Deck 12: Counting and Probability

Question 1

Write down all the subsets of the given set.

Answer 1

D

Question 2

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

A) 25
B) 27
C) 20
D) 15

Answer 2

C

Question 3

Solve the problem.
In a survey of 55 hospital patients, 24 said they were satisfied with the nursing care, 26 said they were satisfied with the medical treatment, and 6 said they were satisfied with both. How many patients were satisfied with
Neither? How many were satisfied with only the medical treatment?

A) 11; 26
B) 17; 26
C) 18; 20
D) 11; 20

Answer 3

D

Question 4

Write down all the subsets of the given set.

Question 5

Solve the problem.

A) 89
B) 51
C) 19
D) 38

Question 6

Solve the problem.

A) 38
B) 24
C) 7
D) 31

Question 7

Solve the problem.
In a survey of 421 computer buyers, 213 put price as a main consideration, 205 put performance as a main consideration, and 57 listed both price and performance. How many computer buyers listed other
Considerations? How many looked only for performance?

A) 117; 205
B) 156; 148
C) 60; 205
D) 60; 148

Question 8

Solve the problem.
In a student survey, 97 students indicated that they speak Spanish, 30 students indicated that they speak French, 8 students indicated that they speak both Spanish and French, and 124 students indicated that they speak
Neither. How many students participated in the survey?

A) 119
B) 235
C) 243
D) 251

Question 9

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

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

Question 10

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

A) 62
B) 3
C) 8
D) 70

Question 11

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

A) 6
B) 51
C) 42
D) 50

Question 12

Solve the problem.

A) 69
B) 68
C) 48
D) 70

Question 13

Write down all the subsets of the given set.

Question 14

Write down all the subsets of the given set.

Question 15

Solve the problem.

A) 83
B) 63
C) 53
D) 73

Question 16

Solve the problem.

A) 21
B) 18
C) 23
D) 25

Question 17

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

A) 42
B) 50
C) 39
D) 43

Question 18

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

A) 13
B) 5
C) 83
D) 79

Question 19

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

A) 37
B) 35
C) 30
D) 34

Question 20

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

A) 5
B) 51
C) 7
D) 38

Question 21

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 are allowed.

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

Question 22

Find the value of the permutation.
P(9, 1)

A) 362,880
B) 1
C) 40,320
D) 9

Question 23

Solve the problem.
Lisa has 4 skirts, 10 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

A) 320 possible outfits
B) 18 possible outfits
C) 160 possible outfits
D) 40 possible outfits

Question 24

Solve the problem.
A survey of 2,504 credit card users indicated that 1,167 had bought books online, 1,226 had bought music online, 431 had bought pet supplies online, 128 had bought both books and music, 227 had bought both books and pet
Supplies, 198 had bought both music and pet supplies, and 99 had bought all three. How many credit card users
Did not buy any of the three? How many bought either books or pet supplies but not music?

A) 233; 1,016
B) 134; 1,115
C) 134; 1,144
D) 134; 1,016

Question 25

Solve the problem.
In a survey of 189 vacationers in a popular beach resort town, 73 indicated they would consider buying a home there, 73 would consider buying a beach villa, 59 would consider buying a lot, 24 would consider both a home
And a villa, 27 would consider both a home and a lot, 26 would consider both a villa and a lot, and 12 would
Consider all three. How many vacationers would not consider any of the three? How many would consider only
A home?

A) 49; 18
B) 49; 35
C) 61; 46
D) 49; 34

Question 26

Solve the problem.
A restaurant offers a choice of 5 salads, 7 main courses, and 3 desserts. How many possible 3-course meals are there?

A) 210 possible meals
B) 105 possible meals
C) 35 possible meals
D) 15 possible meals

Question 27

Solve the problem.
How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 5 possible answers?

A) 78,125
B) 21
C) 2,520
D) 42

Question 28

Solve the problem.
A man has 10 shirts and 9 ties. How many different shirt and tie arrangements can he wear?

A) 180
B) 90
C) 100
D) 81

Question 29

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) 373,000
B) 366,000
C) 308,000
D) 431,000

Question 30

Solve the problem.
How many different license plates can be made using 3 letters followed by 3 digits selected from the digits 0 through 9, if letters and digits may be repeated?

A) 17,576,000
B) 36
C) 260
D) 9

Question 31

Find the value of the permutation.
P(3, 3)

A) 6
B) 2
C) 1
D) 3

Question 32

Solve the problem.
How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

A) 360
B) 4,096
C) 30
D) 15

Question 33

Solve the problem.
A student must choose 1 of 5 mathematics electives, 1 of 7 science electives, and 1 of 7 programming electives. How many possible course selections are there?

A) 490 course selections
B) 19 course selections
C) 245 course selections
D) 35 course selections

Question 34

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

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

Question 35

Solve the problem.
Among a group of 80 investors, 19 owned shares of Stock A, 29 owned shares of Stock B, 40 owned shares of Stock C, 12 owned shares of both Stock A and Stock B, 9 owned shares of Stock A and Stock C, 13 owned shares
Of Stock B and Stock C, and 7 owned shares of all three. How many investors did not have shares in any of the
Three? How many owned shares of either Stock A or Stock C but not Stock B?

