Download B - Atlanta Public Schools

Unit 1 - Outcomes and Likelihoods - 8th Grade - B
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
____
____
1. Akira reviewed the recent records for dog license applications. He counted the number of applications for
different types of dogs. The table shows the information that Akira collected. Estimate the probability that the
next dog license application will be for a husky. Express your answer as a percent. If necessary, round your
answer to the nearest tenth.
Husky
Dalmatian
Collie
Bulldog
Other
Dog
Number of
25
12
10
22
27
Licenses
a. 26%
c. 384%
b. 35.2%
d. 74%
2. Mitsugu took a survey of high school students to see how many had part-time jobs last summer. The results of
the survey are shown in the table. Compare the probability that a student in the sophmore class had a
part-time job to the probability that a student in the freshman class had a part-time job.
Students Who Had a
Grade Level
Students
Summer Job
Freshman
25
37
Sophomore
18
58
Junior
21
39
Senior
13
44
a. A sophmore is just as likely as a freshman to have a job.
b. A sophmore is less likely than a freshman to have a job.
c. A sophmore is more likely than a freshman to have a job.
3. While waiting for the school bus, Paula records the colors of all cars passing through an intersection. The
table shows the results. Estimate the probability that the next car through the intersection will be red. Express
your answer as a percent. If necessary, round your answer to the nearest tenth.
Red
Gray
Green
Yellow
Car Color
8
20
14
5
Number of Cars
a. 83%
c. 8%
b. 17%
d. 20.5%
4. You are playing a game that uses two fair number cubes. If the total on the number cubes is either 11 or 3 on
your next turn, you win the game. What is the probability of winning on your next turn? Express your answer
as a percent. If necessary, round your answer to the nearest tenth.
a. 88.9%
c. 0.3%
b. 11.1%
d. 5.6%
5. An experiment consists of rolling two fair number cubes. The diagram shows the sample space of all equally
likely outcomes. What is the probability of rolling exactly one 3? Express your answer as a fraction in
simplest form.
a.
2
9
c.
5
18
b.
18
5
d.
13
18
During lunch at Urbana Middle School today, several students have brought their lunch from home and
several students are ordering a school lunch as shown in the table. Suppose one student is randomly selected
during lunch time. Find the probability of each event. Write as a fraction in simplest form.
Brought lunch from home
Order school lunch
6th Graders
7th Graders
8th Graders
____
6. P(brought lunch from home or ordered school lunch)
a.
c.
b.
____
d. 1
7. P(not 7th grader)
a.
c.
b.
____
55
45
32
35
33
d.
8. Leon is on the school archery team. The target has a center bull’s-eye and two rings around the bull’s-eye.
The table gives the probabilities of each outcome. What is the probability that Leon will get the next arrow in
the inner or outer ring? Express your answer as a decimal.
Outcome
Bull’s-eye
Inner ring
Outer ring
Miss
Probability
0.042
0.167
0.292
0.499
a. 0.209
c. 0.334
b. 0.459
d. 0.042
____ 9. Josh works at the local deli making sandwiches. Each sandwich has 1 type of cheese and 1 type of meat on
bread. The deli has white, wheat, and rye bread available. The meat choices are turkey and ham, and the
cheese choices are American and Swiss. Describe all possible sandwiches that Josh can make at the deli.
a. The possible sandwich combinations are (wheat, American, turkey), (wheat, American,
ham), (wheat, Swiss, turkey), (wheat, Swiss, ham), (rye, American, turkey), (rye,
American, ham), (rye, Swiss, turkey), and (rye, Swiss, ham).
b. The possible sandwich combinations are (wheat, American, turkey), (wheat, American,
ham), (wheat, Swiss, turkey), (wheat, Swiss, ham), (white, American, turkey), (white,
American, ham), (white, Swiss, turkey), and (white, Swiss, ham).
c. The possible sandwich combinations are (wheat, American, turkey), (wheat, American,
ham), (wheat, Swiss, turkey), (wheat, Swiss, ham), (white, American, turkey), (white,
American, ham), (white, Swiss, turkey), (white, Swiss, ham), (rye, American, turkey),
(rye, American, ham), (rye, Swiss, turkey), (rye, Swiss, ham), (wheat, Swiss, American),
(white, Swiss, American), and (rye, Swiss, American).
d. The possible sandwich combinations are (wheat, American, turkey), (wheat, American,
ham), (wheat, Swiss, turkey), (wheat, Swiss, ham), (white, American, turkey), (white,
American, ham), (white, Swiss, turkey), (white, Swiss, ham), (rye, American, turkey),
(rye, American, ham), (rye, Swiss, turkey), and (rye, Swiss, ham).
