Download Finite Math Exam 3 Review Find the number of subsets of the set. 1

Finite Math Exam 3 Review
Find the number of subsets of the set.
1) {-3, 0, 3, 4, 5}
A) 31
2) {x | x is a day of the week}
A) 128
B) 16
C) 5
D) 32
B) 127
C) 124
D) 256
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.
3) A B'
A) {r, s, t, u, v, w, x, z}
B) {t, v, x}
C) {q, s, t, u, v, w, x, y}
D) {u, w}
4) B C
A) {q, s, y, z, v, w, x, y, z}
C) {q, s, v, w, x, y, z}
B) {q, s, v, x, y, z}
D) {y, z}
5) B'
(A C')
A) {q, r, s, t, u, v, w, x, y}
C) {q, r, s, t, u, w}
B) {r, t, u, w}
D) {r, t, u}
6) C'
A'
A) {q, r, s, t, u, v, x, z}
C) {q, s, u, v, w, x, y, z}
B) {w, y}
D) {r, t}
Shade the Venn diagram to represent the set.
7) A B
A)
B)
C)
D)
1
8) A'
(A
B)
A)
B)
C)
D)
2
9) C'
(A
B)
A)
B)
C)
D)
Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
10) n(U) = 268, n(A) = 92, n(B) = 112, n(A B) = 41, n(A C) = 44, n(A B C) = 21, n(A' B C') = 50, and
n(A' B' C') = 69. Find n(C).
A) 36
B) 59
C) 101
D) 52
11) n(U) = 76, n(A) = 39, n(B) = 31, n(C) = 25, n(A
n(A (B C)').
A) 2
B) 3
12) n(A) = 17, n(A B C) = 8, n(A C) = 12, n(A
C') = 10. Find n(A').
A) 17
B) 30
B) = 8, n(A
C) = 6, n(B
C) = 8, and n(A
C) 28
B') = 6, n(B
C) = 15, n(B
C) 26
A die is rolled twice. Write the indicated event in set notation.
13) The sum of the rolls is 8.
A) {(2, 6), (3, 5), (5, 3), (6, 2)}
C) {(4, 4)}
3
(B
C)) = 3. Find
D) 30
C') = 12, n(B
C) = 32, n(A'
D) 27
B) {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}
D) {(2, 6), (3, 5), (4, 4)}
B'
14) Both rolls are even.
A) {(2, 2), (4, 4), (6, 6)}
B) {(2, 4), (2, 6), (4, 2), (4, 6), (6, 2), (6, 4)}
C) {(2, 2), (2, 4), (2, 6)}
D) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}
Write the indicated event in set notation.
15) Three coins are flipped and more tails are obtained than heads.
A) {ttt, tth, tht, htt}
B) {tth, tht, htt}
C) {ttt, tth}
D) {ttt}
16) The event that Helen gets a prize in a competition in which two people are selected from four finalists to receive
the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the
four finalists are Jim, George, Helen, and Maggie.
[The possible outcomes can be represented as follows.
JG
HJ
JH JM GJ
HG HM MJ
GH GM
MG MH
Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second
prize. ]
A) HJ, HG, HM
B) JH, GH, HJ, JG, HG, HM, MH
C) JH, GH, HJ, HG, HM, MH
D) JH, GH, HJ, HG, HM
Find the probability of the given event.
17) Two fair dice are rolled. The sum of the numbers on the dice is 5.
8
1
A)
B)
C) 4
9
9
18) Two fair dice are rolled. The sum of the numbers on the dice is greater than 10.
1
1
A)
B)
C) 3
18
12
D)
5
6
D)
5
18
Find the probability.
19) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a heart, club, or
diamond?
48
3
12
A)
B)
C)
D) 3
52
4
13
20) A spinner has equal regions numbered 1 through 21. What is the probability that the spinner will stop on an
even number or a multiple of 3?
2
1
10
A)
B)
C)
D) 17
3
3
9
4
Find the indicated probability.
