Deck 2: Probability Concepts and Applications

Question 1

For two events A and B that are not mutually exclusive,the probability that either A or B will occur is P(A)× P(B)- P(A and B).

Answer 1

False

Question 2

The use of "expert opinion" is one way to approximate subjective probability values.

Answer 2

True

Question 3

A probability is a numerical statement about the chance that an event will occur.

Answer 3

True

Question 4

Stating that two events are statistically independent means that the probability of one event occurring is independent of the probability of the other event having occurred.

Question 5

Given two statistically independent events (A,B),the joint probability of P(AB)= P(A)+ P(B).

Question 6

Saying that a set of events is mutually exclusive and collectively exhaustive implies that one and only one of the events can occur on any trial.

Question 7

If two events are mutually exclusive,the probability of both events occurring is simply the sum of the individual probabilities.

Question 8

Given two statistically independent events (A,B),the conditional probability P(A|B)= P(A).

Question 9

A probability density function is a mathematical way of describing Bayes' theorem.

Question 10

Bayes' theorem enables us to calculate the probability that one event takes place knowing that a second event has or has not taken place.

Question 11

Given two statistically dependent events (A,B),the conditional probability of P(A|B)= P(B)/P(AB).

Question 12

If we roll a single die twice,the probability that the sum of the dots showing on the two rolls equals four (4),is 1/6.

Question 13

Given three statistically independent events (A,B,C),the joint probability of P(ABC)= P(A)× P(B)× P(C).

Question 14

A posterior probability is a revised probability.

Question 15

Mutually exclusive events exist if only one of the events can occur on any one trial.

Question 16

Saying that a set of events is collectively exhaustive implies that one of the events must occur.

Question 17

Assume that you have a box containing five balls: two red and three white.You draw a ball two times,each time replacing the ball just drawn before drawing the next.The probability of drawing only one white ball is 0.20.

Question 18

Subjective probability implies that we can measure the relative frequency of the values of the random variable.

Question 19

Suppose that you enter a drawing by obtaining one of 20 tickets that have been distributed.By using the classical method,you can determine that the probability of your winning the drawing is 0.05.

Question 20

The probability,P,of any event or state of nature occurring is greater than or equal to 0 and less than or equal to 1.

Question 21

The number of bad checks written at a local store is an example of a discrete random variable.

Question 22

The probability of obtaining specific outcomes in a Bernoulli process is described by the binomial probability distribution.

Question 23

Assume you have a normal distribution representing the likelihood of completion times.The mean of this distribution is 10,and the standard deviation is 3.The probability of completing the project in 8 or fewer days is the same as the probability of completing the project in 18 days or more.

Question 24

The joint probability of two or more independent events occurring is the sum of their marginal or simple probabilities.

Question 25

The expected value of a binomial distribution is expressed as np,where n equals the number of trials and p equals the probability of success of any individual trial.

Question 26

Consider a standard 52-card deck of cards.The probability of drawing either a seven or a black card is 7/13.

Question 27

In a normal distribution,the Z value represents the number of standard deviations from a value X to the mean.

Question 28

The variance of a binomial distribution is expressed as np/(1 - p),where n equals the number of trials and p equals the probability of success of any individual trial.

Question 29

Given the following distribution: The expected value is 3.

Question 30

Assume that you have an urn containing 10 balls of the following description:
4 are white (W)and lettered (L)
2 are white (W)and numbered (N)
3 are yellow (Y)and lettered (L)
1 is yellow (Y)and numbered (N)
If you draw a numbered ball (N),the probability that this ball is white (W)is 0.667.

Question 31

The standard deviation equals the square of the variance.

Question 32

A new young executive is perplexed at the number of interruptions that occur due to employee relations.She has decided to track the number of interruptions that occur during each hour of her day.Over the last month,she has determined that between 0 and 3 interruptions occur during any given hour of her day.The data is shown below. On average,she should expect 0.8 interruptions per hour.

Question 33

If we flip a coin three times,the probability of getting three heads is 0.125.