____ 10. Jean has one quiz each week in social studies class. The table gives the probability of having a quiz on each
day of the week. What is the probability that Jean will have a quiz Wednesday, Thursday, or Friday? Express
your answer as a percent.
Monday
Tuesday
Wednesday
Thursday
Friday
Day
0.19
0.27
0.070
0.22
0.25
Probability
a. 54%
c. 7%
b. 46%
d. 25%
____ 11. Consider the spinner shown. Give the probability for each outcome of the spinner. Express your answers as
decimals.
a.
c.
b.
d.
____ 12. A bag contains orange, white, and purple marbles. If you randomly choose a marble from the bag, there is a
23% chance of drawing an orange marble and a 50% chance of drawing a white marble. Give the probability
for each outcome. Express your answers as percents.
a.
c.
b.
d.
A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a
marble at random without looking. Find the probability of each event. Write your answer as a fraction in
simplest form.
____ 13. P(red or white)
a.
c.
b.
d.
____ 14. P(not white)
a.
b.
c.
d.
____ 15. A teacher asks each student in the class to randomly choose a number from 1 to 100 and write it down.
Masami and Peter each write down a number. What is the probability that both of their choices will be greater
than 60? Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
a. 0.4
c. 0.84
b. 0.158
d. 0.16
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
____ 16. choosing a card from a deck of cards numbered 10, 11, 12, ..., 25 and picking a day of the week
a. 175
c. 112
b. 124
d. 156
____ 17. choosing a tuna, turkey, or cheese sandwich; on wheat or white bread; with a side of potato chips, corn chips,
or baked potato
a. 18
c. 8
b. 24
d. 9
____ 18. choosing a number from 1 to 15 and a vowel from the word COUNTING
a. 120
c. 90
b. 45
d. 55
____ 19. An experiment consists of spinning the spinner shown. All outcomes are equally likely. What is the
probability that the spinner will land on an even number? Express your answer as a fraction in simplest form.
a.
5
2
c.
4
3
b.
2
5
d.
3
5
____ 20. A state offers specialty license plates that contain 3 letters followed by 2 numbers. License plates are assigned
randomly. All license plates are equally likely. Find the probability of being assigned the license plate JSL 94.
Express your answer as a fraction in simplest form.
1
a. 1
c.
100
b.
4,394
d.
1
1,757,600
1,757,600
1
____ 21. A spinner is divided into three sections: red, blue, and green. The red section is
The blue section is
as fractions.
a.
b.
1
3
1
5
of the area of the spinner.
of the area of the spinner. Give the probability for each outcome. Express your answers
c.
d.
____ 22. A pouch contains 35 green beads, 25 red beads, and 10 yellow beads. How many blue beads should be added
1
so that the probability of drawing a red bead is 2 ?
a. 100 blue beads
c. 50 blue beads
b. 30 blue beads
d. 25 blue beads
____ 23. An experiment consists of spinning the spinner shown. All outcomes are equally likely. What is the
probability that the spinner will land on 1? Express your answer as a fraction in simplest form.
a.
1
3
c.
3
1
b.
2
3
d.
3
2
____ 24. An experiment consists of rolling two fair number cubes. The diagram shows the sample space of all equally
likely outcomes. What is the probability of rolling two 4’s? Express your answer as a fraction in simplest
form.
a.
2
9
c.
1
6
b.
1
36
d.
36
1
For the situation below, make a tree diagram to show the sample space. Then choose the total number of
outcomes.
____ 25. rolling a number cube and choosing a card between the cards marked X and Y
a. 6
c. 8
b. 20
d. 12
____ 26. Kimi is planning her week at science camp. Her options are listed in the table. She has to participate in one
outdoor activity, one clean-up crew, and one science project. How many weekly plans are available? Kimi
wants to go hiking. How many options are available to her that include hiking?
Science Camp
Hiking
Outdoor Activities
Clean-Up Crews
Science Projects
Swimming
Canoeing
Breakfast
Lunch
Dinner
Snacks
Catapult
Butterflies
Mapping
Forestry
a. 48 total options; 16 if Kimi goes hiking
b. 36 total options; 12 if Kimi goes hiking
c. 11 total options; 8 if Kimi goes hiking
d. 24 total options; 12 if Kimi goes hiking
Essay - choose ONE to answer. You may answer the other one for extra credit.