21) The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major
English
Mathematics
Chemistry
Physics
Liberal Arts
Business
Engineering
Frequency
2073
2164
318
856
1358
1676
868
9313
What is the probability that a randomly selected degree is not in Business and is not in Engineering?
A) 0.820
B) 6769
C) 0.273
D) 0.727
22) The following table shows the grades of college students in an advanced mathematics course, broken down by
year. Use the table below to find the probability that a randomly selected sophomore gets a B.
A B
Freshmen
2 5
Sophomores 6 3
Juniors
5 7
Seniors
5 4
Grad Students 3 2
Totals (%)
21 21
A)
1
7
C
6
8
13
1
2
30
D
4
2
6
5
0
17
E
1
3
2
5
0
11
B)
Totals
(%)
18
22
33
20
7
100
4
21
C)
1
11
D)
3
22
23) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the second die is 4
or the sum of the dice is 7.
5
11
1
1
A)
B)
C)
D)
18
36
36
3
24) A spinner has regions numbered 1 through 15. What is the probability that the spinner will stop on an even
number or a multiple of 3?
2
7
1
A)
B) 12
C)
D)
3
9
3
Use a Venn diagram to find the indicated probability.
25) If P(A B) = 0.18, P(A) = 0.37, and P(B) = 0.43, find P(A
A) 0.73
B) 0.58
26) Suppose P(R) = 0.45, P(S) = 0.67, and P(R
Find P(R S').
A) 0.66
B) 0.11
B).
C) 0.62
D) 0.67
C) 0.33
D) 0.32
S) = 0.34.
5
27) Suppose P(R) = 0.82, P(S) = 0.53, and P(R
Find P(R' S).
A) 0.71
B) 0.17
S) = 0.36.
C) 0.64
D) 0.54
Find the odds.
28) Find the odds in favor of drawing a red marble when a marble is selected at random from a bag containing 2
yellow, 5 red, and 6 green marbles.
A) 5 to 13
B) 1 to 5
C) 8 to 13
D) 5 to 8
29) Find the odds in favor of getting a sum of 9 when two fair dice are rolled.
A) 1 to 10
B) 1 to 8
C) 1 to 7
D) 1 to 9
30) Find the odds in favor of getting a sum of 5 or 8 when two fair dice are rolled.
A) 1 to 4
B) 2 to 9
C) 1 to 9
D) 1 to 3
Solve the problem.
31) The odds in favor of Carl beating his friend in a round of golf are 9 : 7 Find the probability that Carl will beat
his friend.
7
9
9
7
A)
B)
C)
D)
16
17
16
9
32) The odds against Carl beating his friend in a round of golf are 9 : 2. Find the probability that Carl will beat his
friend.
1
2
9
2
A)
B)
C)
D)
6
9
11
11
33) The odds in favor of Trudy beating her friend in a round of golf are 1 : 7. Find the probability that Trudy will
lose.
1
1
7
7
A)
B)
C)
D)
10
8
8
9
34) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is
an ace, given that the first card was an ace.
3
1
1
4
A)
B)
C)
D)
52
3
17
51
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
35) Let A be the event that it will be sunny this afternoon.
Let B be the event that Francia will go shopping this afternoon. Given that P(A) = 0.8, P(B) = 0.9, and
P(A B) = 0.2, are events A and B independent? How can you tell?
Find the indicated probability.
36) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red
marbles. Find the probability that both marbles are green.
1
1
1
1
A)
B)
C)
D)
14
4
16
28
6
37) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the
probability that the first card is a king and the second card is a queen.
13
4
1
2
A)
B)
C)
D)
102
663
663
13
Find the probability.
38) If two cards are drawn with replacement from an ordinary deck, find the probability the first card is a heart and
the second is a diamond.
1
1
1
13
A)
B)
C)
D)
204
169
16
204
39) Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are
made and each question has 4 possible answers.
4
1
3
1
A)
B)
C)
D)
3
64
4
81
Solve the problem.
