 35 36 37 38
2. What is the range of the data?
3. What is the median of the data?
4. What is the interquartile range of the data?
Draw a box-and-whisker plot for each set of data.
5. 12, 9, 15, 6, 11, 20, 18, 23, 19, 22, 7, 18
6
10
6. 39, 52, 86, 97, 33, 67, 46, 49, 52, 54, 23
19.5 23
23
39
52
67
97
16.5
0
3
6
9
12 15 18 21 24
20 30 40 50 60 70 80 90 100
For Exercises 7–10, use the parallel box-and-whisker
plot at the right.
A
B
7. Which set of data contains the least value?
40
50
60
70
80
90
100
8. Which set of data contains the greatest value?
9. What percent of the data in plot A is greater than 80?
10. What percent of the data in plot B is between 60 and 85?
Draw a parallel box-and-whisker plot for each pair of data. Compare the data.
10
15
34
41
19
25 27 34
22
39
A
B
10
12. A: 39, 28, 29, 42, 51, 34, 32, 31, 41, 38, 36
B: 44, 67, 21, 53, 42, 57, 68, 54, 47, 58, 46
20
30
31 36 41
44
21
807
51
53 58
42
20
Glencoe/McGraw-Hill
50
28
A
B
©
40
30
40
50
60
68
70
Glencoe Algebra 1
Lesson 13-5
11. A: 20, 32, 15, 10, 18, 41, 17, 34, 19, 40, 15
B: 27, 33, 26, 31, 39, 23, 34, 25, 36, 22, 27
NAME ______________________________________________ DATE
____________ PERIOD _____
13-5 Practice
Box-and-Whisker Plots
For Exercises 1–4, use the parallel box-and-whisker
plot at the right.
A
B
1. Which set of data has the greatest range?
70
60
80
90
100
110
120
2. Which set of data has the greatest interquartile range?
3. What percent of the data in plot A are less than 80?
4. What percent of the data in plot B are less than 80?
16.5
12
5. Draw a box-and-whisker plot for the data.
14, 55, 27, 32, 12, 14, 19, 32, 21, 46, 26, 19
10
6. Draw a parallel box-and-whisker plot for each pair of data.
Compare the data.
A: 9, 22, 16, 10, 15, 11, 18, 14, 19, 30, 23
B: 27, 49, 13, 31, 29, 33, 44, 21, 16, 22, 37
23.5 32
20
30
40
11 16 22
A
55
50
60
30
9
13
21
29 37
49
20
30
50
B
0
10
40
EARTHQUAKES For Exercises 7–9, use the following list of the numbers of
earthquakes measuring between 5.0–5.9 on the Richter scale for the years 1990–2000.
1635, 1469, 1541, 1449, 1542, 1327, 1223, 1118, 979, 1106, 1318
Source: USGS National Earthquake Center
7. Draw a box-and-whisker plot for the data.
Number of Earthquakes
979 1118
1327
1541
1635
8. What are the extremes of the data?
900
1100
1300
1500
1700
9. What is the interquartile range?
CLIMATE For Exercises 10 and 11, use the following list of all-time record high
temperatures for 50 states.
112, 100, 128, 120, 134, 118, 106, 110, 109, 112, 100, 118, 117, 116, 118, 121, 114, 114,
105, 109, 107, 112, 114, 115, 118, 117, 118, 125, 106, 110, 122, 108, 110, 121, 113, 120,
119, 111, 104, 111, 120, 113, 120, 117, 105, 110, 118, 112, 114, 114
Source: National Climatic Data Center
10. Draw a box-and-whisker plot for the data.
Record High Temperatures
100 110
114 118
128
134
11. Describe the data distribution.
90
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110
120
130
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Glencoe Algebra 1
NAME ______________________________________________ DATE
____________ PERIOD _____
13-5 Reading to Learn Mathematics
Box-and-Whisker Plots
Pre-Activity
How are box-and-whisker plots used to display data?
Read the introduction to Lesson 13-5 at the top of page 737 in your textbook.
In the box-and-whisker plot, the least value and the greatest value let you
find the
of the data, Q1 is the
Q2 is the
, and Q3 is the
,
.
