Deck 5: A Survey of Probability Concepts

Question 1

A combination of a set of objects is defined by the order of the objects.

Answer 1

False

Question 2

A study of 200 computer service firms revealed these incomes after taxes: What is the probability that a particular firm selected has $1 million or more in income after taxes?

A) 0.00
B) 0.25
C) 0.49
D) 0.51

Answer 2

C

Question 3

Bayes' theorem is used to calculate a subjective probability.

Answer 3

False

Question 4

The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.

Question 5

If there are 'm' ways of doing one thing and 'n' ways of doing another thing, the multiplication formula states that there are (m) · (n) ways of doing both.

Question 6

To apply the special rule of addition, the events must be mutually exclusive.

Question 7

Bayes' theorem is a method to revise the probability of an event given additional information.

Question 8

A joint probability measures the likelihood that two or more events will happen concurrently.

Question 9

The probability of rolling a 3 or 2 on a single die is an example of conditional probability.

Question 10

Which approach to probability is exemplified by the following formula? Probability of an Event =

A) Classical approach
B) Empirical approach
C) Subjective approach
D) None of the above

Question 11

The National Center for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer and 333 from heart disease. What is the probability that a particular death is due to an automobile accident?

A) 24/883 or 0.027
B) 539/883 or 0.610
C) 24/333 or 0.072
D) 182/883 or 0.206

Question 12

The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.

Question 13

If two events A and B are mutually exclusive, what does the special rule of addition state?

A) P(A or B) = P(A) + P(B)
B) P(A and B) = P(A) + P(B)
C) P(A and/or B) = P(A) + P(B)
D) P(A or B) = P(A) - P(B)

Question 14

An individual can assign a subjective probability to an event based on the individual's knowledge about the event.

Question 15

A coin is tossed four times. The joint probability that all four tosses will result in a head is ¼ or 0.25.

Question 16

The joint probability of two events, A and B, that are not independent is computed as: P(A and B) = P(A) P(B|A).

Question 17

What does the complement rule state?

A) P(A) = P(A) - P(B)
B) P(A) = 1 - P(not A)
C) P(A) = P(A) · P(B)
D) P(A) = P(A)X + P(B)

Question 18

If two events are mutually exclusive, then P(A or B) = P(A) P(B).

Question 19

The joint probability of two independent events, A and B, is computed as: P(A and B) = P(A) P(B).

Question 20

An illustration of an experiment is turning the ignition key of an automobile as it comes off the assembly line to determine whether or not the engine will start.

Question 21

A tire manufacturer advertises, "the median life of our new all-season radial tire is 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles." You purchased four of these tires. What is the probability that all four tires will wear out before traveling 50,000 miles?

A) 1/10 or 0.10
B) ¼ or 0.25
C) 1/64 or 0.0156
D) 1/16 or 0.0625

Question 22

How many permutations of the two letters C and D are possible?

A) 1
B) 0
C) 2
D) 8

Question 23

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?

A) 0.20
B) 0.08
C) 0.25
D) 0.80

Question 24

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?

A) 0.20
B) 0.08
C) 0.25
D) 0.72

Question 25

A survey of top executives revealed that 35% of them regularly read Time magazine, 20% read Newsweek and 40% read U.S. News & World Report. Ten percent read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?

A) 0.85
B) 0.06
C) 1.00
D) 0.65

Question 26

A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?

A) 1/120 or 0.00083
B) 1/16 or 0.0625
C) ⅛ or 0.125
D) 1/495 or 0.002

Question 27

What does equal?

A) 640
B) 36
C) 10
D) 120

Question 28

There are 10 rolls of film in a box and 3 are defective. Two rolls are selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?

A) ½ or 0.50
B) ¼ or 0.25
C) 1/120 or about 0.0083
D) 1/15 or about 0.07

Question 29

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?

A) P (female) P(did not attend college | female)
B) P (did attend college) P (female | did not attend college)
C) P (female) P(did attend college | female)
D) P (did attend college)

Question 30

Giorgio offers the person who purchases an 8 ounce bottle of Allure two free gifts, either an umbrella, a 1 ounce bottle of Midnight, a feminine shaving kit, a raincoat or a pair of rain boots. If you purchased Allure what is the probability you randomly selected an umbrella and a shaving kit in that order?