Question 34

Although one revision of prior probabilities can provide useful posterior probability estimates,additional information can be gained from performing the experiment a second time.

Question 35

Assume that you have an urn containing 10 balls of the following description:
4 are white (W)and lettered (L)
2 are white (W)and numbered (N)
3 are yellow (Y)and lettered (L)
1 is yellow (Y)and numbered (N)
If you draw a numbered ball (N),the probability that this ball is white (W)is 0.60.

Question 36

The mean and standard deviation of the Poisson distribution are equal.

Question 37

Assume that you have an urn containing 10 balls of the following description:
4 are white (W)and lettered (L)
2 are white (W)and numbered (N)
3 are yellow (Y)and lettered (L)
1 is yellow (Y)and numbered (N)
If you draw a lettered ball (L),the probability that this ball is white (W)is 0.571.

Question 38

The F distribution is a continuous probability distribution that is helpful in testing hypotheses about variances.

Question 39

If a bucket has three black balls and seven green balls,and we draw balls without replacement,the probability of drawing a green ball is independent of the number of balls previously drawn.

Question 40

A new young executive is perplexed at the number of interruptions that occur due to employee relations.She has decided to track the number of interruptions that occur during each hour of her day.Over the last month,she has determined that between 0 and 3 interruptions occur during any given hour of her day.The data is shown below. On average,she should expect 1.0 interruptions per hour.

Question 41

Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same.Six of the entrants are female and two of those are older than 40 years old.Three of the men are older than 40 years old.What is the probability that the winner will be a female who is older than 40 years old?

A)0.000
B)1.100
C)0.198
D)0.200
E)0.900

Question 42

"The probability of event B,given that event A has occurred" is known as a ________ probability.

A)continuous
B)marginal
C)simple
D)joint
E)conditional

Question 43

A conditional probability P(B|A)is equal to its marginal probability P(B)if

A)it is a joint probability.
B)statistical dependence exists.
C)statistical independence exists.
D)the events are mutually exclusive.
E)P(A)= P(B).

Question 44

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients.To be fair,the firm is randomly selecting two different employee names to "win" the tickets.There are 6 secretaries,5 consultants,and 4 partners in the firm.Which of the following statements is true?

A)The probability of two secretaries winning is the same as the probability of a secretary winning on the second draw given that a consultant won on the first draw.
B)The probability of a secretary and a consultant winning is the same as the probability of a secretary and secretary winning.
C)The probability of a secretary winning on the second draw given that a consultant won on the first draw is the same as the probability of a consultant winning on the second draw given that a secretary won on the first draw.
D)The probability that both tickets will be won by partners is the same as the probability that a consultant and secretary will win.
E)None of the above are true.

Question 45

Bayes' theorem is used to calculate

A)revised probabilities.
B)joint probabilities.
C)prior probabilities.
D)subjective probabilities.
E)marginal probabilities.

Question 46

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients.To be fair,the firm is randomly selecting two different employee names to "win" the tickets.There are 6 secretaries,5 consultants,and 4 partners in the firm.Which of the following statements is true?

A)The probability of a partner winning on the second draw given that a partner won on the first draw is 3/14.
B)The probability of a secretary winning on the second draw given that a secretary won on the first draw is 2/15.
C)The probability of a consultant winning on the second draw given that a consultant won on the first draw is 5/14.
D)The probability of a partner winning on the second draw given that a secretary won on the first draw is 8/30.
E)None of the above are true.

Question 47

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients.To be fair,the firm is randomly selecting two different employee names to "win" the tickets.There are 6 secretaries,5 consultants and 4 partners in the firm.Which of the following statements is not true?

A)The probability of a secretary winning a ticket on the first draw is 6/15.
B)The probability of a secretary winning a ticket on the second draw given that a consultant won a ticket on the first draw is 6/15.
C)The probability of a consultant winning a ticket on the first draw is 1/3.
D)The probability of two secretaries winning both tickets is 1/7.
E)The probability of a partner winning a ticket on the second draw given that a secretary won a ticket on the first draw is 4/14.

