Deck 5: A Survey of Probability Concepts

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

Bayes' theorem is used to calculate a subjective probability.

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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 10

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 11

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 12

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 13

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

Question 14

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

Question 15

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 16

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 17

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

Question 18

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

Question 19

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

Question 20

Which approach to probability is exemplified by the following formula?

A) The classical approach
B) The empirical approach
C) The subjective approach
D) None of these.

Question 21

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 22

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 23

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 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 24

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 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. 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 26

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 27

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 28

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 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 29

What does equal?

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

Question 30

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 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 31

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 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 attended college?

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

Question 32

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

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

Question 33

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, 2,256, 2,562, or 5,559 would not be permitted. How many different code groups can be designed?

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

Question 34

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

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

Question 35

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 36

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 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 attended 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 37

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 38

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 39

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 40

Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts, chosen from the following: 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 41

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 42

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 43

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 44

You are assigned to design 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 are available?

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

Question 45

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 46

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 47

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

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

Question 48

An experiment may have ____________.

A) only one outcome
B) only two outcomes
C) one or more outcomes
D) several events

Question 49

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 50

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 51

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

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

Question 52

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
It is a conditional probability, expressed as P(B | A), or the probability of B givenA.

Question 53

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 54

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
P(A | B) is a conditional probability indicating that the probability of the event A is affected by eventB.

Question 55

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 56

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 57

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

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

Question 58

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 59

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 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 classified as a maintenance employee?

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

Question 61

If P(A) = 0.62, P(B) = 0.47, and P(A or B) = 0.88, then P(A and B) = _____.

A) 0.2914
B) 1.9700
C) 0.6700
D) 0.2100

Question 62

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 63

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 64

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

Question 65

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 66

A method of assigning probabilities based upon judgment, opinions, and available information is referred to as the:

A) empirical method
B) probability method
C) classical method
D) subjective method

Question 67

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 68

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

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

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 average sales ability and good potential for advancement?

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

Question 70

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 71

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

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

Question 72

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed the following: 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

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 74

If A and B are mutually exclusive events with P(A) = 0.2 and P(B) = 0.6, then P(A or B) = _____.

A) 0.00
B) 0.12
C) 0.8
D) 0.4

Question 75

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 76

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 77

Your favorite soccer team has two remaining matches to complete the season. The possible outcomes of a soccer match are win, lose, or tie. What is the possible number of outcomes for the season?

A) 2
B) 4
C) 6
D) 9

Question 78

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 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 below average sales ability and fair potential for advancement?

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

Question 80

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