40) In a certain U.S. city, 51.6% of adults are women. In that city, 13.5% of women and 9.5% of men suffer from
depression. If an adult is selected at random from the city, find the probability that the person suffers from
depression.
A) 0.116
B) 0.115
C) 0.070
D) 0.135
41) The probability that a person passes a test on the first try is 0.65. The probability that a person who fails the first
test will pass on the second try is 0.75. The probability that a person who fails the first and second tests will pass
the third time is 0.64. Find the probability that a person fails the first and second tests and passes on the third
try.
A) 0.64
B) 0.3120
C) 0.0315
D) 0.0560
Use the given table to find the indicated probability.
42) The following table contains data from a study of two airlines which fly to Smalltown, USA.
Number of flights
arrived on time
Podunk Airlines
33
Upstate Airlines
43
Number of flights
arrived late
6
5
Totals
39
48
If a flight is selected at random, what is the probability that it was on Upstate Airlines and that it arrived on
time?
43
43
43
11
A)
B)
C)
D)
76
48
87
76
7
Find the indicated probability.
43) The following contingency table provides a joint frequency distribution for the popular votes cast in the 1984
presidential election by region and political party. Data are in thousands, rounded to the nearest thousand.
Political Party
Region
Democratic Republican Other
Northeast
9046
11,336
101
Midwest
10,511
14,761
169
South
10,998
17,699
136
West
7022
10,659
214
Totals
37,577
54,455
620
Totals
20,483
25,441
28,833
17,895
92,652
A person who voted in the 1984 presidential election is selected at random. Compute the probability that the
person selected is not from the South given that they voted Democrat.
A) 0.293
B) 0.707
C) 0.881
D) 0.287
Find the probability.
44) Assuming that boy and girl babies are equally likely, find the probability that a family with three children has
all boys given that the first two are boys.
1
1
1
A)
B)
C)
D) 1
2
4
8
Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary.
45) For two events M and N, P(M) = 0.7, P(N M) = 0.2, and P(N M') = 0.7. Find P(M' N).
A) 0.60
B) 1.0
C) 0
D) 0.40
Use the rule of total probability to find the indicated probability.
46) Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 5% of
its contents defective, while shipment II has 4% of its contents defective. If it is equally likely an employee will
go to either bin and select a component randomly, what is the probability a selected component is defective?
A) 4.5
B) 0.045
C) 9
D) 0.09
Use Bayes' rule to find the indicated probability.
47) A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store. Box A has 3%
of its contents being winners, while 5% of the contents of box B are winners. Box A contains 37% of the total
tickets. The contents of both boxes are mixed in a drawer and a ticket is chosen at random. What is the
probability it came from box A if it is a winner?
A) 0.258
B) 0.188
C) 0.009
D) 0.375
48) The incidence of a certain disease in the town of Springwell is 4%. A new test has been developed to diagnose
the disease. Using this test, 90% of those who have the disease test positive while 5% of those who do not have
the disease test positive ("false positive"). If a person tests positive, what is the probability that he or she
actually has the disease?
A) 0.855
B) 0.386
C) 0.90
D) 0.429
Solve the problem.
49) How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?
A) 119 five-digit numbers
B) 120 five-digit numbers
C) 2520 five-digit numbers
D) 16,807 five-digit numbers
8
50) A restaurant offered salads with 7 types of dressings and one choice of 5 different toppings. How many
different types of salads could be offered?
A) 35 types
B) 49 types
C) 12 types
D) 25 types
Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, count the different ways of
choosing the following officers or representatives for student congress. Assume that no one can hold more than one
office.
51) Three representatives, if two must be female and one must be male
A) 3
B) 5
C) 6
D) 2
Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions
with a large company. Use the following information to find the number of different ways that five of these could be
hired.
52) The four accounting majors must be hired first, and then the final position would be chosen from the remaining
majors.
A) 480 ways
B) 100 ways
C) 2880 ways
D) 120 ways
Suppose a traveler wanted to visit a museum, an art gallery, and the state capitol building. 45-minute tours are offered at
each attraction hourly from 10 a.m. through 3 p.m. (6 different hours). Solve the problem, disregarding travel time.