27. John is playing a computer game where he has to shoot a ball at a goal. If he misses on the first try, he can
shoot a second time. John says he misses about 40% of the time on his first try and 30% of the time on his
second try.
a. John plays the game once. What is the chance that John misses the goal both times?
b. What is the chance that John misses on his first try and hits the goal on his second try?
c. John plays the game 10 times. Is it possible for him to hit the goal 8 out of 10 times on his first try?
.
28. Mary wants to know whether students at her school, Julian Middle School, prefer to go to the movies or
prefer to watch TV. She interviewed 12 of her friends, and based on their preferences, she decided that of
the school prefers to go to the movies and
prefers to watch TV.
a. Do you think Mary’s results are reliable? Explain why or why not.
b. Julian Middle School has a total of 324 students. Describe another way to find out whether students at
Julian Middle School prefer going to the movies or stay home to watch TV. Make sure your method will
provide reliable results.
Unit 1 - Outcomes and Likelihoods - 8th Grade - B
Answer Section
MULTIPLE CHOICE
1. ANS: A
To estimate the probability from experimental observations, use the information in the table.
To express the probability as a percent, multiply the fractional probability by 100%.
Feedback
A
B
C
D
Correct!
Divide the number of dog licenses of the specified breed by the total number of dog
license applications.
The probability of any event is a number between 0% to 100%.
This is the probability that the next dog license application will NOT be for the
specified type of dog.
PTS: 1
DIF: Average
REF: Page 527
OBJ: 10-2.1 Estimating the Probability of an Event
STA: M8D3.a
TOP: 10-2 Experimental Probability
2. ANS: B
To estimate the probability, use the information in the table.
NAT: 8.4.4.c
KEY: estimate | probability
Compare these probabilities for each of the grade levels mentioned in the question.
Feedback
A
B
C
Find the probabilities and compare.
Correct!
Use the correct numbers.
PTS: 1
DIF: Average
REF: Page 528
OBJ: 10-2.2 Application
NAT: 8.4.4.c
STA: M8D3.a
TOP: 10-2 Experimental Probability
KEY: experimental probability | probability
3. ANS: B
To estimate the probability from experimental observations, use the information in the table.
To express the probability as a percent, multiply the fractional probability by 100%.
Feedback
A
B
This is the probability of NOT seeing a car of the specified color.
Correct!
C
D
Divide the number of cars with the specified color by the total number of cars observed.
Divide the number of cars with the specified color by the total number of cars observed.
PTS: 1
DIF: Average
REF: Page 527
OBJ: 10-2.1 Estimating the Probability of an Event
NAT: 8.4.4.c
STA: M8D3.a
TOP: 10-2 Experimental Probability
KEY: estimate | probability
4. ANS: B
It is impossible to roll two different totals at the same time, so the events are mutually exclusive. Add the
probabilities to find the probability of winning on your next turn. To find the probabilities, first list the sample
space.
1, 1
2, 1
3, 1
4, 1
5, 1
6, 1
1, 2
2, 2
3, 2
4, 2
5, 2
6, 2
1, 3
2, 3
3, 3
4, 3
5, 3
6, 3
1, 4
2, 4,
3, 4
4, 4
5, 4
6, 4
1, 5
2, 5
3, 5
4, 5
5, 5
6, 5
1, 6
2, 6
3, 6
4, 6
5, 6
6, 6
The number of outcomes in the sample space is 36.
Feedback
A
B
C
D
This is the probability of NOT rolling either of the specified totals. Find the probability
of rolling either of the specified totals.
Correct!
For mutually exclusive events, add the probabilities.
For mutually exclusive events, add the probabilities.
PTS: 1
DIF: Average
REF: Page 542
OBJ: 10-4.4 Finding the Probability of Mutually Exclusive Events
NAT: 8.4.4.h
STA: M8D3.a
TOP: 10-4 Theoretical Probability
KEY: mutually exclusive events | probability
5. ANS: C
The probability is the number of pairs of number cubes matching the criteria divided by the total number of
pairs in the sample space.
Feedback
A
B
C
D
Divide the number of outcomes in the event by the total number of outcomes.
The probability of any event is a number from 0 to 1.
Correct!
Use the formula for theoretical probability.
