Algebra 2 Ch10 Review - SHOW ALL WORK FOR FULL CREDIT Name: _________________
1. You spin a spinner with five equal spaces and roll a six-sided die. How many possible outcomes are in the
sample space?
____
2. A number is randomly chosen between 1 and 99. What is the probability that the number is not a multiple of 9?
a. 29
c. 10
33
99
b. 1
d. 8
9
9
3. A yard game requires players to toss a bean bag onto a board as shown below. The bean bag is equally likely to
land on any part of the board. Which region does the bean bag have a higher probability of landing on, region D
or region B?
6
4
A
6
B
C
4
2
10
D
____
4. A card is chosen at random from a deck of 24 cards, 4 red, 8 black, 6 blue, and 6 green. Then, the card is
returned to the deck and a new card is chosen. The table below shows the results of choosing 18 cards. For
which color of card is the experimental probability the same as the theoretical probability?
Results
red
black
blue
green
3
5
2
8
a. blue
b. black
____
c. red
d. green
5. A research study asked 2892 homeowners how many bedrooms were in their homes. The results are shown in
the table below. What is the probability that a homeowner chosen at random has 3 bedrooms?
Number of
Bedrooms
2 or less
Number of
Homeowners
318
3
1099
4
781
5 or more
694
a. about 11%
b. about 38%
c. about 24%
d. about 27%
6. You roll a six-sided die and then flip a coin. Make a sample space.
____
7. You play a game that requires rolling a six-sided die then randomly choosing a colored card from a deck
containing 3 red cards, 8 blue cards, and 6 yellow cards. Find the probability that you will roll a 2 on the die and
then choose a blue card.
a. 4
c. 8
51
17
b. 1
d. 1
6
17
8. A girl and a boy each randomly grab a piece of candy from a bowl containing 9 pieces of chocolate, 7 fruit
chews, 9 lollipops, and 9 peppermints. Find the probability that both events A and B will occur. Give your
answer as a fraction in reduced form.
Event A: A girl grabs a lollipop
Event B: A boy grabs a fruit chew
9. You are packing clothes for vacation and don’t want to take any t-shirts. You randomly choose 3 shirts from a
drawer containing 4 t-shirts, 3 polo shirts, and 3 button-downs.
a. What is the probability that the first 3 shirts are t-shirts when you replace each shirt before choosing the next
one?
b. What is the probability that the first 3 shirts are t-shirts when you do not replace each shirt before choosing
the next one?
c. Compare the probabilities.
10. Teacher 1 and Teacher 2, math teachers at the local high school, both gave their students the same test. The table
below shows the results from the two classes.
Teacher 1
Teacher 2
Pass
12
15
Fail
12
13
a. Find the probability that a randomly selected student from Teacher 1's class failed the test.
b. Find the probability that a randomly selected student who failed the test is from Teacher 1's class.
____ 11. At a sandwich shop, 42% of customers buy a drink with their sandwich. Only 28% of customers buy a drink and
chips with their sandwich. What is the probability that a customer who buys a drink also buys chips?
a. about 66.7%
c. 70%
b. 1.5%
d. 14%
12. You randomly survey 104 men and 113 women at a fitness center and ask if they regularly attend an exercise
class. Of those surveyed, 59 men and 71 women do regularly attend a class. Organize these results in a two-way
table. Then find and interpret the marginal frequencies.
13. The two-way table below shows the results of a survey of male and female drivers asking whether they text
while driving.
Male
Female
Text
228
200
Do Not Text
76
90
Use these survey results to make a two-way table that shows the joint and marginal relative frequencies.
14. An Eastern Caribbean tourism agency surveyed visitors to three different islands and asked whether they stayed
in a beachfront resort or condominium. The results, given as joint relative frequencies, are shown in the
two-way table.
Location
Beachfront Resort
Condominium
U.S. Virgin
Islands
0.28
0.04
St. Lucia
Barbados
0.27
0.05
0.28
0.08
a. What is the probability that a randomly selected visitor to Barbados stayed in a beachfront resort?
b. What is the probability that a randomly selected visitor who did not stay in a beachfront resort visited St.
Lucia?
c. Determine whether staying in a beachfront resort and visiting St. Lucia are independent events.
____ 15. A custom furniture builder wants to earn at least $30 per hour building four different types of furniture: dressers,
nightstands, armoires, and chests. Over the course of a year, the builder records the selling and hours worked for
each piece and determines whether or not the earning goal is met. The table shows these findings. Which type of
furniture best helps meet the earning goal? Show work to support your reasoning.
 $30 per Hour
< $30 per Hour
Dresser
Nightstand
Armoire
Chest
a. Chest
b. Nightstand
c. Dresser
d. Armoire
____ 16. You spin a spinner with 9 equal spaces numbered 1 through 9. What is the probability that the spinner lands on
a 5 or a 9.
a. 8
c. 1
9
9
b. 7
d. 2
9
9
17. One letter tile is randomly drawn from a set of 26 alphabet tiles representing letters A through Z. What is the
probability that the letter drawn is a vowel or is in the word “now”? Give your answer as a fraction in reduced
form.