A) 0.00
B) 1.00
C) 0.05
D) 0.20

Question 31

An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the four types of components are sold together, they form a "system." How many different systems can the electronics firm offer?

A) 36
B) 18
C) 72
D) 144

Question 32

A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim, each, purchased one gumball. What is the likelihood both Sue and Jim get red gumballs?

A) 0.50
B) 0.062
C) 0.33
D) 0.75

Question 33

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?

A) P (male) P (did not attend college | male)
B) P (did not attend college) P (male | did not attend college)
C) P (male) P (did not attend college)
D) P (did not attend college)

Question 34

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?

A) 4
B) 24
C) 120
D) 37

Question 35

A lamp manufacturer has developed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?

A) 5
B) 10
C) 15
D) 20

Question 36

The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?

A) 5,040
B) 620
C) 10,200
D) 120

Question 37

A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?

A) 0.20
B) 0.25
C) 0.50
D) 1.00

Question 38

A study by the National Park Service revealed that 50% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?

A) 0.95
B) 0.35
C) 0.55
D) 0.05

Question 39

Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?

A) 3/20 or 0.15
B) 3/17 or 0.176
C) ¼ or 0.25
D) 3/190 or 0.01579

Question 40

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?

A) 0.044
B) 0.440
C) 0.256
D) 0.801

Question 41

When applying the special rule of addition for mutually exclusive events, the joint probability is:

A) 1
B) .5
C) 0
D) unknown

Question 42

A graphical method used to calculate joint and conditional probabilities is

A) a tree diagram.
B) a Venn diagram.
C) a histogram.
D) inferential statistics.

Question 43

A builder has agreed NOT to build all "look alike" homes in a new subdivision. The builder has three different interior plans that can be combined with any of the five different home exteriors. How many different homes can be built?

A) 8
B) 10
C) 15
D) 30

Question 44

The probability of two or more events occurring concurrently is called a(n)

A) conditional probability.
B) empirical probability.
C) joint probability.
D) tree diagram.

Question 45

Which approach to probability assumes that the events are equally likely?

A) Classical
B) Empirical
C) Subjective
D) Mutually exclusive

Question 46

The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?

A) 1/4 or 0.25
B) 1/13 or 0.077
C) 12/13 or 0.923
D) 1/3 or 0.33

Question 47

When an event's probability depends on the likelihood of another event, the probability is a(n)

A) conditional probability.
B) empirical probability.
C) joint probability.
D) mutually exclusive probability.

Question 48

If two events are independent, then their joint probability is computed with

A) the special rule of addition
B) the special rule of multiplication
C) the general rule of multiplication
D) Bayes' theorem

Question 49

When an experiment is conducted "without replacement,"

A) events are dependent
B) events are equally likely
C) the experiment can be illustrated with a Venn Diagram
D) the probability of two or more events is computed as a joint probability

Question 50

In a finance class, the final grade is based on three tests. Historically, the instructor tells the class that the joint probability of scoring "A"'s on the first two tests is 0.5. A student assigns a probability of 0.9 that she will get an "A" on the first test. What is the probability that the student will score an "A" on the second test given that she scored an "A" on the first test?

A) 0.50
B) 0.95
C) 0.55
D) 0.90

Question 51

Probabilities are important information when

A) using inferential statistics.
B) applying descriptive statistics.
C) predicting a future outcome.
D) A and C

Question 52

Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color, blue as a complementary color, red as the accent color and touches of white. Another unit might have blue as the principal color, white as the complimentary color, gold as the accent color and touches of red. If repetitions are permitted, how many different units can be decorated?

A) 7,825
B) 25
C) 125
D) 1,296

Question 53

The result of a particular experiment is called a(n)

A) observation.
B) conditional probability.
C) event.
D) outcome.

