Download 7th Grade Probability Chapter Questions How can the collection

7th Grade Probability Chapter Questions
1. How can the collection, organization and display of data help to interpret, evaluate inferences
and make predictions about real-life situations and circumstances?
2. How does probability relate to real world application problems?
3. How can measures of center and variation be used to compare two sets of data?
4. How are different events classified and what can I use to solve them?
5. How can finding the ways to count the possible outcomes of compound events be used to
determine their probability?
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Chapter Problems
Introduction to Probability
Classwork
A jar contains 6 red, 8 blue, one white, 7 black, and two yellow marbles.
Use this information to determine the probability of selecting:
1)
2)
3)
4)
5)
a white marble
a red marble
a yellow marble
a purple marble
a black marble
Homework
A spinner is divided into 8 sections of equal size. The sections are numbered 1 through 8.
Use this information to determine the probability of the needle landing on:
6)
7)
8)
9)
10)
section 7
an even numbered section
section 1, 2, 3, or 4
section 9
section 8
Experimental and Theoretical Probability
Classwork
11) A die is rolled. Complete the table.
Roll Theoretical Probability
1
2
3
4
5
6
12) A die is rolled 10 times and the outcomes are:
Outcome
Roll 1
Roll 2
Roll 3
Roll 4
Roll 5
Roll 6
Number of Times
0
3
1
3
2
1
Use the above table to find the experimental probability for the following questions.
a. rolling a 1
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b.
c.
d.
e.
rolling a 2
rolling a 3
rolling a 4
rolling a 5
Homework
A spinner contains 8 equally divided sections, two sections have the letter A, 3 sections have the letter
B, one section has the letter C, one section has the letter D, and one section has the letter E.
13) Draw a picture of the spinner.
14) Use your drawing to fill in the chart.
Spin Theoretical Probability
A
B
C
D
E
15) The spinner is spun 10 times and the outcomes are:
Outcome
A
B
C
D
E
Number of Times
4
1
3
2
0
Use the table above to find the experimental probability for the following questions.
a. spinning an A
b. spinning a B
c. spinning a C
d. spinning a D
e. spinning an E
Sampling
Classwork
16) In a survey of 300 voters, 68 said they voted for Candidate A. How many votes can Candidate
A expect to receive if the population of the town is 10,000?
17) In a capture-recapture study, 97 grizzly bears were tagged and released back into the wild. A
month later, 200 bears were captured of which 36 were tagged. About how many grizzly bears
are in the population?
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18) From a survey of 100 commuters about how they get to work, 38 said they drive their cars, 47
said they take the bus, 14 said they take the subway, and 1 said they ride their bicycle. Out of
4,800 commuters, predict how many will commute to work in each of the following way.
a. Car
b. Bus
c. Subway
d. Bicycle
19) To determine the consistency of a printer, 100 printed sheets are randomly checked and 4
sheets are defective. Is this sample reliable? About how many defective sheets would be
expected if 2,400 sheets were printed?
20) The cafeteria employees would like to start selling fruit in the morning. They surveyed 24
students by asking every 8th student that entered the cafeteria for breakfast. Four students
said they preferred apples, 3 preferred oranges, and 1 preferred peaches. If 336 students
purchase breakfast daily, about how many students can they expect to pick an orange?
Homework
21) In a capture-recapture study, 83 mountain lions were tagged and released back into the wild.
Several months later, 300 mountain lions were captured, of which 54 were tagged. About how
many mountain lions are in the population?
22) In a survey of 1056 voters at Roberts School, 274 said they voted for Candidate A. How many
votes can Candidate A expect to receive if there were 5,101 votes?
23) From a survey of 80 students about their favorite subjects, 24 said Language Arts, 16 said
Science, 31 said Mathematics, and 9 said Social Studies. Out of 960 students, predict how
many will favor each subject.
a. Language Arts
b. Science
c. Mathematics
d. Social Studies
24) A DVD player manufacturing company wants to test the quality of their DVD players. They
randomly pick 50 DVD players to test and determine that 4 are defective. Is this sample
reliable? About how many defective DVD players would you expect if 1,000 DVD players are
made?
25) A library wants to expand their children’s book section. The librarians surveyed 30 children by
asking every 6th child that visited the library to figure out what genres were most popular. The
children’s responses were: 12 liked fiction, 8 liked non-fiction, 4 liked science fiction, and 6
liked mystery. If the library expects 540 children to visit the library in a week, about how many
children will check out a mystery book?