A) 19; 37
B) 19; 30
C) 26; 30
D) 19; 32

Question 36

Solve the problem.
A group of 7 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

A) 6
B) 7
C) 5,040
D) 720

Question 37

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, bc, bd, be, bf, cd, ce, cf, de, df, ef P(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 P(6, 2) = 30
C) 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
D) 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, fa, fb, fc, fd, fe, ff
P(6, 2) = 36

Question 38

Find the value of the permutation.
P(11, 4)

A) 1,663,200
B) 10,080
C) 7,920
D) 3,960

Question 39

Solve the problem.
How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

A) 9,000
B) 3,024
C) 6,561
D) 6,480

Question 40

Solve the problem.
A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

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

Question 41

Solve the problem.
How many different vertical arrangements are there of 8 flags if 3 are white, 3 are blue, and 2 are red?

A) 560
B) 18
C) 56
D) 21

Question 42

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, 321, 432 C(4, 3) = 6
B) 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
C) 123, 124, 134, 234 C(4, 3) = 4
D) 123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 C(4, 3) = 24

Question 43

Solve the problem.

A) Yes
B) No

Question 44

Solve the problem.

A) Yes
B) No

Question 45

Solve the problem.
How many 5-card poker hands consisting of three 5's and two cards that are not 5's are possible in a 52-card deck?

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

Question 46

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

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

Question 47

Find the value of the combination.
C(5, 1)

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

Question 48

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, 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
B) ab, ac, ad, ae, bc, bd, be, cd, ce, cf, de, df C(6, 2) = 12
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, fa, fb, fc, fd, fe, ff
C(6, 2) = 36
D) ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef C(6, 2) = 15

Question 49

Solve the problem.
An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 5 of the multiple-choice questions and 3 of the essay questions, in how many ways can the questions be chosen?

A) 810
B) 2520
C) 1,814,400
D) 261,273,600

Question 50

Solve the problem.
How many different 11-letter words (real or imaginary) can be formed from the letters in the word ENGINEERING?

A) 39,916,800
B) 554,400
C) 25,200
D) 277,200

Question 51

Solve the problem.
How many different 11-letter words (real or imaginary) can be formed from the letters of the word
MISSISSIPPI? Leave your answer in factorial form.

Question 52

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 many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a
Must?

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

Question 53

Solve the problem.
An environmental organization has 31 members. Each member will be placed on exactly 1 of 4 teams. Each team will work on a different issue. The first team has 4 members, the second has 9, the third has 10, and the
Fourth has 8. In how many ways can these teams be formed?

Question 54

Solve the problem.
A committee is to be formed consisting of 2 men and 3 women. If the committee members are to be chosen from 13 men and 9 women, how many different committees are possible?

A) 6,552
B) 78,624
C) 26,334
D) 162

Question 55

Solve the problem.

A) Yes
B) No

Question 56

Solve the problem.
From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention. How many different committees are possible?

A) 3,024
B) 15,120
C) 7,560
D) 126

Question 57

Solve the problem.
A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 3 of the extras?

A) 840
B) 105
C) 210
D) 35

Question 58

Solve the problem.
How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 7 midfield players, and 5 defensive players?

A) 6,048,000
B) 7,000
C) 65
D) 43,758

Question 59

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

Question 60

Solve the problem.

A) Yes
B) No

Question 61

onstruct 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, labeled Red, Yellow,
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 62

onstruct a probability model for the experiment.
Tossing one fair coin three times

Question 63

Solve the problem.
A twelve-sided die is weighted so that only the numbers 1 through 8 will appear and they will occur with the
same probability. What probability should be assigned to each face?

Question 64

Solve the problem.
A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Question 65

Solve the problem.

A) Yes
B) No

Question 66

onstruct 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, labeled Red,
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 67

Solve the problem.

A) Yes
B) No

Question 68

onstruct 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 69

Solve the problem.
A coin is weighted so that heads is 16 times as likely as tails to occur. What probability should be assigned to
heads? to tails?

Question 70

onstruct a probability model for the experiment.
Rolling a 6-sided fair die once and tossing a fair coin once.

Question 71

Solve the problem.
A 6-sided die is rolled. What is the probability of rolling a number less than 3?

Question 72

Solve the problem.

Question 73

Solve the problem.
What is the probability that the arrow will land on an odd number? Assume that all sectors have equal area.

Question 74

onstruct 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 to occur.

Question 75

onstruct a probability model for the experiment.
Rolling a 6-sided fair die twice

Question 76

Solve the problem.
A bag contains 9 red marbles, 3 blue marbles, and 7 green marbles. If one marble is selected at random, determine the probability that it is blue.

Question 77

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

Question 78

onstruct a probability model for the experiment.
Tossing two fair coins once

Question 79

onstruct a probability model for the experiment.
Rolling a 6-sided fair die once

Question 80

Solve the problem.
Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 3?