____ 18. An amusement park has two featured rides that require an additional ticket, the Slingshot and the Scream Flyer.
On a summer day, 1279 visitors entered the park. 280 visitors bought tickets for either the Slingshot or the
Scream Flyer. 247 visitors bought a ticket for the Slingshot and 237 visitors bought a ticket for the Scream
Flyer. What is the probability that a randomly selected visitor bought tickets for both the Slingshot and the
Scream Flyer?
a. 0.159
c. 0.378
b. 0.219
d. 0.597
____ 19.
In how many ways can you arrange 5 of the numerals 1 through 7?
a. 5040
c. 120
b. 2520
d. 35
____ 20. In how many ways can you arrange all the numerals 1 through 5?
a. 24
c. 15
b. 120
d. 25
____ 21. Players on a volleyball team wear jerseys numbered 1 through 9. In how many different ways could you arrange
5 of the players?
a. 120
c. 24
b. 15,120
d. 362,880
____ 22. Your shirt drawer contains 8 different colored shirts that you will wear over the next 8 days. What is the
probability that you will randomly choose the orange shirt to wear today and the red shirt to wear tomorrow?
a. 1
c. 1
8
56
b. 1
d. 1
16
4
____ 23. Count the possible combinations of 2 numbers chosen from the list {99, 98, 97, 96, 95, 94, 93, 92, 91}.
a. 36
c. 2
b. 5040
d. 72
____ 24. A soccer team roster has 14 players on it. How many groups of 11 players can be created?
a. 14,529,715,200
c. 364
b. 2184
d. 6
____ 25. A math teacher randomly assigns seats in the classroom to students each quarter. Each student randomly
chooses their row number out of a hat. In the classroom, there are 4 desks in each row and 27 students in your
class. What is the probability that you and your 3 friends will get to sit together in the same row?
a.
c.
b.
d.
____ 26. Use the probability distribution to determine which is the most likely outcome.
1
P(x)
0.9
0.8
Probability
0.7
0.6
0.5
0.4
0.3
0.2
0.1
A
B
C
Outcome
D
x
a. D
b. C
c. A
d. B
____ 27. Use the probability distribution to determine the probability of an odd number.
P(x)
Probability
0.6
0.5
0.4
0.3
0.2
0.1
1
a.
3
10
b. 1
5
2
3
Outcome
4
x
c.
1
2
d. 7
10
28. According to a survey, 44% of Americans are college graduates. You ask 5 randomly chosen Americans if they
are college graduates.
a. Draw a histogram of the binomial distribution for your survey.
b. What is the most likely outcome of the survey?
c. What is the probability that at least 3 of the Americans surveyed are college graduates?
29. Among a couple’s 13 grandchildren, 8 of them come from their eldest child’s family. Four grandchildren are
randomly selected for a team game at the family reunion. Let x represent how many of the grandchildren on the
team are from their eldest child’s family.
a. Make a histogram showing the probability distribution for x.
b. What is the probability that there will be a team of grandchildren entirely from their eldest child’s family?
Algebra 2 Ch10 Review - SHOW ALL WORK FOR FULL CREDIT
Answer Section
1. ANS: 30
PTS: 1
NAT: HSS-CP.A.1
NOT: Example 1
2. ANS: D
NAT: HSS-CP.A.1
NOT: Example 3
3. ANS:
region D
DIF: Level 1
REF: Algebra 2 Sec. 10.1
KEY: sample space | outcome | application
PTS:
NAT:
NOT:
4. ANS:
NAT:
NOT:
5. ANS:
NAT:
NOT:
6. ANS:
DIF: Level 2
REF: Algebra 2 Sec. 10.1
KEY: theoretical probability | geometric probability | application
1
HSS-CP.A.1
Example 4-2
C
HSS-CP.A.1
Example 5
B
HSS-CP.A.1
Example 6
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.1
KEY: theoretical probability | probability of the complement of an event | application
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.1
KEY: experimental probability | application
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.1
KEY: experimental probability | application
1
1
; P(getting tails) = ;
6
2
1
P(rolling a 6 then getting tails) =
12
P(rolling a 6) =
Because
PTS:
NAT:
KEY:
NOT:
7. ANS:
NAT:
KEY:
NOT:
8. ANS:
, the events are independent
1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.5 | HSS-CP.B.8
independent events | application | determining whether events are independent
Example 1 and 2
A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
independent events | application | probability of independent events
Example 3
21/374
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
NAT: HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
KEY: dependent events | application | probability of dependent events
NOT: Example 4
9. ANS:
8
a.
 0.064
125
1
b.
 0.033
30
c. You are 1.9 times more likely to choose 3 t-shirts when you replace each shirt before you select the next
shirt.
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.2
NAT: HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
KEY: dependent events | application | independent events
NOT: Example 5-2
10. ANS:
1
a.
 0.5, or 50%
2
12
b.