Question 48

Assume you have a normal distribution representing the likelihood of completion times.The mean of this distribution is 10,and the standard deviation is 3.The probability of completing the project in 7 or fewer days is the same as the probability of completing the project in 13 days or more.

Question 49

Subjective probability assessments depend on

A)the total number of trials.
B)the relative frequency of occurrence.
C)the number of occurrences of the event.
D)experience and judgment.
E)None of the above

Question 50

Suppose that we determine the probability of a warm winter based on the number of warm winters experienced over the past 10 years.In this case,we have used

A)relative frequency.
B)the classical method.
C)the logical method.
D)subjective probability.
E)None of the above

Question 51

When does P(A|B)= P(A)?

A)when A and B are mutually exclusive
B)when A and B are statistically independent
C)when A and B are statistically dependent
D)when A and B are collectively exhaustive
E)when P(B)= 0

Question 52

A ________ is a numerical statement about the likelihood that an event will occur.

A)mutually exclusive construct
B)collectively exhaustive construct
C)variance
D)probability
E)standard deviation

Question 53

If the sale of ice cream and pizza are independent,then as ice cream sales decrease by 60 percent during the winter months,pizza sales will

A)increase by 60 percent.
B)increase by 40 percent.
C)decrease by 60 percent.
D)decrease by 40 percent.
E)be unrelated.

Question 54

The equation P(A|B)= P(AB)/P(B)is

A)the marginal probability.
B)the formula for a conditional probability.
C)the formula for a joint probability.
D)only relevant when events A and B are collectively exhaustive.
E)None of the above

Question 55

Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same.What is the probability that one of the first three golfers that registered for the tournament will win?

A)0.100
B)0.001
C)0.300
D)0.299
E)0.700

Question 56

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random,what is the probability that the student is either enrolled in accounting or statistics,but not both?

A)0.45
B)0.50
C)0.40
D)0.05
E)None of the above

Question 57

The classical method of determining probability is

A)subjective probability.
B)marginal probability.
C)objective probability.
D)joint probability.
E)conditional probability.

Question 58

The F statistic is the ratio of two sample standard deviations from independent normal distributions.

Question 59

If two events are mutually exclusive,then

A)their probabilities can be added.
B)they may also be collectively exhaustive.
C)the joint probability is equal to 0.
D)if one occurs,the other cannot occur.
E)All of the above

Question 60

Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same.Six of the entrants are female and two of those are older than 40 years old.Three of the men are older than 40 years old.What is the probability that the winner will be either female or older than 40 years old?

A)0.000
B)1.100
C)0.198
D)0.200
E)0.900

Question 61

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random,what is the probability that the student is enrolled in both statistics and accounting?

A)0.05
B)0.06
C)0.20
D)0.25
E)None of the above

Question 62

A company is considering producing some new Gameboy electronic games.Based on past records,management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure.Market research may be used to revise these probabilities.In the past,the successful products were predicted to be successful based on market research 90 percent of the time.However,for products that failed,the market research predicted these would be successes 20 percent of the time.If market research is performed for a new product,what is the probability that the results indicate a successful market for the product and the product is actually not successful?

A)0.63
B)0.06
C)0.07
D)0.24
E)0.27

Question 63

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge.Management believes 60 percent of the existing customers will take advantage of this service.They are also considering offering customers the option of opening an account and receiving monthly bills.They believe 60 percent of customers (regardless of whether or not they use the pick-up service)will use the account service.If the two services are introduced to the market,what is the probability a customer uses neither of these services?

A)0.16
B)0.24
C)0.80
D)0.36
E)None of the above

Question 64

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random and found to be enrolled in statistics,what is the probability that the student is also enrolled in accounting?

A)0.05
B)0.30
C)0.20
D)0.25
E)None of the above

Question 65

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random,what is the probability that the student is enrolled in accounting?