Reading the Lesson
1. Use the parallel box-and-whisker plots at the right
to complete the sentences that follow.
A
B
a. The bullets located at 2 and 17 in plot A and 5
2
4
6
8
10 12 14 16 18 20
and 19 in plot B represent the
values of the data sets.
b. The bullets at the ends of the whiskers are the
values that are not
c. The
and
. Plot
has an outlier.
(left/right) whisker contains values in the lower
the data set. The
of
(left/right) whisker contains values in the upper
of the data set.
d. The length of the box represents the
. The vertical line
drawn inside the box represents the
lower half of plot A is
half of the data are
. The box and whisker for the
than for the upper half. Therefore, the lower
(more/less) dispersed than the upper half. In plot B,
the lower half of the data are
(more/less) dispersed than the upper half.
e. The range of values in plot A is
(greater/less) than the range in
plot B. The data in the lower half of plot A are
(more/less) dispersed
Helping You Remember
2. How can you remember that outliers are not part of the box or whiskers in a box-andwhisker plot?
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Glencoe Algebra 1
Lesson 13-5
than in the lower half of plot B. The data in the upper half of plot A are
(more/less) dispersed than in the upper half of plot B.
NAME ______________________________________________ DATE______________ PERIOD _____
14-1 Skills Practice
Counting Outcomes
Draw a tree diagram to show the sample space for each event. Determine the
number of possible outcomes.
Lesson 14-1
1. planting a garden with roses, zinnias, or cosmos, in yellow, red, orange, or purple
There are 12 possible outcomes.
2. selecting monogrammed or plain stationery, in white or buff, with lined or unlined
envelopes
There are 8 possible outcomes.
Find the value of each expression.
3. 1! 1
4. 3! 6
5. 6! 720
6. 9! 362,880
7. Two dice are rolled. How many outcomes are possible? 36
8. If students can choose between 7 elective subjects, 6 class periods, and 5 teachers, how
many elective classes are possible? 210
9. How many different ways can a carpenter build a bookcase using one each of 4 types of
wood, 3 stains, 5 widths, and 6 heights? 360
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Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
14-1 Practice
Counting Outcomes
Draw a tree diagram to show the sample space for each event. Determine the
number of possible outcomes.
1. dining at an Italian, Mexican, or French restaurant, for lunch, early bird (early dinner
special), or dinner, and with or without dessert
Find the value of each expression.
2. 5!
3. 8!
4. 10!
5. 12!
6. How many different vacation plans are possible when choosing one each of
12 destinations, 3 lengths of stay, 5 travel options, and 4 types of accommodations?
7. How many different ways can you arrange your work if you can choose from 7 weekly
schedules, 6 daily schedules, and one of 3 types of duties?
8. How many different ways can you treat a minor cut if you can choose from 3 methods of
cleansing the cut, 5 antibiotic creams, 2 antibacterial sprays, and 6 types of bandages?
9. TESTING A teacher gives a quick quiz that has 4 true/false questions and 2 multiple
choice questions, each of which has 5 answer choices. In how many ways can the quiz be
answered if one answer is given for each question?
CLASS RINGS Students at Pacific High can choose class rings in one each of
8 styles, 5 metals, 2 finishes, 14 stones, 7 cuts of stone, 4 tops, 3 printing styles, and
30 inscriptions.
10. How many different choices are there for a class ring?
11. If a student narrows the choice to 2 styles, 3 metals, 4 cuts of stone, and 5 inscriptions
(and has already made the remaining decisions), how many different choices for a ring
remain?
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NAME ______________________________________________ DATE______________ PERIOD _____
14-1 Reading to Learn Mathematics
Counting Outcomes
Pre-Activity
How are possible win/loss football records counted?
Read the introduction to Lesson 14-1 at the top of page 754 in your
textbook. Then complete the diagram.
Game 2
win
win
lose
win
lose
lose
Game 3
win
lose
win
lose
win
lose
win
lose
Outcomes
win-win-win
Lesson 14-1
Game 1
Reading the Lesson
Use the tree diagram above for Exercises 1–4.