Word Problems
Classwork
26) You made 8 out of 15 shots on goal. Use experimental probability to predict how many goals
you will make tomorrow if you take 70 shots.
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27) There are 1000 buttons in the jar. You randomly select 10 buttons and get 3 red, 4 blue, 2
white, 1 black. Use experimental probability to predict how many buttons in the jar are:
a. Red
b. Blue
c. White
d. Black
28) A die is rolled. What is the theoretical probability for rolling a 3?
Mary rolls a die six times and rolls a 3, on two of the rolls. What is the experimental probability
for rolling a 3?
29) Create a situation where the experimental probability and the theoretical probability have the
same value.
30) A coin is flipped. What is the theoretical probability for flipping a tail?
Mark and John flip a coin twenty times and get 8 heads, 12 tails. What is the experimental
probability for flipping a tail? If Mark & John flip the coin 100 times, what do you think will
happen to the experimental probability?
Homework
31) Bart makes 20% of his free throws. If he takes 500 free throws, how many go in the basket?
Predict how many baskets Bart makes when he takes 25 free throws.
32) A factory produces 1000 light bulbs per minute. Each minute, one bulb produced will be
defective. What is the theoretical probability of selecting the defective bulb from the light
bulbs produced in one minute? What is the theoretical probability of selecting a defective bulb
from the light bulbs produced in one hour?
33) Every 100th box of candy contains a prize. What is the theoretical probability for selecting the
box of candy with a prize? A case contains 1000 boxes and how many prizes? What is the
probability of selecting a box containing a prize from a case?
34) Create a situation where the experimental probability is greater than the theoretical
probability.
35) How does understanding probability help someone who plays cards?
Probability of Compound Events
Classwork
36) You are given a pair of dice. One die is numbered 1 through 6 but the other die is numbered 7
through 12. What are the odds of rolling a 3 and an 8?
37) A machine generates numbers randomly from balls numbered 5 through 15. Two numbers are
selected, with replacement. What are the odds that both the numbers picked will be 8?
38) A bag with 6 blue marbles, 3 green marbles, and 4 orange marbles is lying on a table. What is
the probability that John will pick 2 green marbles? (without replacement)
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39) What is the probability that the first three cards drawn from a full deck of cards are clubs?
(without replacement)
40) There are 6 male puppies and 3 female puppies. What is the probability that the first two
puppies chosen will be males? (without replacement)
Homework
41) What is the probability that the first three cards drawn from a full deck of cards are kings?
(without replacement)
42) You dropped two coins. What is the probability that they will both land on heads?
43) Bill Gates wrote a computer program that generates three random numbers between 1 and
10. What is the probability that all three values will be three?
44) A lottery machine generates numbers randomly. Three numbers are picked between 1 and
20. What is the probability that all three numbers that are picked are 17?
45) There are 4 blue marbles and 2 red marbles. A marble is selected and not returned. What is
the probability that two red marbles will be chosen?
Fundamental Counting Principle
Classwork
46)
A restaurant has 4 appetizers, 9 entrees, and 5 dessert choices. How many meals are
possible? If the restaurant wants to increase their meals as much as possible by adding one
more item, should they add an appetizer, an entrée or a dessert?
47)
Martha has 8 shirts, 6 pair of pants, and 4 different pair of shoes. Assuming everything
matches, how many days can Martha go without wearing the same outfit?
48)
How many different 7 digit telephone numbers are there, if the first digit cannot be 0?
49)
By adding an area code to each 7 digit telephone number, the phone company increased the
amount of telephone numbers by how many? (Remember that the first digit in the area code
and the phone number itself cannot be 0.)
50)
One state is considering creating license plates where letters cannot be repeated.
If the state has license plates consisting of three letters, followed by three different digits, how
many fewer license plates are available when repetition of letters is not allowed?
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Homework
51)
A phone comes in 12 different colors, 5 different head sets, and 7 different styles. How many
different phones are available?
52)
Mark is taking a 10 question, True/False quiz. How many different ways can the quiz be
answered?
53)
Frank is calling his sister and can’t remember the first two digits of her phone number. He
remembers the remaining five digits. What is the greatest number of attempts that Frank would
have to make to complete the call? (He knows that the first digit of his sister’s phone number is
not 0.)
54)
A combination lock has a combination of 5 single digits, none of which are repeated. How many
different combinations are there?
