Name: ___________________________ Date: _______________________ Color: ___________
Unit 1: Set Theory and Math 6/7 Review
Study Guide ~ Unit 1 Test
Use These Sets For Questions 1-3:
A={1, 2, 5, 8, 9} ;
B={2, 4, 6, 8, 10} ;
C={}.
1. Which of the following statements is untrue?
a. 2  A
b. 2  B
c. 2  C
2. Which of the statements is true?
a. A is a subset of C.
c. B is a subset of A and C.
3. The A  C’ = B
True
d.
2  A and B
b. C is a subset of B.
d. A is a subset of B and C.
or
False
4. List an example of a pair of dependent events.
Getting every answer on a test correct.
5. A  B  C
7. A  B  C
6. A’  (B  C)
5. A  B
8. What is the P(tossing head and a prime number) if you toss a coin and pull a card from a standard
deck?
1
16
=

2
52
1
2
1
1


4
13
2
13
=
=
2
13
9. The student council is selling sweatshirts with the school name and emblem. The shirts come in the
colors, styles, and sizes shown below. How many different types of sweatshirts are available? (Make
a tree diagram.)
Colors:
Styles:
Sizes:
Sweatshirt Choices
White
Gray
Hooded
Plain
Small
Medium
Black
Large
Small
Hooded
Medium
Large
White
Small
Plain
Medium
Large
Small
Hooded
Medium
Large
Gray
Small
Plain
Medium
Large
Small
Hooded
Medium
Large
Black
Small
Plain
Medium
Large
18
Total
10. An even number is chosen randomly from a set of cards labeled with the numbers 1 through 8.
a second even number is chosen without the first card being replaced. Are these events
independent or dependent events? What is the probability of both events occurring?
Dependent.
4
3
=

8
7
1
2

3
7
=
3
14
11. Francisco has 7 quarters in his pocket. Of these, 3 depict the state of Delaware, 2 depict
Georgia, 1 depicts Connecticut, and 1 depicts Pennsylvania. Francisco removes 1 quarter from
his pocket then removes a second quarter without replacing the first. What is the probability
that both will be Delaware quarters?
3
7
3
7
1
7



2
6
1
3
1
1
=
=
=
1
7
12. Create a Venn diagram using the given sets. (Use diagrams to answer questions 13 and 14)
A = {vowels}
B = {consonants}
I, O
C = {m, a, t, h, r, u, l, e, s}
Y
A, E, U
B, C, D, F,
G, J, K, N,
P, Q, V, W,
X, Z
H, L, M,
R, S, T
13. Using your diagram: A  B  C = { ) OR {}.
14. Write a statement representing the relationship of sets B and C using proper set theory
notation.
B  C = {B, C, D, F, G, H, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}
15. What is A  B if set A = {s, e, t} and B = { b, r, a, c, k, e, t}?
a. {e, t}
b. {s, b, r, a, c, k}
c. {s, e, t}
d. {s, b, r, a, c, k, e, t}
16. A bank code consists of 3 letters or numbers. The password is cases sensitive, which means
upper-case and lower-case letter are different characters. What is the probability of randomly
being assigned the password 7C2? 26 lower-case letters + 26 upper-case letters + 10 numbers
(only 0-9) = 62 possibilities.
1
1
1
1


=
62
62
62
238,328
17. At Palmer Middle School 4/5 of all students play and instrument, and 2/3 sing in the choir.
What is the probability that a student picked at random will play an instrument and sing in the
choir.
4
2
8

=
5
3
15
18. If A and B are dependent events such that P(A) = 0.14 and P(B) = 0.28, what is the probability
that a or B will occur? [P(A)  P(B)]
a. 0.0392
b. 0.0784
c. 0.24
d. 0.42
19. The set of all men is a proper subset of all people.
True
or
False
20. The local animal shelter has 19 cats and dogs ready for adoption. Seven are purebreds and 12
are mixed breads. Of the six dogs, four are purebreds. If you are heading to the animal
shelter to adopt a new pet was is the probability that you will at randomly select a purebred or
a cat?
7
13
20
+
=
19
19
19