1. What is the sample space?
2. Name two different outcomes.
3. Three different outcomes result in a win/loss record of 2-1. What are they?
4. Use the Fundamental Counting Principle to complete the chart.
Game 1
Number of Choices
Game 2
?
Game 3
?
Number of Outcomes
5
Helping You Remember
5. Suppose you are training the new disc jockey for a school radio station. He has chosen
10 selections to play from a new CD. How could you use factorials to explain to him the
number of different ways the selections could be played?
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NAME ______________________________________________ DATE______________ PERIOD _____
14-2 Skills Practice
Permutations and Combinations
Determine whether each situation involves a permutation or combination. Explain
your reasoning.
1. dinner guests seated around a table
2. a pattern of different widths of bars and spaces for a bar code
3. selecting two yellow marbles out of a sack of yellow and blue marbles
Lesson 14-2
4. placing one can of each of 15 different types of soup along a store shelf
5. selecting four candles from a box of ten
6. the placement of the top ten finishers in a school’s spelling bee
7. choosing two colors of paint out of twenty to paint the walls and trim of a bedroom
8. choosing a set of twelve pencils from a selection of thirty-six
Evaluate each expression.
9. 5 P2
10. 6 P4
11. 7 P3
12. 9 P4
13. 7 P5
14. 5 P3
15. 6C2
16. 9C7
17. 8C4
18. 7C5
19. 12C2
20. 13C7
21. 11C2
22. 5 P4
23. 14C5
24. 11C6
25. (4 P2)(3 P2)
26. (8C6)(5 P1)
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NAME ______________________________________________ DATE______________ PERIOD _____
14-2 Practice
Permutations and Combinations
Determine whether each situation involves a permutation or combination. Explain
your reasoning.
1. choosing two dogs from a litter of two males and three females
2. a simple melody formed by playing the notes on 8 different piano keys
3. a selection of nine muffins from a shelf of twenty-three
4. the selection of a four-letter acronym (word formed from the initial letters of other
words) in which two of the letters cannot be C or P
5. choosing an alphanumeric password to access a website
Evaluate each expression.
6. 11P3
7. 6 P3
8. 15 P3
9. 10C9
10. 12C9
11. 7C3
12. 7C4
13. 12C4
14. 13 P3
15. (8C4)(8C5)
16. (17 C2)(8C6)
17. (16C15)(16C1)
18. (8 P3)(8 P2)
19. (5 P4)(6 P5)
20. (13 P1)(15 P1)
21. (10C3)(10 P3)
22. (15 P4)(4C3)
23. (14C7)(15 P3)
24. SPORT In how many orders can the top five finishers in a race finish?
JUDICIAL PROCEDURE The court system in a community needs to assign 3 out of
8 judges to a docket of criminal cases. Five of the judges are male and three are
female.
25. Does the selection of judges involve a permutation or a combination?
26. In how many ways could three judges be chosen?
27. If the judges are chosen randomly, what is the probability that all 3 judges are male?
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Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
14-2 Reading to Learn Mathematics
Permutations and Combinations
Pre-Activity
How can combinations be used to form committees?
Read the introduction to Lesson 14-2 at the top of page 760 in your
textbook.
What is meant by the term combination?
Reading the Lesson
Complete the chart.
Situation
Permutation or
Combination?
Explain Your Choice
1. 3 of 7 students are chosen
Lesson 14-2
to go to a job fair
2. arrangement of student
work for the school art show
3. 4-digit student I.D. numbers
4. choosing 4 out of
12 possible pizza toppings
Helping You Remember
5. To help you remember how the terms permutation and combination are different, think
of everyday words that start with the letters P and C and that illustrate the meaning of
each word. Explain how the words illustrate the two terms.
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Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
14-3 Skills Practice
Probability of Compound Events
A bag contains 2 green, 9 brown, 7 yellow, and 4 blue marbles. Once a marble is
selected, it is not replaced. Find each probability.
4
231
3
22
2. P(green, then blue) }
1
11
4. P(blue, then blue) }
1. P(brown, then yellow) }
2
77
3. P(yellow, then yellow) }
17
231
57
154
5. P(green, then not blue) }
6. P(brown, then not green) }
A die is rolled and a spinner like the one at
the right is spun. Find each probability.