55)
A pizza parlor provides customers with the opportunity to create their own single topping pizza
by selecting from 4 different crusts, 5 different sauces, 3 different cheeses, and 15 different
toppings. How many pizzas are possible? If a second different topping choice is allowed, how
many pizzas are possible?
Measures of Center
Classwork
Use the stem-and-leaf plot to answer the following questions.
Stem
1
2
3
Leaf
0 0 1
4 5 7
2
Key
56)
57)
58)
59)
1
2 = 12
What is the mean?
What is the median?
What is the mode?
Which measure of center best describes the data set? Explain.
Homework
Use the stem-and-leaf plot to answer the following questions.
Stem
4
5
6
Leaf
5 5
2 2 5 6
Key
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60)
61)
62)
63)
What is the mean?
What is the median?
What is the mode?
Which measure of center best describes the data set? Explain.
Measures of Variation
Classwork
Use the data set to answer the following questions.
6, 6, 8, 2, 3, 2, 5, 0, 1, 2, 3
64) What is the median?
65) What is the lower quartile?
66) What is the upper quartile?
67) What is the least value?
68) What is the greatest value?
69) What is the interquartile range?
70) What is the range?
Homework
Use the data set to answer the following questions.
12, 21, 15, 12, 27, 22, 19, 19, 20, 23
71) What is the median?
72) What is the lower quartile?
73) What is the upper quartile?
74) What is the least value?
75) What is the greatest value?
76) What is the interquartile range?
77) What is the range?
Mean Absolute Deviation
Classwork
Use the following data to answer the next set of questions. Round your answers to the nearest
hundredth.
Number of Students per Class at the Local Community College
x
x
x
x
30
31
x
x
x
x
x
x
x
32
33
34
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35
36
x
x
x
37
38
39
40
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Number of Students per Class at the State College
30
31
x
x
x
x
x
x
x
32
33
34
x
x
x
x
x
x
35
36
37
38
x
x
x
x
x
x
x
39
40
78) What is the mean number of students per class at the local community college?
79) What is the mean number of students per class at the state college?
80) What is the difference of the means?
81) What is the mean absolute deviation of the data set for the local community college?
82) What is the mean absolute deviation of the data set for the state college?
83) Which college has more variability in the number of students it has per class? Explain your
answer.
Homework
Use the following data to answer the next set of questions. Round your answers to the nearest
hundredth.
Points Earned per Game for the Timberwolves
x
0
x
1
2
x
x
x
x
x
x
0
1
2
3
4
x
x
x
x
x
5
6
7
x
x
x
x
x
x
x
x
x
8
9
10
9
10
Points Earned per Game for the Little Giants
x
x
x
x
x
x
x
x
x
x
3
4
5
6
7
8
84) What is the mean number of points earned by the Timberwolves per game?
85) What is the mean number of points earned by the Little Giants per game?
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86) What is the difference of the means?
87) What is the mean absolute deviation of the data set for the Timberwolves?
88) What is the mean absolute deviation of the data set for the Little Giants?
89) Which team has more variability in the number of points it earns per game? Explain your
answer.
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Probability Unit Review
Multiple Choice – Choose the correct answer for each question.
1) A bag contains 12 red marbles, 4 black marbles, 4 purple marbles and 2 pink marbles. What
is the probability of selecting a black marble?
a.
4
7
2
11
b.
c. 4
4
23
d.
2) A bag contains 12 red marbles, 4 black marbles, 4 purple marbles and 2 pink marbles. What
is the probability of selecting a white marble?
a.
4
7
b. 1
c. 0
d.
4
23
3) A die is rolled 8 times and a “5” is rolled three times. What is the experimental probability for
rolling a 5?
a.
5
8
b.
3
8
c.
3
5
d. 1
4) Sam hits the baseball 15% of the time. If he swings the bat 40 times, how many hits should
he expect to make?
a. 6
b. 15
c. 20
d. 40
5) An ice cream stand has 15 flavors of ice cream, 3 types of syrup, and 10 different
toppings. How many different sundaes, consisting of one flavor of ice cream, one
s yr u p , a n d o n e t o p p i n g d o e s t h e s t a n d s e r ve ?
a. 15
b. 45
c. 225
d. 450
6) A town has all phone numbers beginning with the same three digits, followed by 4 digits
where repetition is allowed. How many different phone numbers are possible?
a.
