Deck 10: Counting and Probability

Question 1

Solve the problem.
In survey of 50 households, 25 responded that they have an HDTV television, 35 responded that they hada multimedia personal computer and 15 responded they had both. How many households had neither anHDTV television nor a multimedia personal computer?

A)5
B)35
C)15
D)25

Answer 1

5

Question 2

Use the information given in the figure.
How many are in set A?

A)31
B)26
C)33
D)22

Answer 2

31

Question 3

Write down all the subsets of the given set.
{p, q, r}

A)∅, {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, q, r}
B){p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, q, r}
C)∅, {p}, {q}, {r}, {p, q}, {p, r}, {q, r}
D)∅, {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, p}, {q, q}, {r, r}, {p, q, r}

Answer 3

∅, {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, q, r}

Question 4

Solve the problem.
Among a group of 85 investors, 27 owned shares of Stock A, 34 owned shares of Stock B, 44 owned sharesof Stock C, 12 owned shares of both Stock A and Stock B, 13 owned shares of Stock A and Stock C, 18owned shares of Stock B and Stock C, and 8 owned shares of all three. How many investors did not haveshares in any of the three? How many owned shares of either Stock A or Stock C but not Stock B?

A)15; 36
B)23; 31
C)15; 31
D)15; 39

Question 5

Use the information given in the figure.
How many are in B or C?

A)65
B)63
C)61
D)7

Question 6

Use the information given in the figure.
How many are not in C?

A)62
B)53
C)59
D)57

Question 7

Solve the problem.
If n(A)= 27, n(B)= 42, and n = 4, find n

A)65
B)61
C)69
D)73

Question 8

Use the information given in the figure.
How many are in B but not in A?

A)19
B)26
C)22
D)17

Question 9

Solve the problem.
In a survey of 361 computer buyers, 201 put price as a main consideration, 160 put performance as a mainconsideration, and 59 listed both price and performance. How many computer buyers listed otherconsiderations? How many looked only for performance?

A)59; 101
B)118; 160
C)59; 160
D)142; 101

Question 10

Use the information given in the figure.
How many are in B and C?

A)6
B)4
C)44
D)56

Question 11

Write down all the subsets of the given set.
{4, α, 10, π}

A){4}, {α}, {10}, {π}, {4, α}, {4, 10}, {4, π}, {α, 10}, {α, π}, {10, π}, {4, α, 10}, {4, α, π}, {4, 10, π}, {α, 10, π},
{4, α, 10, π}, ∅
B){4}, {α}, {10}, {π}, {4, α}, {4, 10}, {4, π}, {α, 10}, {α, π}, {10, π}, {4, α, 10}, {4, α, π}, {4, 10, π}, {α, 10, π}, ∅
C){4}, {α}, {10}, {π}, {4, α}, {4, 10}, {4, π}, {α, 10}, {α, π}, {10, π}, {4, α, 10}, {4, α, π}, {4, 10, π}, {α, 10, π},
{4, α, 10, π}
D){4}, {α}, {10}, {π}, {4, α}, {4, 10}, {4, π}, {α, 10}, {α, π}, {10, π}, {4, α, π}, {4, 10, π}, {α, 10, π},
{4, α, 10, π}, ∅

Question 12

Solve the problem.
In a student survey, 119 students indicated that they speak Spanish, 25 students indicated that they speakFrench, 9 students indicated that they speak both Spanish and French, and 122 students indicated thatthey speak neither. How many students participated in the survey?

A)257
B)266
C)248
D)135

Question 13

Solve the problem.
A survey of 1,981 credit card users indicated that 911 had bought books online, 876 had bought musiconline, 439 had bought pet supplies online, 139 had bought both books and music, 200 had bought bothbooks and pet supplies, 160 had bought both music and pet supplies, and 93 had bought all three. Howmany credit card users did not buy any of the three? How many bought either books or pet supplies butnot music?