53) In how many ways could the traveler schedule all three tours in one day, with the museum tour being after
noon?
A) 60
B) 40
C) 30
D) 20
Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain the
following cards?
54) All diamonds
A) 2574 hands
B) 143 hands
C) 3861 hands
D) 1287 hands
55) Two black cards and three red cards
A) 845,000 hands
B) 1,267,500 hands
C) 422,500 hands
D) 1,690,000 hands
Solve the problem.
56) If a license plate consists of two letters followed by four digits, how many different licenses could be created
having at least one letter or digit repeated.
A) 4,009,824 licenses
B) 6,760,000 licenses
C) 3,276,000 licenses
D) 3,484,000 licenses
57) How many two-digit counting numbers do not contain any of the digits 1, 3, or 9?
A) 72 numbers
B) 42 numbers
C) 81 numbers
D) 49 numbers
A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the
probability.
58) All orange
A) 0.0011
B) 0.0182
C) 0.7272
D) 0.0061
59) One of each flavor
A) 0.1818
B) 0.3636
C) 0.2182
D) 0.0667
60) 2 orange, 1 lemon
A) 0.3636
B) 0.0303
C) 0.1091
D) 0.0364
9
Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand
is made up of 13 cards.
61) In poker, a flush (5 in same suit) in any suit
A) 0.000495
B) 0.000347
C) 0.00198
D) 0.00122
Solve the problem.
62) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C.
If the council consists of 5 people, find the probability of 3 from town A and 2 from town B.
A) 0.072
B) 0.076
C) 0.036
D) 0.023
Solve.
63) In a state lotto you have to pick 4 numbers from 1 to 45. If your numbers match those that the state draws, you
win. If you buy 3 tickets, what is your probability of winning?
1
1
8
1
A)
B)
C)
D)
148995
63855
446985
49665
Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the
probability.
64) Four coins are tossed and the number of heads is counted.
A)
B)
C)
D)
x P(x)
x P(x)
x P(x)
x P(x)
0 1/4
0 1/16
0 3/8
0 1/8
1 1/8
1 1/4
1 1/16
1 1/8
2 1/8
2 3/8
2 1/4
2 3/8
3 1/4
3 1/4
3 1/4
3 2/8
4 1/2
4 1/16
4 1/16
4 1/8
Find the expected value for the random variable.
65)
y
6
8
10
12
P(y) 0.4 0.4 0.16 0.04
A) 7.68
B) 9
C) 7.92
D) 7.28
66) A business bureau gets complaints as shown in the following table. Find the expected number of complaints per
day.
Complaints per Day 0
1
2
3
4
5
Probability
0.04 0.11 0.26 0.33 0.19 0.07
A) 2.85
B) 2.73
C) 3.01
D) 2.98
Find the expected value of the random variable in the experiment.
67) A bag contains six marbles, of which four are red and two are blue. Suppose two marbles are chosen at random
and X represents the number of red marbles in the sample.
A) 0.933
B) 1.4
C) 1
D) 1.33
Solve the problem.
68) Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be
$500. What is your expected payback?
A) $0
B) -$1.00
C) -$0.50
D) -$0.40
10
69) Numbers is a game where you bet $1.00 on any three-digit number from 000 to 999. If your number comes up,
you get $600.00. Find the expected payback.
A) -$0.42
B) -$1.00
C) -$0.40
D) -$0.50
11
Answer Key
Testname: EXAM 3 REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
D
A
D
C
B
D
A
C
D
C
C
D
B
D
A
C
B
B
B
A
D
D
B
A
C
B
D
D
B
D
C
D
C
C
No, because P(A
D
B
C
B
A
D
C
B
A
A
B
A
D
C
A
B)
P(A) · P(B)
12
Answer Key
Testname: EXAM 3 REVIEW
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
C
D
A
D
A
D
B
D
C
D
C
B
D
B
A
B
D
C
C
13