7,200,000
b. 10,000
c. 720
d. none of these
7) Awards are given to the first, second and third place winners of a race in which 10 people
participated. How many possible ways can the awards be given?
a. 6
b. 720
c. 10!
d. none of these
8) Ted is choosing 4 songs from an album that contains 18 songs. How many possible
arrangements are there for Ted to create if the order of the songs doesn’t matter?
a. 24
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b. 3,060
c. 18!
d. none of these
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9) What is the probability of selecting two red cards from a deck of cards? (with replacement)
a.
1
4
b.
1
2
c.
3
4
d. none of these
10) In a sample of 75 randomly selected students at a school, 32 are female. There are 1,371
students in the school. Using these results, predict the number of females in the school.
a. 275
b. 343
c. 585
d. 686
11) The car dealership’s inventory is shown below
Sunrise Car Dealership
Car Make
Number of Cars
Ford
550
Nissan
425
BMW
630
If a car is selected at random, what is the probability that the car selected is not a
Ford or Nissan?
a.
b.
c.
d.
0.26
0.34
0.39
0.40
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12) What is the probability of rolling a prime number or a number greater than 3 on a die?
a.
5
6
b.
2
3
c. 1
d. none of these
Short Constructed Response – Write the correct answer for each question.
13) Determine how many three-letter arrangements are possible with the letters
R , A , N , D , O , a n d M if no letter may be repeated.
14) What is the probability of rolling snake eyes on a pair of dice?
15) What is the probability of selecting a club and a heart from a deck of cards (without
replacement)?
16) P(rain) = 10% ; P(no rain ) = ___________
17) What is the probability of selecting a club or a jack from a deck of cards?
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Extended Constructed Response – Solve the problem, showing all work.
18) The amount of December snowfall, in inches, was recorded on the dot plots below. Use the
following dot plots to answer the questions below.
Snowfall – Oswego, NY
x
x
x
x
x
x
18
19
20
21
x
x
22
23
x
x
x
x
x
24
x
x
x
x
x
x
x
x
x
x
x
x
x
25
26
27
28
Snowfall – Fulton, NY
x
x
x
x
x
x
24
25
26
27
x
x
x
x
x
x
x
x
28
29
30
x
31
32
x
33
34
a. What is the mean amount of snowfall in each town?
b. What is the difference of the means?
c. What is the mean absolute deviation of each of the data sets?
d. Which town has more variability in the amount of December snowfall?
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Answer Key
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
1/24
1/4
1/12
0
7/24
1/8
1/2
1/2
0
1/8
Roll
1
2
3
4
5
6
Theoretical Probability
1/6
1/6
1/6
1/6
1/6
1/6
12)
a.
b.
c.
d.
e.
0
3/10
1/10
3/10
1/5
13)
A
A
E
B
D
B
C
B
14)
Spin
A
B
C
D
E
Theoretical Probability
¼
3/8
1/8
1/8
1/8
15)
a.
b.
c.
d.
e.
16) 2,266
2/5
1/10
3/10
1/5
0
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17) 539
18)
a. 1,824
b. 2,256
c. 672
d. 48
19) Yes; 96
20) 42
21) 461
22) 1323
23)
a. 288
b. 192
c. 372
d. 108
24) Yes; 80
25) 108
26) 37 shots
27)
a. 300 Red
b. 400 blue
c. 200 white
d. 100 black
28) 1/6; 1/3
29) Multiple answers
30) ½; 3/5 multiple answers ex: odds will even out
31) 100; 5
32) 1/1000; 60/60000
33) 1/100; 10; 10/1000
34) Multiple answers
35) Multiple answers
36) 1/36
37) 1/121
38) 1/26
39) 11/850
40) 5/12
41) 1/5525
42) 1/4
43) 1/1000
44) 1/8000
45) 1/15
46) 180, Appetizer
47) 192
48) 9,000,000
49) 8.1x109
50) 1,422,720
51) 420
52) 1,024
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53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
81)
82)
83)
84)
85)
86)
87)
88)
89)
90
30,240
900, 960
19.86
24
10
Mean/median; explanations will vary
5.75
6.2
4.5 and 6.2
Median; explanations will vary
3
2
6
0
8
4
8
19.5
15
22
12
27
7
15
33.36
36.25
2.89
1.89
2.4
State college
6.75
3.5
3.25
2.03
2
Very similar but timberwolves have a slightly higher variability
Unit Review Answers
1) B
2) C
3) B
4) A
5) D
6) B
7) B
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8)
9)
10)
11)
12)
13)
14)
15)
B
B
C
C
A
120
1
36
13
204
16) 90%
17)
4
13
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