Deck 5: A Survey of Probability Concepts

Question 1

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)

Answer 1

P(A) = 1 - P(not A)

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

0.49

Question 3

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.

Answer 3

True

Question 4

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

Question 5

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 6

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. A total of 10% 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 7

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

Question 8

Which approach to probability is exemplified by the following formula?

A)Classical approach
B)Empirical approach
C)Subjective approach
D)None Apply

Question 9

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

Question 10

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

Question 11

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

Question 12

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 13

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

Question 14

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 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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 20

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 21

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

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 22

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 78% 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 23

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-in other words, 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 24

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 78% 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 25

A lamp manufacturer designed 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 26

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 27

How many permutations of the three letters C, D, and E are possible?

A)3
B)0
C)6
D)8

Question 28

What does equal?

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

Question 29

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 30

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 78% 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 31

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 78% 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 32

A gumball machine is filled with 50 black, 150 white, 100 red, and 100 yellow gumballs 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

A supplier delivers an order for 20 electric toothbrushes to a store. By accident, three of the electric toothbrushes are defective. What is the probability that the first two electric toothbrushes sold will be returned 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 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

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 78% 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 36

An electronics firm sells four models of stereo receivers, three amplifiers, 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 37

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 38

You have the assignment of designing color codes for different parts. Three colors are used to code on each part. Once a combination of three colors is used-such as green, yellow, and red-these three colors cannot be rearranged to use as a code for another part. If there are 35 combinations, how many colors were available?

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

Question 39

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 40

A developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?

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

Question 41

An experiment may have ____________.

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

Question 42

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

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

Question 43

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 complementary 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 44

A rug manufacturer has decided to use seven compatible colors in her rugs. However, in weaving a rug, only five 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 five different colors will go into each rug-in other words, there are no repetitions of color.)

A)7
B)21
C)840
D)42

Question 45

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 46

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

A)Observation
B)Conditional probability
C)Event
D)Outcome

Question 47

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 48

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 49

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 50

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 51

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 52

Probabilities are important information when __________.

A)Summarizing a data set with a frequency chart
B)Applying descriptive statistics
C)Computing cumulative frequencies
D)Using inferential statistics

Question 53

When are two experimental outcomes mutually exclusive?

A)When they overlap on a Venn diagram.
B)If one outcome occurs, then the other cannot.
C)When the probability of one affects the probability of the other.
D)When the joint probability of the two outcomes is not equal to zero.

Question 54

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 55

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

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

Question 56

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 57

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 58

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)The Bayes theorem

Question 59

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 60

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 61

If a set of outcomes is collectively exhaustive and mutually exclusive, the sum of the probabilities equals __________.

Question 62

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

Question 63

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

Question 64

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

Question 65

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 66

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 67

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 68

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 69

In a tree diagram that illustrates the joint probabilities for a probability problem, the sum of all the joint probabilities must equal _______________.

Question 70

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

Question 71

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 72

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 73

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 has excellent potential for advancement?

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

Question 74

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 75

The probability that a flipped coin will show heads on four consecutive flips is _______________.

Question 76

The probability of selecting a professor who is male and has a master's degree is called a ______________.

Question 77

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 78

To summarize the frequencies of two nominal or ordinal variables and compute conditional probabilities, a ___________ can be used.

Question 79

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

Question 80

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)0.0004219
C)0.0000001
D)0.075