A)161; 944
B)254; 837
C)161; 837
D)161; 930

Question 14

Write down all the subsets of the given set.
{3, 5, 9, 10}

A){3}, {5}, {9}, {10}, {3, 5}, {3, 9}, {3, 10}, {5, 9}, {5, 10}, {9, 10}, {3, 5, 9}, {3, 5, 10}, {3, 9, 10}, {5, 9, 10}, {3, 5, 9, 10}, ∅
B){3}, {5}, {9}, {10}, {3, 5}, {3, 9}, {3, 10}, {5, 9}, {5, 10}, {3, 5, 9}, {3, 5, 10}, {3, 9, 10}, {5, 9, 10},
{3, 5, 9, 10}, ∅
C){3}, {5}, {9}, {10}, {3, 5}, {3, 9}, {3, 10}, {5, 9}, {5, 10}, {9, 10}, {3, 5, 9}, {3, 5, 10}, {3, 9, 10}, {5, 9, 10}, {3, 5, 9, 10}
D){3}, {5}, {9}, {10}, {3, 5}, {3, 9}, {3, 10}, {5, 9}, {5, 10}, {9, 10}, {3, 5, 9}, {3, 5, 10}, {3, 9, 10},
{5, 9, 10}, ∅

Question 15

Solve the problem.
If n(A)= 46, n(B)= 45, and n( = 85, find n

A)6
B)79
C)12
D)91

Question 16

Solve the problem.
In a survey of 50 hospital patients, 24 said they were satisfied with the nursing care, 17 said they weresatisfied with the medical treatment, and 5 said they were satisfied with both. How many patients weresatisfied with neither? How many were satisfied with only the medical treatment?

A)14; 12
B)19; 17
C)14; 17
D)19; 12

Question 17

Use the information given in the figure.
How many are in A and B and C?

A)3
B)9
C)72
D)81

Question 18

Write down all the subsets of the given set.
{a}

A)∅, {a}
B){a}
C){a, b}
D)a

Question 19

Solve the problem.
In a survey of 137 vacationers in a popular beach resort town, 70 indicated they would consider buying ahome there, 62 would consider buying a beach villa, 57 would consider buying a lot, 27 would considerboth a home and a villa, 34 would consider both a home and a lot, 24 would consider both a villa and a lot,and 15 would consider all three. How many vacationers would not consider any of the three? How manywould consider only a home?

A)18; 24
B)33; 36
C)18; 14
D)18; 26

Question 20

Use the information given in the figure.
How many are in A or B or C?

A)73
B)77
C)4
D)13

Question 21

Solve the problem.
In how many ways can 8 people be lined up?

A)40,320
B)8
C)20,160
D)1

Question 22

Solve the problem.
A man has 7 shirts and 11 ties. How many different shirt and tie arrangements can he wear?

A)77
B)49
C)154
D)121

Question 23

Find the value of the permutation.
P(5, 1)

A)5
B)120
C)2.5
D)48

Question 24

Solve the problem.
How many different 5-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used andno letter can be used more than once?

A)15,120
B)59,049
C)126
D)5

Question 25

Find the value of the permutation.
P(5, 1)

A)5
B)120
C)1
D)24

Question 26

Solve the problem.
How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digitcannot be 0? Repeated digits are allowed.

A)900
B)504
C)810
D)729

Question 27

Find the value of the permutation.
P(4, 0)

A)1
B)24
C)2
D)48

Question 28

Solve the problem.
9 different books are to be arranged on a shelf. How many different arrangements are possible?

A)362,880
B)9
C)181,440
D)40,320

Question 29

Find the value of the permutation.
P(9, 9)

A)362,880
B)1
C)181,440
D)2

Question 30

Solve the problem.
How many different license plates can be made using 3 letters followed by 2 digits selected from the digits0 through 9, if letters and digits may be repeated?

A)1,757,600
B)6
C)36
D)260

Question 31

Solve the problem.
How many 7-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

A)16,384
B)210
C)35
D)840

Question 32

Solve the problem.
The following data represent the marital status of females 18 years and older in a certain U.S. city. Determine the number of females 18 years old and older who are married or widowed.

A)368,000
B)307,000
C)431,000
D)370,000

Question 33

Solve the problem.
A restaurant offers a choice of 4 salads, 7 main courses, and 2 desserts. How many possible 3-coursemeals are there?

A)56 possible meals
B)13 possible meals
C)28 possible meals
D)112 possible meals

Question 34

Solve the problem.
How many arrangements of answers are possible in a multiple-choice test with 9 questions, each of whichhas 3 possible answers?

A)19,683
B)60,480
C)84
D)504

Question 35

Solve the problem.
List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. What isP(4, 3)?