 0.48, or 48%
25
PTS:
NAT:
KEY:
11. ANS:
NAT:
KEY:
12. ANS:
1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
conditional probability | application
NOT: Example 6
A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
conditional probability | application
NOT: Example 7
Gender
Men
Women
Total
Exercise Class Attendance
Attend
Do Not Attend
59
45
71
42
130
87
Total
104
113
217
217 people were surveyed, 130 attend an exercise class regularly, 87 do not regularly attend an exercise class,
104 men were surveyed, 113 women were surveyed.
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.3
NAT: HSS-CP.A.4 KEY: two-way table | application | making two-way tables
NOT: Example 1
13. ANS:
Text
Do Not Text
Total
0.384
0.128
0.512
Male
0.337
0.152
0.488
Female
0.721
0.279
1
Total
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.3
NAT: HSS-CP.A.4
KEY: two-way table | application | joint relative frequency | marginal relative frequency
NOT: Example 2
14. ANS:
a. 77.8%
b. 29.4%
c. P(St. Lucia) = 0.32; P(St. Lucia | Yes)  0.33
Because
, the two events are not independent.
PTS:
NAT:
NOT:
15. ANS:
NAT:
NOT:
16. ANS:
NAT:
KEY:
NOT:
17. ANS:
1
DIF: Level 1
REF: Algebra 2 Sec. 10.3
HSS-CP.A.4 | HSS-CP.A.5
KEY: two-way table | application | conditional probability
Example 4
C
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.3
HSS-CP.A.4 | HSS-CP.A.5
KEY: conditional probability | application
Example 5-2
D
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.4
HSS-CP.A.1 | HSS-CP.B.7
application | compound event | disjoint | finding probabilities of compound events
Example 1
7/26
18.
19.
20.
21.
22.
23.
24.
25.
26.
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.4
NAT: HSS-CP.A.1 | HSS-CP.B.7
KEY: application | compound event | overlapping events
NOT: Example 2
ANS: A
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.4
NAT: HSS-CP.A.1 | HSS-CP.B.7
KEY: application | compound event
NOT: Example 3
ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.5
NAT: HSS-CP.B.9 KEY: permutation NOT: Example 1
ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.5
NAT: HSS-CP.B.9 KEY: permutation NOT: Example 1
ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.5
NAT: HSS-CP.B.9 KEY: permutation | application
NOT: Example 2
ANS: C
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.5
NAT: HSS-CP.B.9 KEY: permutation | application
NOT: Example 3
ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.5
NAT: HSS-CP.B.9 KEY: combination NOT: Example 4
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.5
NAT: HSS-CP.B.9 KEY: combination | application
NOT: Example 5
ANS: D
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.5
NAT: HSS-CP.B.9 KEY: combination | application
NOT: Example 6-2
ANS:
1
2
f (value)
Outcomes
P(f)
5
5
7
2
2
7
Choosing a Number from a Set
P(f)
Probability
1
5
7
3
7
1
7
1
2
S ign of Chosen Number
PTS:
NAT:
NOT:
27. ANS:
NAT:
NOT:
28. ANS:
NAT:
NOT:
29. ANS:
a.
1
HSS-CP.B.9
Example 1
D
HSS-CP.B.9
Example 2
A
HSS-CP.B.9
Example 2
f
DIF: Level 1
REF: Algebra 2 Sec. 10.6
KEY: probability distribution | constructing probability distributions
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.6
KEY: probability distribution | interpreting probability distributions
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.6
KEY: probability distribution | interpreting probability distributions
Binomial Distribution of Your Survey
P(k)
0.7
Probability
0.6
0.5
0.4
0.3
0.2
0
1
2
3
4
5
Number who are college graduates
k
b. The most likely outcome is that 2 of the 5 Americans surveyed are college graduates.
c. about 0.389
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.6
NAT: HSS-CP.B.9 KEY: binomial distribution | interpreting binomial distributions | application
NOT: Example 3 and 4-1
30. ANS:
a.
Binomial Distribution of Grandchildren on
Team from the Eldest Child’s Family
P(x)
Probability
0.4
0.3
0.2
0.1
0
1
2
3
Grandchildren
4
x
b. 14.3%
31.
32.
33.
34.
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.6
NAT: HSS-CP.B.9 KEY: binomial distribution | interpreting binomial distributions | application
NOT: Example 3 and 4-2
ANS: G
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.6
NAT: HSS-CP.B.9
KEY: probability distribution | constructing probability distributions | binomial distribution | interpreting
binomial distributions | application
NOT: Combined Concept
ANS: D
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.6
NAT: HSS-CP.B.9
KEY: probability distribution | constructing probability distributions | binomial distribution | interpreting
binomial distributions | application
NOT: Combined Concept
ANS: B
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.6
NAT: HSS-CP.B.9
KEY: probability distribution | constructing probability distributions | binomial distribution | interpreting
binomial distributions | application
NOT: Combined Concept
ANS: F
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.6
NAT: HSS-CP.B.9
KEY: probability distribution | constructing probability distributions | binomial distribution | interpreting
binomial distributions | application
NOT: Combined Concept