PTS: 1
DIF: Average
REF: Page 541
OBJ: 10-4.2 Calculating Theoretical Probability for Two Fair Number Cubes
NAT: 8.4.4.b
STA: M8D3.a
TOP: 10-4 Theoretical Probability
KEY: probability | theoretical probability
6. ANS: D
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
How many of the students at Urbana either brought their lunch from home or are
ordering a school lunch?
How many of the students at Urbana either brought their lunch from home or are
ordering a school lunch?
Make sure your answer seems reasonable. Try again.
Correct!
PTS: 1
DIF: Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
TOP: Find the probability of a real-world simple event.
KEY: Probability | Simple event
MSC: 1999 Lesson 4-8
7. ANS: B
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
Double check your work and try again.
Correct!
Be careful when simplifying your fraction. Try again.
This is the probability that the student is a 7th grader. What is the probability that the
student is not a 7th grader?
PTS: 1
DIF: Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
TOP: Find the probability of a real-world simple event.
KEY: Probability | Simple event
MSC: 1999 Lesson 4-8
8. ANS: B
To find the probability of the next arrow hitting the inner ring or outer ring, add the individual probabilities
together, P(inner or outer rings) = P(inner ring) + P(outer ring). This sum represents the combined probability
of hitting either ring.
Feedback
A
B
C
D
This is the probability that the arrow will hit the bull's-eye or inner ring. Find the
probability of hitting the outer ring or inner ring.
Correct!
This is the probability that the arrow will hit the bull's-eye or the outer ring. Find the
probability of hitting the outer ring or inner ring.
This is the probability of NOT hitting the inner ring or outer ring while hitting the
target. In other words, this is the probability of hitting the bull's-eye.
PTS: 1
DIF: Average
REF: Page 523
OBJ: 10-1.2 Finding Probabilities of Events
NAT: 8.4.4.c
STA: M8D3.a
TOP: 10-1 Probability
KEY: probability
9. ANS: D
One way to find all possible combinations is by making a tree diagram where the breads, cheeses, and meats
are on different levels of the tree diagram.
Feedback
A
B
C
D
There are more combinations.
There are more combinations.
Make a tree diagram to find all of the possible combinations.
Correct!
PTS: 1
DIF: Average
REF: Page 559
OBJ: 10-8.2 Using a Tree Diagram
NAT: 8.4.4.e
STA: M8D2.a
TOP: 10-8 Counting Principles
10. ANS: A
To find the probability of having a quiz during a range of days, add the individual probability values for each
day of the week that is being considered. Then convert the total to a percent by multiplying by 100.
Feedback
A
B
C
D
Correct!
This is the probability of NOT having a quiz during the days considered. Find the
probability of having a quiz on those days.
This is the probability of having a quiz only on the first day. Find the probability of
having a quiz on the correct days.
This is the probability of having a quiz only on the last day. Find the probability of
having a quiz on the correct days.
PTS:
OBJ:
STA:
11. ANS:
Since
1
DIF: Average
REF: Page 523
10-1.2 Finding Probabilities of Events
NAT: 8.4.4.b
M8D3.a
TOP: 10-1 Probability
KEY: probability
C
of the spinner is labeled A, a reasonable estimate of the probability that the spinner will land on A is
.
Since
of the spinner is labeled B, a reasonable estimate of the probability that the spinner will land on B is
.
Finally, only
land on C is
of the spinner is labeled C, so a reasonable estimate of the probability that the spinner will
.
Feedback
A
B
C
The probabilities must add to 1.
It is not reasonable for the probability that the spinner will land on A to be greater than
the probability that it will land on B.
Correct!
D
The probabilities must add to 1.
PTS: 1
DIF: Basic
REF: Page 522
OBJ: 10-1.1 Finding Probabilities of Outcomes in a Sample Space
NAT: 8.4.4.f
STA: M8D3.a
TOP: 10-1 Probability
KEY: outcome | probability | sample space
12. ANS: B
The probabilities for the first two colors are given. To find the probability of the third color, subtract the first
two probabilities from 1.
Feedback
A
B
C
D
Not all the outcomes are equally likely to happen.
Correct!
The probabilities must add to 100%.
The probabilities must add to 100%.
PTS:
OBJ:
NAT:
KEY:
13. ANS:
1
DIF: Basic
REF: Page 522
10-1.1 Finding Probabilities of Outcomes in a Sample Space
8.4.4.b
STA: M8D3.a
TOP: 10-1 Probability
outcome | probability | sample space
A
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
Correct!
Double check your work and try again.
Be sure to write your answer in simplest form.
