Download ExamView - Mod 21 Test Review.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
Mod 21 Test Review GEO
Multiple Choice
Identify the choice that best completes the statement or answers the question.
4. You spin the numbered spinner shown below.
Event A is landing on a prime number. Event B is
landing on an odd number. What is the intersection
of A and B?
1. Let U be the set of all integers from 1 to 20. Let A
= {1, 3, 6, 9, 12, 15, 18} and
B = {1, 6, 12, 18}. Which choice describes the set
given below?
{2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20}
A
B
C
D
AB
AB
AB
AB
2. Let U be the set of all integers from 1 to 20. Let A
= {1, 3, 6, 9, 12, 15, 18} and B = {2, 9, 11, 20}.
Which choice describes the set {4, 5, 7, 8, 10, 13,
14, 16, 17, 19}?
A AB
B AB
C AB
D AB
 
3. If P  A  0.36 , what is P  A  ?
 
A 0.06
B 0.54
C 0.60
D 0.64
E 0.72
A
B
C
D

{3, 5, 7}
{1, 2, 3, 5, 7}
{1, 2, 3, 4, 5, 6, 7, 8}
A
B
C
D
0.2
0.5
0.74
0.8
5. Of 50 students going on a class trip, 35 are student
athletes and 5 are left-handed. Of the student
athletes, 3 are left-handed. Which is the probability
that one of the students on the trip is an athlete or is
left-handed?
1
Name: ________________________
ID: A
6. Darren randomly chooses a card from a standard
deck of 52 playing cards. What is the probability
that Darren chooses a club or a queen?
A
B
C
D
4
52
13
52
16
52
17
52
Numeric Response
1. According to the Small Business Administration, the probability that a newly started business will last four years
is 44%. What is the probability that a newly started business will NOT last four years?
Short Answer
1. Suppose you roll two fair number cubes. You want
to know the pairs of numbers that will result in an
odd product less than 10.
a. Complete the table to show the sample space
for the product of the two numbers on the
number cubes.
1
2
3
4
5
6
1
1
2
4
3
9
4
16
5
25
3. A box contains 100 small rubber balls. The table
below shows how many balls are red, how many
are black, how many have stars, and how many do
not have stars. What is the probability that a
randomly selected ball is black or does not have
stars on it? Justify your answer.
6
Red
Black
Total
36
Stars
0
10
10
No
stars
65
25
90
Total
65
35
100
4. A bank assigns random 4-digit numbers for ATM
access codes. In each code, no digit is repeated.
Use combinations to find the number of ways that 4
digits can be chosen from 10 digits, if order is not
important. What is the probability that Edmond is
assigned a code with the digits 6, 7, 8, and 9 in any
order? Show your work.
b. Find the subset A of the sample space that
describes two numbers with an odd product.
c. Find the subset B of your answer from part a
that describes an odd product less than 10.
2. 16 cards numbered 1 through 16 are placed face
down and Stephanie chooses one at random. What
is the probability that the number on Stephanie’s
card is less than 5 or greater than 10? Show your
work.
2
Name: ________________________
ID: A
5. The table shows the distribution of male and female students and left- and right-handed students in the math club.
Find the probability that a female student selected at random is left-handed. Express your answer as a fraction in
simplest form.
Left-handed
Right-handed
2
35
Male
6
36
Female
6. There are 7 singers competing at a talent show. In
how many different ways can the singers appear?
8. Thirteen people are entered in a race. If there are
no ties, in how many ways can the first three places
be awarded?
7. Caleb and Drew are playing a game with a pair of
dice. Caleb needs a sum of 5 or greater to win.
What is his probability of winning on his next turn?
9. 6 high school seniors choose from among 20 quotes
for their yearbook. What is the probability that at
least 2 of them choose the same quote?
Problem
1. Travis’s collection of DVDs contains 14 comedies, 12 dramas, and 10 action movies. Use combinations to find the
probability of each of the following compound events, and then order the events A, B, C, and D from least likely
to most likely.
Event A:
Event B:
Event C:
Event D:
Randomly selecting 3 comedies
Randomly selecting 3 dramas
Randomly selecting 3 action movies
Randomly selecting 3 movies that are not dramas
3
ID: A
Mod 21 Test Review GEO
Answer Section
MULTIPLE CHOICE
1. ANS: C
PTS: 1
DIF: DOK 2
NAT: S-CP.A.1
STA: S-CP.1
TOP: Apply Set Theory
KEY: probability | complement
2. ANS: C
PTS: 1
DIF: DOK 2
NAT: S-CP.A.1
STA: S-CP.1
KEY: probability | complement
3. ANS: B
PTS: 1
DIF: DOK 1
NAT: S-CP.A.1
STA: S-CP.1
4. ANS: B
The possible outcomes are {1, 2, 3, 4, 5, 6, 7, 8}.
A  {2, 3, 5, 7}
B  {1, 3, 5, 7}
The intersection of A and B contains the elements that are both in set A and in set B.
A  B  {3, 5, 7}
A
B
C
D
Feedback
The intersection of A and B contains the elements that are both in set A and in set B .
There are elements in this set.
That’s correct!
You found the union of A and B, not the intersection of A and B.
You found the sample space.
PTS:
STA:
5. ANS:
STA:
6. ANS:
1
DIF: DOK 1
NAT: S-CP.A.1* | MP.4
S-CP.1* | MP.4
KEY: outcomes | subset | intersection
C
PTS: 1
DIF: DOK 2
NAT: S-CP.B.7
S-CP.7
C
13
4
1
P(club) 
; P(queen) 
; P(club and queen) 
52
52
52
Use the addition rule:
P(club or queen)  P(club)  P(queen)  P(club and queen) 
A
B
C
D
13 4
1
16