Question 54

The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)

A) 45
B) 50
C) 125
D) 14

Question 55

You have the assignment of designing color codes for different parts. Three colors are used on each part, but a combination of three colors used for one part cannot be rearranged and used to identify a different part. This means that if green, yellow and violet were used to identify a camshaft, yellow, violet and green (or any other combination of these three colors) could not be used to identify a pinion gear. If there are 35 combinations, how many colors were available?

A) 5
B) 7
C) 9
D) 11

Question 56

An experiment may have:

A) Only one outcome
B) Only two outcomes
C) Two or more outcomes
D) Several events

Question 57

The probability of an event that is affected by two or more different events is called a(n)

A) conditional probability.
B) empirical probability.
C) joint probability.
D) tree diagram.

Question 58

The first card selected from a standard 52-card deck was a king. If it is NOT returned to the deck, what is the probability that a king will be drawn on the second selection?

A) 1/3 or 0.33
B) 1/51 or 0.0196
C) 3/51 or 0.0588
D) 1/13 or 0.077

Question 59

A rug manufacturer has decided to use 7 compatible colors in her rugs. However, in weaving a rug, only 5 spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different color groupings for sale. How many color groupings using the seven colors taken five at a time are there? (This assumes that 5 different colors will go into each rug, i.e., there are no repetitions of color.)

A) 120
B) 2,520
C) 6,740
D) 36

Question 60

When are two events mutually exclusive?

A) They overlap on a Venn diagram
B) If one event occurs, then the other cannot
C) Probability of one affects the probability of the other
D) Both a and b

Question 61

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows. What is the probability that the first person selected is either in maintenance or in secretarial?

A) 0.200
B) 0.015
C) 0.059
D) 0.001

Question 62

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that: What is the probability that a designer does not prefer blue?

A) 1.0000
B) 0.9075
C) 0.8850
D) 0.7725

Question 63

When the special rule of addition is used, the events must be _______________.

Question 64

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. What is the probability that a salesperson selected at random will have below average sales ability and fair potential for advancement?

A) 0.032
B) 0.10
C) 0.16
D) 0.32

Question 65

The process used to calculate the probability of an event given additional information has been obtained through

A) Bayes' theorem.
B) classical probability.
C) permutation.
D) subjective probability

Question 66

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?

A) 0.09
B) 0.12
C) 0.30
D) 0.525

Question 67

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows. What is the probability that the first person selected is classified as a maintenance employee?

A) 0.20
B) 0.50
C) 0.025
D) 1.00

Question 68

When the special rule of multiplication is used, the events must be _______________.

Question 69

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have average sales ability?

A) 0.27
B) 0.30
C) 0.404
D) 0.45

Question 70

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. What is the probability that a salesperson selected at random has above average sales ability and is an excellent potential for advancement?

A) 0.20
B) 0.50
C) 0.27
D) 0.75

Question 71

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows. What is the probability that the first person selected is a supervisor and in management?

A) 0.00
B) 0.06
C) 0.15
D) 0.21

Question 72

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight. What is the probability of selecting three packages that are overweight?

A) 0.0000156
B) 0.0004218
C) 0.0000001
D) 0.075

Question 73

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows. What is the probability that the first person selected is either in management or in supervision?

A) 0.00
B) 0.06
C) 0.15
D) 0.21

Question 74

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight. What is the probability of selecting three packages that are satisfactory?

A) 0.900
B) 0.810
C) 0.729
D) 0.075

Question 75

Complete the following analogy: an experiment relates to outcome, as the role of a die relates to _____.

Question 76

If a set of events are collectively exhaustive and mutually exclusive, what does the sum of the probabilities equal? ___

Question 77

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that: What is the probability that a designer does not prefer yellow?

A) 0.000
B) 0.765
C) 0.885
D) 1.000

Question 78

Using the terminology of Bayes' Theorem, a posterior probability can also be defined as:

A) a conditional probability
B) a joint probability
C) 1
D) 0

Question 79

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have above average sales ability?

A) 0.27
B) 0.60
C) 0.404
D) 0.45

Question 80

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that: What is the probability that a designer does not prefer red?

A) 1.00
B) 0.77
C) 0.73
D) 0.23