Prof. Israel N. Nwaguru
MATH 1324
CHAPTER 8 - REVIEW
WORK OUT EACH PROBLEM NEATLY AND ORDERLY BY SHOWING ALL THE STEPS AS
INDICATED IN CLASS ON SEPARATE SHEET, THEN CHOSE THE BEST ANSWER.
TO EARN ANY CREDIT, YOU MUST SHOW WORK.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Tell whether the statement is true or false.
1) {x | x is an even counting number between 6 and 12} = {4}
A) True
B) False
Answer: B
2) {57, 58, 57, 58} = {57, 58}
A) True
B) False
Answer: A
3) {2, 17, 28, 9, 35} = {35, 17, 9, 82, 2}
A) True
B) False
Answer: B
4) 13 {x | x is an even counting number}
A) True
B) False
Answer: A
5) {x | x is a counting number greater than 31} = {31, 32, 33, . . . }
A) True
B) False
Answer: B
6) 11 {22, 33, 44, 55, 66}
A) True
B) False
Answer: B
Insert " " or " " in the blank to make the statement true.
7) {b, d, j, f}
{b, d, j, f, p}
A)
B)
Answer: A
8)
A)
B)
Answer: B
9) {f, a, m}
A)
{f, a, m}
B)
Answer: A
1
10) {x | x is a counting number larger than 5}
A)
{7, 8, 9, . . . }
B)
Answer: A
Find the number of subsets of the set.
11) {1, 2, 3, . . . , 9}
A) 1024
B) 508
C) 16
D) 512
C) 127
D) 124
C) 8
D) 256
C) 12
D) 8
Answer: D
12) {x | x is a day of the week}
A) 128
B) 256
Answer: A
13) {x | x is an even number between 13 and 33}
A) 32
B) 1024
Answer: B
14) {mom, dad, son, daughter}
A) 16
B) 14
Answer: A
Decide whether the statement is true or false.
= {0}
15) {0}
A) True
B) False
Answer: B
16) {5, 15, 9}
A) True
= {5, 15, 9}
B) False
Answer: A
17) {5, 7, 9} {6, 8, 10} = {5, 7, 9, 6, 8, 10}
A) True
B) False
Answer: B
18)
=
A) True
B) False
Answer: A
19) {6, 8, 10} {7, 9, 11} = {6, 8, 10, 7, 9, 11}
A) True
B) False
Answer: B
Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of the
indicated set, using set braces.
20) C' A'
A) {q, s, u, v, w, x, y, z}
B) {q, r, s, t, u, v, x, z}
C) {r, t}
D) {w, y}
Answer: C
2
21) C' A'
A) {w, y}
C) {q, r, s, t, u, v, x, z}
B) {s, t}
D) {q, s, u, v, w, x, y, z}
Answer: C
22) A
(B C)
A) {q, w, y}
B) {q, r, w, y, z}
C) {q, y, z}
D) {q, s, u, w, y, z}
Answer: D
23) (A B)'
A) {t, v, x}
C) {r, t, v, x}
B) {s, u, w}
D) {r, s, t, u, v, w, x, z}
Answer: C
24) (A B)'
A) {t, v, x}
C) {q, s, t, u, v, w, x, y}
B) {r, t, u, v, w, x, z}
D) {s, u, w}
Answer: B
25) A
B'
A) {q, s, t, u, v, w, x, y}
C) {r, s, t, u, v, w, x, z}
B) {u, w}
D) {t, v, x}
Answer: B
The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana.
Alabama
soybeans (s)
peanuts (p)
corn (c)
hay (h)
wheat (w)
Arkansas
soybeans (s)
rice (r)
cotton (t)
hay (h)
wheat (w)
Louisiana
soybeans (s)
sugarcane (n)
rice (r)
corn (c)
cotton (t)
Let U be the smallest possible universal set that includes all of the crops listed; and let A, K, and L be the sets of
five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.
26) L K
A) {c, n, r, s, t}
B) {r, s, t}
C) {c, h, n, w}
D) {c, h, n, r, s, t, w}
Answer: B
27) A
K L
A) {n, p}
C) {c, h, n, p, r, s, t, w}
B) {n, p, s}
D) {s}
Answer: D
28) K
L
A) {r, s, t}
B) {n, r, t}
C) {c, h, n, w}
Answer: D
3
D) {c, h, n, r, s, t, w}
Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
= 44, n(B) = 64, n(A B) = 17, n(A C) = 20, n(A B C) = 9, n(A' B C') = 38, and
29) n(U) = 136, n(A)
n(A' B' C') = 33. Find n(C).
A) 23
B) 28
C) 41
D) 12
Answer: C
30) n(A B C) = 37, n(A B C) = 6, n(A
n(C) = 16. Find n(A' B C)
A) 5
B) 4
B) = 14, n(A
C) = 11, n(B
C) 3
C) = 9, n(A) = 31, n(B) = 18, and
D) 2
Answer: C
Use a Venn diagram to answer the question.
31) At East Zone University (EZU) there are 634 students taking College Algebra or Calculus. 516 are taking
College Algebra, 202 are taking Calculus, and 84 are taking both College Algebra and Calculus. How
many are taking Calculus but not Algebra?
A) 118
B) 550
C) 432
D) 348
Answer: A
32) A local television station sends out questionnaires to determine if viewers would rather see a
documentary, an interview show, or reruns of a game show. There were 250 responses with the following
results:
75 were interested in an interview show and a documentary, but not reruns;
10 were interested in an interview show and reruns, but not a documentary;
35 were interested in reruns but not an interview show;
60 were interested in an interview show but not a documentary;
25 were interested in a documentary and reruns;
15 were interested in an interview show and reruns;
20 were interested in none of the three.