1
24
A
D
7. P(4 and A) }
B
C
1
8. P(an even number and C) }
8
1
6
9. P(2 or 5 and B or D) }
1
2
One card is drawn from a standard deck of 52 cards. Find each probability.
2
13
12. P(red or black) 1
11. P(jack or ten) }
7
13
4
13
13. P(queen or club) }
14. P(red or ace) }
11
26
3
4
15. P(diamond or black) }
16. P(face card or spade) }
Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30
are placed in a second box. The first tile is randomly drawn from the first box.
The second tile is randomly drawn from the second box. Find each probability.
3
16
17. P(both are greater than 15) }
7
20
18. The first tile is odd and the second tile is less than 25. }
3
80
19. The first tile is a multiple of 6 and the second tile is a multiple of 4. }
21
50
20. The first tile is less than 15 and the second tile is even or greater than 25. }
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Glencoe Algebra 1
Lesson 14-3
10. P(a number less than 5 and B, C, or D) }
NAME ______________________________________________ DATE______________ PERIOD _____
14-3 Practice
(Average)
Probability of Compound Events
A bag contains 5 red, 3 brown, 6 yellow, and 2 blue marbles. Once a marble is
selected, it is not replaced. Find each probability.
1
84
3
112
1. P(brown, then yellow, then red) }
2. P(red, then red, then blue) }
3
28
3. P(yellow, then yellow, then not blue) }
1
70
4. P(brown, then brown, then not yellow) }
A die is rolled and a card is drawn from a standard deck of 52 cards. Find each
probability.
1
4
1
78
5. P(6 and king) }
6. P(odd number and black) }
1
12
7. P(less than 3 and heart) }
5
156
8. P(greater than 1 and black ace) }
One card is drawn from a standard deck of 52 cards. Find each probability.
10
13
9. P(spade or numbered card) }
23
26
11. P(red or not face card) }
3
26
49
12. P(heart or not queen) }
52
10. P(ace or red queen) }
Tiles numbered 1 through 25 are placed in a box. Tiles numbered 11 through 30
are placed in a second box. The first tile is randomly drawn from the first box.
The second tile is randomly drawn from the second box. Find each probability.
4
125
13. P(both are greater than 15 and less than 20) }
51
100
16
15. The first tile is a multiple of 3 or prime and the second tile is a multiple of 5. }
125
14. The first tile is greater than 10 and the second tile is less than 25 or even. }
16. The first tile is less than 9 or odd and the second tile is a multiple of 4 or less than 21.
51
}
125
17. WEATHER The forecast predicts a 40% chance of rain on Tuesday and a 60% chance on
Wednesday. If these probabilities are independent, what is the chance that it will rain on
both days? 24%
FOOD Tomaso places favorite recipes in a bag for 4 pasta dishes, 5 casseroles,
3 types of chili, and 8 desserts.
18. If Tomaso chooses one recipe at random, what is the probability that he selects a pasta
9
dish or a casserole? }
20
19. If Tomaso chooses one recipe at random, what is the probability that he does not select a
3
dessert? }
5
20. If Tomaso chooses two recipes at random without replacement, what is the probability that
2
the first recipe he selects is a casserole and the second recipe he selects is a dessert? }
19
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Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
14-3 Reading to Learn Mathematics
Probability of Compound Events
Pre-Activity
How are probabilities used by meteorologists?
Read the introduction to Lesson 14-3 at the top of page 769 in your
textbook.
Is it more likely to rain or not rain on Saturday? on Sunday? Explain.
Reading the Lesson
1. Complete the chart.
Term
independent events
Example
Formula
Rolling two dice
P(A and B) 5 P(A) ? P(B)
dependent events
Lesson 14-3
mutually exclusive
events
inclusive events
2. In probability, what is meant by the phrase with replacement?
Helping You Remember
3. Look up the following terms in a dictionary. Write the definitions that best relate to the
way these terms are used in probability.
independent
dependent
exclusive
inclusive
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847
Glencoe Algebra 1