How many favorable outcomes are there? How many total outcomes are there?
PTS:
TOP:
MSC:
14. ANS:
1
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
Find the probability of a simple event.
KEY: Probability | Simple event
1999 Lesson 4-8
C
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
This is the probability of drawing a white marble. What is the probability that a white
marble is not drawn?
Double check your work and try again.
Correct!
How many marbles are not white? Compare this number with the total number of
possible outcomes.
PTS: 1
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
TOP: Find the probability of a simple event.
KEY: Probability | Simple event
MSC: 1999 Lesson 4-8
15. ANS: D
Each person’s choice is not affected by the other person’s choice, so the events are independent. Since the
numbers are chosen at random, all outcomes are equally likely, so the probability that a number is greater than
a given value is
. The events are independent, so multiply the
probabilities.
Feedback
A
B
C
D
This is the probability that one person will make the number choice specified in the
question. Find the probability that both people will make the number choice.
Determine whether the events are independent first.
This is the probability that the people will NOT choose numbers greater than the
specified value. Find the probability that they will choose numbers greater than the
specified value.
Correct!
PTS: 1
DIF: Average
REF: Page 545
OBJ: 10-5.2 Finding the Probability of Independent Events
NAT: 8.4.4.h
STA: M8D3.b
TOP: 10-5 Independent and Dependent Events
KEY: independent events | probability
16. ANS: C
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
16(7) = 112
Feedback
A
B
C
D
How many numbers are there between 10 and 25?
Double check your work and try again.
Correct!
Multiply the number of outcomes for each event to find the total number of outcomes in
the sample space.
PTS: 1
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
TOP: Use multiplication to count outcomes.
KEY: Probability | Counting
MSC: 1999 Lesson 13-3
17. ANS: A
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
3(2)(3) = 18
Feedback
A
B
C
D
Correct!
Multiply the number of outcomes for each event to find the total number of outcomes in
the sample space.
How many possible outcomes are there for each of the three choices?
Double check your work and try again.
PTS: 1
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
TOP: Use multiplication to count outcomes.
KEY: Probability | Counting
MSC: 1999 Lesson 13-3
18. ANS: B
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
15(3) = 45
Feedback
A
B
C
D
How many vowels are there in the word COUNTING?
Correct!
Double check your work and try again.
Multiply the number of outcomes for each event to find the total number of outcomes in
the sample space.
PTS:
TOP:
MSC:
19. ANS:
1
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
Use multiplication to count outcomes.
KEY: Probability | Counting
1999 Lesson 13-3
B
Since all outcomes are equally likely, the probability of the event is
.
Feedback
A
B
C
D
The probability of any event is a number from 0 to 1.
Correct!
Use the formula for theoretical probability.
Divide the number of outcomes in the event by the total number of outcomes.
PTS: 1
DIF: Average
REF: Page 540
OBJ: 10-4.1 Calculating Theoretical Probability
NAT: 8.4.4.b
STA: M8D3.a
TOP: 10-4 Theoretical Probability
KEY: probability | theoretical probability
20. ANS: B
The probability of being assigned a single particular license plate is:
.
Use the Fundamental Counting Principle find the number of possible license plates. For each letter on the
license plate, multiply by 26 (the number of letters in the alphabet). For each number on the license plate,
multiply by 10 (for the digits zero through nine).
Feedback
A
B
C
D
Use the Fundamental Counting Principle.
Correct!
Use the Fundamental Counting Principle.
Use the number of possible license plates as the denominator.
PTS: 1
DIF: Average
REF: Page 558
OBJ: 10-8.1 Using the Fundamental Counting Principle
NAT: 8.4.4.e
STA: M8D2.b
TOP: 10-8 Counting Principles
KEY: Fundamental Counting Principle
21. ANS: B
Reasonable probability estimates for the first two colors are the areas of the corresponding sections. To find
the probability of the third color, subtract the first two probabilities from 1.
Feedback
A
B
C
D
The probabilities must add to 1.
Correct!
Not all the outcomes are equally likely to happen.
The probabilities must add to 1.
PTS: 1
DIF: Average
REF: Page 522
OBJ: 10-1.1 Finding Probabilities of Outcomes in a Sample Space
NAT: 8.4.4.f
STA: M8D3.a
TOP: 10-1 Probability
KEY: outcome | probability | sample space
22. ANS: B
Adding beads to the pouch will increase the number of possible outcomes.
Set up a proportion, and find the cross products.