A)123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431 P(4, 3)= 24
B)123, 124, 134, 234 P(4, 3)= 4
C)123, 124, 132, 142, 143, 213, 214, 231, 241, 243, 312, 314, 321, 341, 342, 412, 413, 421, 423, 431 P(4, 3)= 20
D)111, 112, 113, 114, 121, 122, 123, 124, 131, 132, 133, 134, 141, 142, 143, 144, 211, 212, 213, 214, 221, 222, 223, 224, 231, 232, 233, 234, 241, 242, 243, 244, 311, 312, 313, 314, 321, 322, 323, 324, 331, 332, 333, 334,
341, 342, 343, 344, 411, 412, 413, 414, 421, 422, 423, 424, 431, 432, 433, 434, 441, 442, 443, 444
P(4, 3)= 64

Question 36

Solve the problem.
A certain mathematics test consists of 20 questions. Goldie decides to answer the questions withoutreading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true andfalse?

A)1,048,576
B)400
C)40
D)190

Question 37

Solve the problem.
How many 2-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters areallowed.

A)81
B)72
C)36
D)512

Question 38

Solve the problem.
Lisa has 4 skirts, 8 blouses, and 2 jackets. How many 3-piece outfits can she put together assuming anypiece goes with any other?

A)64 possible outfits
B)14 possible outfits
C)32 possible outfits
D)128 possible outfits

Question 39

Solve the problem.
List all the ordered arrangements of 6 objects a, b, c, d, e, and f choosing 2 at a time without repetition.What is P(6, 2)?

A)ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef, fa, fb, fc, fd, fe P(6, 2)= 30
B)ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef P(6, 2)= 15
C)aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df, ea, eb, ec, ed, ee, ef, fb, fc, fd, fe, ff
P(6, 2)= 36
D)ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef P(6, 2)= 25

Question 40

Solve the problem.
A student must choose 1 of 4 mathematics electives, 1 of 6 science electives, and 1 of 9 programmingelectives. How many possible course selections are there?

A)216 course selections
B)19 course selections
C)24 course selections
D)432 course selections

Question 41

Solve the problem.
A committee is to be formed consisting of 5 men and 2 women. If the committee members are to be chosenfrom 13 men and 9 women, how many different committees are possible?

A)46,332
B)170,544
C)11,119,680
D)1,323

Question 42

Solve the problem.
A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How manydifferent hot dogs can be concocted using any 5 of the extras?

A)21
B)2,520
C)42
D)1,260

Question 43

Write the word or phrase that best completes each statement or answers the question.
How many different 11-letter words (real or imaginary)can be formed from the letters of the wordMISSISSIPPI? Leave your answer in factorial form.

Question 44

Solve the problem.
In how many ways can 5 people each have different birth months?

A)95,040
B)792
C)248,832
D)60

Question 45

Solve the problem.
How many 5-card poker hands consisting of three 7ʹs and two cards that are not 7ʹs are possible in a52-card deck?

A)4512
B)2256
C)5304
D)2652

Question 46

Solve the problem.
An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 6 of themultiple-choice questions and 2 of the essay questions, in how many ways can the questions be chosen?

A)1260
B)648
C)261,273,600
D)1,814,400

Question 47

Solve the problem.
Mary finds 8 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how manyways can she make her selection? How many ways can she make her selection if he decides that one of thefish is a must?

A)56; 35
B)6,720; 840
C)336; 210
D)3,360; 420

Question 48

Solve the problem.
How many different license plates can be made using 2 letters followed by 3 digits selected from the digits0 through 9, if digits may be repeated but letters may not be repeated?

A)650,000
B)128.968254
C)486,720
D)676,000

Question 49

Write the word or phrase that best completes each statement or answers the question.
An environmental organization has 27 members. Each member will be placed on exactly 1 of 4 teams.Each team will work on a different issue. The first team has 10 members, the second has 5, the third has 4,and the fourth has 8. In how many ways can these teams be formed?

A)
B)
C)
D)

Question 50

Solve the problem.
List all the combinations of 6 objects a, b, c, d, e, and f taken 2 at a time. What is C(6, 2)?

A)ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef C(6, 2)= 15
B)ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef, fa, fb, fc, fd, fe C(6, 2)= 30
C)aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df, ea, eb, ec, ed, ee, ef, fb, fc, fd, fe, ff
C(6, 2)= 36
D)ab, ac, ad, ae, bc, bd, be, cd, ce, cf, de, df C(6, 2)= 12

Question 51

Solve the problem.
How many different license plates can be made using 3 letters followed by 2 digits selected from the digits0 through 9, if neither letters nor digits may be repeated?