How many are interested in exactly one kind of show?
A) 100
B) 120
C) 110
D) 130
Answer: B
33) A survey of a group of 112 tourists was taken in St. Louis. The survey showed the following:
61 of the tourists plan to visit Gateway Arch;
44 plan to visit the zoo;
9 plan to visit the Art Museum and the zoo, but not the Gateway Arch;
14 plan to visit the Art Museum and the Gateway Arch, but not the zoo;
17 plan to visit the Gateway Arch and the zoo, but not the Art Museum;
6 plan to visit the Art Museum, the zoo, and the Gateway Arch;
16 plan to visit none of the three places.
How many plan to visit the Art Museum only?
A) 56
B) 14
C) 32
D) 96
Answer: B
4
34) A survey of 136 college students was done to find out what elective courses they were taking. Let A = the
set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing.
The study revealed the following information:
n(A) = 45; n(B) = 55; n(C) = 40;
n(A B) = 12; n(A C) = 15; n(B C) = 23;
n(A B C) = 2.
How many students were not taking any of these electives?
A) 10
B) 46
C) 54
D) 44
Answer: D
Write the sample space for the given experiment.
35) An 8-sided die is rolled. (The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, and 8.)
A) {1, 2, 3, 4, 5, 6, 7, 8}
B) {8}
C) {1, 8}
D) {64}
Answer: A
36) An ordinary die is rolled.
A) {6}
B) {1, 6}
C) {1, 2, 3, 4, 5, 6}
D) {36}
Answer: C
37) A box contains 13 white cards numbered 1 through 13. One card with a number greater than 6 is chosen.
A) {7, 8, 9, 10, 11, 12, 13}
B) {11}
C) {1, 2, 3, . . . , 13}
D) {6, 7, 8, 9, 10, 11, 12, 13}
Answer: A
38) A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. A blue card
is picked, followed by a green card.
A) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}
B) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}
C) {12}
D) {7}
Answer: A
39) A group of 19 people are assigned numbers 1 through 19. A person assigned a number of 5 or less is
chosen.
A) {1}
B) {1, 2, 3, 4, 5}
C) {19}
D) {1, 2, 3, 4}
Answer: B
Determine whether the given events are disjoint.
40) Knowing Spanish and knowing Chinese
A) No
B) Yes
Answer: A
41) Drawing a spade from a deck of cards and drawing an ace
A) No
B) Yes
Answer: A
5
42) Being a teenager and being a United States Senator
A) No
B) Yes
Answer: B
43) Having good reading skills and having good math skills
A) Yes
B) No
Answer: B
Find the probability of the given event.
44) A card drawn from a well-shuffled deck of 52 cards is a face card or a 6.
2
12
4
A)
B)
C)
13
13
13
D) 16
Answer: C
45) A card drawn from a well-shuffled deck of 52 cards is an ace or a 7.
13
4
A)
B)
C) 8
2
13
D)
2
13
D)
13
52
D)
1
26
Answer: D
46) A card drawn from a well-shuffled deck of 52 cards is red.
1
1
1
A)
B)
C)
26
2
52
Answer: B
47) A card drawn from a well-shuffled deck of 52 cards is a red ace.
1
1
1
A)
B)
C)
13
52
2
Answer: D
48) A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. A randomly drawn marble is not blue.
2
1
3
A)
B) 6
C)
D)
3
3
2
Answer: A
49) A bag contains 13 balls numbered 1 through 13. A randomly chosen ball has an even number.
2
13
6
A) 6
B)
C)
D)
13
6
13
Answer: D
Solve the problem.
50) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.
1
1
A)
B) 0
C)
D) 1
6
2
Answer: B
6
51) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd.
1
1
1
2
A)
B)
C)
D)
2
3
6
3
Answer: B
Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary.
52) For two events M and N, P(M) = .1, P(N|M) = .1, and P(N|M') = .1. Find P(M'|N).
A) 1.0
B) 0
C) .90
D) .10
Answer: C
53) For two events M and N, P(M) = .2, P(N|M) = .9, and P(N|M') = .6. Find P(M|N).
A) .27
B) 1.0
C) 0
D) .73
Answer: A
54) For mutually exclusive events X1 , X2 , and X3 , let P(X1 ) = .32, P(X2 ) = .30, and P(X3 ) = .38. Also,
P(Y|X1 ) = .40, P(Y|X2 ) = .30, and P(Y|X3 ) = .60. Find P(X1 |Y).
A) .22
B) .51
C) .20
D) .29
Answer: D
55) For mutually exclusive events X1 , X2 , and X3 , let P(X1 ) = .12, P(X2 ) = .48, and P(X3 ) = .40. Also,
P(Y|X1 ) = .40, P(Y|X2 ) = .30, and P(Y| X3 ) = .60. Find P(X2 |Y).
A) .11
B) .56
C) .33
D) .67
Answer: C
56) For mutually exclusive events X1 , X2 , and X3 , let P(X1 ) = .45, P(X2 ) = .32, and P(X3 ) = .23. Also,
P(Y|X1 ) = .40, P(Y|X2 ) = .30 and P(Y|X3 ) = .60. Find P(X3 |Y).
A) .23
B) .43
C) .22
Answer: D
7
D) .33