Feedback
A
B
C
D
Adding beads to the pouch will increase the number of possible outcomes.
Correct!
Set up a proportion and solve.
Check that the ratio of the number of red beads to the total number of beads is equal to
the required probability.
PTS: 1
NAT: 8.4.4.b
23. ANS: A
DIF: Average
STA: M8D3.a
REF: Page 541
OBJ: 10-4.3 Altering Probability
TOP: 10-4 Theoretical Probability
Since all outcomes are equally likely, the probability of each outcome is
.
Feedback
A
B
C
D
Correct!
This is the probability that the spinner will NOT land on the given number. Find the
probability that the spinner will land on the given number.
The probability of any event is a number from 0 to 1.
Use the total number of outcomes as the denominator.
PTS: 1
DIF: Basic
REF: Page 540
OBJ: 10-4.1 Calculating Theoretical Probability
NAT: 8.4.4.b
STA: M8D3.a
TOP: 10-4 Theoretical Probability
KEY: probability | theoretical probability
24. ANS: B
The probability is the number of outcomes where the number cubes show the same number divided by the
total number of outcomes in the sample space. No matter what the number, there is only 1 way the number
cubes will show this number. The total number of pairs in the sample space is 36. The probability is .
Feedback
A
B
C
D
Divide the number of outcomes in the event by the total number of outcomes.
Correct!
Find the number of possible outcomes in the sample space first.
The probability of any event is a number from 0 to 1.
PTS: 1
DIF: Average
REF: Page 541
OBJ:
NAT:
KEY:
25. ANS:
10-4.2 Calculating Theoretical Probability for Two Fair Number Cubes
8.4.4.b
STA: M8D3.a
TOP: 10-4 Theoretical Probability
probability | theoretical probability
D
There are twelve possible outcomes: 1X, 1Y, 2X, 2Y, 3X, 3Y, 4X, 4Y, 5X, 5Y, 6X, and 6Y.
Feedback
A
B
C
D
Double check your work and try again.
List all of the possible outcomes to make sure they are all unique.
List all of the possible outcomes for the number cube. Then branch off to list all of the
outcomes for choosing the card.
Correct!
PTS: 1
DIF: Average
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability | Tree diagram
MSC: 1999 Lesson 13-2
26. ANS: A
There are 3 outdoor activities, 4 clean-up crews, and 4 science projects. Using the Fundamental Counting
Principle, there are
weekly plans available to Kimi.
Since Kimi wants to go hiking, her only variability is in her choice of clean-up crew and science project.
Therefore she has
weekly plans available after choosing hiking.
Feedback
A
B
C
D
Correct!
Check your counting. There are 3 outdoor activities, 4 clean-up crews, and 4 science
projects. Use the Fundamental Counting Principle.
Use the Fundamental Counting Principle, multiplying together the total options in each
category.
Use the Fundamental Counting Principle, multiplying together the total options in each
category.
PTS: 1
DIF: Advanced
STA: M8D2.b
TOP: 10-8 Counting Principles
ESSAY
27. ANS:
Possible student answer
2.a. The chance is about 12%.
Sample explanations:
• I started with 100 first tries and found that 12 out of
100 times both shots failed to hit the goal.
• The chance both shots failed is
.
40% of 30% is 12%.
Suggested
Problem level
number of
score points
3
I
(Award 2
points for a
correct chance
tree and 1 point
for a correct
answer.)
b. The chance is 28%.
c. Yes, this is possible. You would expect John to hit the
goal 60% of the time on his first try. So 8 out of 10
seems quite possible. It is actually possible for John to
hit 10 in a row, although it is not likely.
d. He has an expected score of 88 points for the 100 games,
which is an average expected score per game of 0.88
points. For 100 games, he scores 60 on his first try and
28 on his second try. So he scores 88 points in all over
100 games.
PTS: 1
28. ANS:
Possible student answer
1.a. Mary’s results are probably NOT
reliable.
2
I
2
(Award 1 point
for “yes” and 1
point for a
correct
explanation.)
2
(Award 1 point
for the answer
and 1 point for
the calculation.)
I
Suggested number
of score points
2
Problem level
II
II
Sample explanation: Mary only asked
her friends, and these may not represent
the preferences of most students.
b. Different answers are possible. Sample
answer:
• Mary could randomly choose 10
students from each class or grade
level and interview them.
PTS: 1
2
(Award 1 point for
an alternative
method and 1 point
for a correct
explanation.)
II