A)1,404,000
B)1,757,600
C)117,000
D)1,123,200

Question 52

Solve the problem.
From 8 names on a ballot, a committee of 5 will be elected to attend a political national convention. Howmany different committees are possible?

A)56
B)6,720
C)336
D)3,360

Question 53

Solve the problem.
How many different 10-letter words (real or imaginary)can be formed from the letters in the wordPHILOSOPHY?

A)453,600
B)3,628,800
C)907,200
D)45,360

Question 54

Solve the problem.
List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)?

A)123, 124, 134, 234 C(4, 3)= 4
B)123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431 C(4, 3)= 24
C)123, 124, 134, 234, 321, 432 C(4, 3)= 6
D)111, 112, 113, 114, 121, 122, 123, 124, 131, 132, 133, 134, 141, 142, 143, 144, 211, 212, 213, 214, 221, 222, 223, 224, 231, 232, 233, 234, 241, 242, 243, 244, 311, 312, 313, 314, 321, 322, 323, 324, 331, 332, 333, 334,
341, 342, 343, 344, 411, 412, 413, 414, 421, 422, 423, 424, 431, 432, 433, 434, 441, 442, 443, 444
C(4, 3)= 64

Question 55

Solve the problem.
How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can beused more than once.

A)90
B)1,814,400
C)45
D)3,628,800

Question 56

Find the value of the combination.
C(11, 8)

A)165
B)990
C)3,326,400
D)12

Question 57

Write the word or phrase that best completes each statement or answers the question.
How many different vertical arrangements are there of 9 flags if 4 are white, 3 are blue, and 2 are red?

A)1260
B)24
C)26
D)126

Question 58

Find the value of the combination.
C(7, 7)

A)1
B)5,040
C)1,260
D)0.5

Question 59

Solve the problem.
How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3defensive players, if the players are chosen from 10 forwards, 7 midfield players, and 5 defensive players?

A)42,000
B)646,646
C)36,288,000
D)165

Question 60

Solve the problem.
A group of 6 friends goes bowling. How many different possibilities are there for the order in which theyplay if the youngest person is to bowl first?

A)120
B)720
C)5
D)6

Question 61

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Tossing a fair coin twice given that the coin is weighted so that heads is three times as likely as tails tooccur.

Question 62

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4, and Spinner II has 4 sections of equal area, labRed, Yellow, Green, and Blue. Spin Spinner I and then spin Spinner II.What is the probability of getting a 1 or 3 followed by Red?

Question 63

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Rolling a 6-sided fair die once

Question 64

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Rolling a 6-sided fair die once and tossing a fair coin once.

Question 65

Solve the problem.
A coin is weighted so that heads is 14 times as likely as tails to occur. What probability should be assignedto heads? to tails?

Question 66

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Spinner I has 3 sections of equal area, numbered 1, 2, and 3. Spinner II has 3 sections of equal area, labeledYellow, and Green. Spin Spinner I twice, then Spinner II.What is the probability of getting a 2, followed by a 1, followed by Yellow or Red?

Question 67

Determine whether the following is a probability model.

A)Yes
B)No

Question 68

Solve the problem.
A die is weighted so that an even-numbered face is three times as likely to occur as an odd-numberedface. What probability should be assigned to each face?

Question 69

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4. Spinner II has 3 sections of equal area,labeled Red, Yellow, and Green. Spinner III has 2 sections of equal area labeled A and B. Spin Spinner I,then Spinner II, then Spinner III.What is the probability of getting a 2, followed by Yellow or Green, followed by B?

Question 70

Determine whether the following is a probability model.

A)Yes
B)No

Question 71

Solve the problem.
In a probability model, which of the following numbers could be the probability of an outcome:

A)
B)
C)
D)

Question 72

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Tossing one fair coin three times

Question 73

Determine whether the following is a probability model.

A)Yes
B)No

Question 74

Determine whether the following is a probability model.

A)Yes
B)No

Question 75

Determine whether the following is a probability model.

A)Yes
B)No

Question 76

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Rolling a 6-sided fair die twice

Question 77

Determine whether the following is a probability model.

A)Yes
B)No

Question 78

Solve the problem.
A bag contains 2 red marbles, 7 blue marbles, and 8 green marbles. If one marble is selected at random,determine the probability that it is blue.

A)
B)
C)
D)

Question 79

Solve the problem.
A twelve-sided die is weighted so that only the numbers 1 through 5 will appear and they will occur withthe same probability. What probability should be assigned to each face?

Question 80

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
Tossing two fair coins once