52 52 52 52
Feedback
You found the probability that Darren chooses a queen.
You found the probability that Darren chooses a club.
That’s correct!
Do not count the queen of clubs twice.
PTS: 1
DIF:
STA: S-CP.7* | MP.4
DOK 1
NAT: S-CP.B.7* | MP.4
KEY: addition rule | probability
1
ID: A
NUMERIC RESPONSE
1. ANS: 56%
PTS: 1
LOC: 12.4.4.h
DIF: DOK 1
NAT: S-CP.A.1
KEY: complementary | probability
STA: S-CP.1
SHORT ANSWER
1. ANS:
a.
1
2
3
4
5
6
1
1
2
3
4
5
6
2 3 4 5
2 3 4 5
4 6 8 10
6 9 12 15
8 12 16 20
10 15 20 25
12 18 24 30
6
6
12
18
24
30
36
b. A  {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}
c. B  {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (5, 1)}
Rubric
a. 1 point
b. 2 points
c. 2 points
PTS: 5
DIF: DOK 2
NAT: S-CP.A.1* | MP.4
STA: S-CP.1* | MP.4
KEY: outcomes | sample space | subset
2. ANS:
4
6
0
P(less than 5) 
; P(greater than 10) 
; P(less than 5 and greater than 10) 
16
16
16
4
6
10
P(less than 5 or greater than 10) 


 0.625
16 16 16
Rubric
1 point for answer; 2 points for work
PTS: 3
DIF:
STA: S-CP.7* | MP.4
DOK 2
NAT: S-CP.B.7* | MP.4
KEY: addition rule | probability
2
ID: A
3. ANS:
The probability is 1.
35
90
25
P(black) 
; P(no stars) 
; P(black and no stars) 
100
100
100
35
90
25
100
P(black or no stars) 



1
100 100 100 100
Any randomly selected ball will either be black or not have stars on it.
Rubric
1 point for answer; 1 point for justification
PTS: 2
DIF: DOK 2
NAT: S-CP.B.7* | MP.4
STA: S-CP.7* | MP.4
KEY: addition rule | probability
4. ANS:
10!
10  9  8  7

 210 combinations of 4 digits.
There are 10 C 4 
4! (10  4)!
4321
1
The probability of being assigned a code with the digits 6, 7, 8, and 9 is
.
210
Rubric
1 point for number of combinations; 1 point for probability; 1 point for work
PTS: 3
DIF:
STA: S-CP.9(+)* | MP.4
5. ANS:
1
7
DOK 1
NAT: S-CP.B.9(+)* | MP.4
KEY: combinations | probability | compound events
PTS: 1
DIF: DOK 1
NAT: S-CP.A.4
TOP: Find Probabilities of Independent and Dependent Events
6. ANS:
5,040 ways
STA: S-CP.4
KEY: conditional | probability
PTS: 1
DIF: DOK 1
NAT: S-CP.B.9
STA: S-CP.9
TOP: Permutations and Combinations
7. ANS:
5
6
OBJ: Finding Permutations
LOC: MTH.C.13.06.02.02.004
KEY: permutation | ordering
PTS: 1
8. ANS:
1716
DIF:
DOK 1
NAT: S-CP.A.1
STA: S-CP.1
PTS: 1
DIF:
TOP: Permutations
DOK 1
NAT: S-CP.B.9
KEY: permutation
STA: S-CP.9
3
ID: A
9. ANS:
0.56
PTS: 1
DIF:
DOK 2
NAT: S-CP.B.9
STA: S-CP.9
PROBLEM
1. ANS:
There are 14  12  10  36 DVDs, and
36
C3 
36!
36  35  34

 7140 different ways to pick 3 DVDs.
3! (36  3)!
321
14!
14  13  12

 364 different ways to pick 3 of the 14 comedies.
3! (14  3)!
321
364
13

The probability of randomly selecting 3 comedies is
.
7140 255
12!
12  11  10

 220 different ways to pick 3 of the 12 dramas.
B: There are 12 C 3 
3! (12  3)!
321
220
11

The probability of randomly selecting 3 dramas is
.
7140 357
10!
10  9  8

 120 different ways to pick 3 of the 10 action movies.
C: There are 10 C 3 
3! (10  3)!
321
120
2

The probability of randomly selecting 3 action movies is
.
7140 119
24!
24  23  22

 2024 different ways to pick 3 of the 24 movies that are not
D: There are 24 C 3 
3! (24  3)!
321
dramas.
2024 506

The probability of randomly selecting 3 movies that are not dramas is
.
7140 1785
A: There are
14
C3 
In order from least likely to most likely:
C, B, A, D
Rubric
1.5 points for each probability and work involving combinations; 1 point for correct order
PTS: 7
DIF:
STA: S-CP.9(+)* | MP.4
DOK 3
NAT: S-CP.B.9(+)* | MP.4
KEY: combinations | probability | compound events
4