A)0.20
B)0.25
C)0.30
D)0.50
E)None of the above

Question 66

A production process is known to produce a particular item in such a way that 5 percent of these are defective.If two items are randomly selected as they come off the production line,what is the probability that both are defective (assuming that they are independent)?

A)0.0100
B)0.1000
C)0.2000
D)0.0025
E)0.0250

Question 67

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random,what is the probability that the student is not enrolled in accounting?

A)0.20
B)0.25
C)0.30
D)0.50
E)None of the above

Question 68

A company is considering producing some new Gameboy electronic games.Based on past records,management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure.Market research may be used to revise these probabilities.In the past,the successful products were predicted to be successful based on market research 90 percent of the time.However,for products that failed,the market research predicted these would be successes 20 percent of the time.If market research is performed for a new product,what is the probability that the results indicate an unsuccessful market for the product and the product is actually successful?

A)0.63
B)0.06
C)0.07
D)0.24
E)0.21

Question 69

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge.Management believes 60 percent of customers will take advantage of this service.They are also considering offering customers the option of opening an account and receiving monthly bills.They believe 60 percent of their customers (regardless of whether or not they use the pick-up service)will use the account service.If the two services are introduced to the market,what is the probability a customer uses both services?

A)0.12
B)0.60
C)0.36
D)0.24
E)None of the above

Question 70

A company is considering producing some new Gameboy electronic games.Based on past records,management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure.Market research may be used to revise these probabilities.In the past,the successful products were predicted to be successful based on market research 90 percent of the time.However,for products that failed,the market research predicted these would be successes 20 percent of the time.If market research is performed for a new product,what is the probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful?

A)0.63
B)0.06
C)0.07
D)0.24
E)0.21

Question 71

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random,what is the probability that the student is enrolled in statistics?

A)0.05
B)0.20
C)0.25
D)0.30
E)None of the above

Question 72

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random,what is the probability that the student is not enrolled in statistics?

A)0.05
B)0.20
C)0.25
D)0.80
E)None of the above

Question 73

A company is considering producing some new Gameboy electronic games.Based on past records,management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure.Market research may be used to revise these probabilities.In the past,the successful products were predicted to be successful based on market research 90 percent of the time.However,for products that failed,the market research predicted these would be successes 20 percent of the time.If market research is performed for a new product,what is the probability that the product will be successful if the market research indicates a failure?

A)0.20
B)0.90
C)0.91
D)0.63
E)0.23

Question 74

Which distribution is helpful in testing hypotheses about variances?

A)binomial distribution
B)distribution
C)normal distribution
D)Poisson distribution
E)exponential distribution

Question 75

At a university with 1,000 business majors,there are 200 business students enrolled in an introductory statistics course.Of these 200 students,50 are also enrolled in an introductory accounting course.There are an additional 250 business students enrolled in accounting but not enrolled in statistics.If a business student is selected at random,what is the probability that the student is enrolled in neither accounting nor statistics?

A)0.45
B)0.50
C)0.55
D)0.05
E)None of the above

Question 76

Suppose that,historically,April has experienced rain and a temperature between 35 and 50 degrees on 20 days.Also,historically,the month of April has had a temperature between 35 and 50 degrees on 25 days.You have scheduled a golf tournament for April 12.If the temperature is between 35 and 50 degrees on that day,what will be the probability that the players will get wet?

A)0.333
B)0.667
C)0.800
D)1.000
E)0.556

Question 77

A company is considering producing some new Gameboy electronic games.Based on past records,management believes that there is a 70 percent chance that each of these will be successful,and a 30 percent chance of failure.Market research may be used to revise these probabilities.In the past,the successful products were predicted to be successful based on market research 90 percent of the time.However,for products that failed,the market research predicted these would be successes 20 percent of the time.If market research is performed for a new product,what is the probability that the product will be successful if the market research indicates a success?

A)0.10
B)0.90
C)0.91
D)0.63
E)0.09

Question 78

A production process is known to produce a particular item in such a way that 5 percent of these are defective.If two items are randomly selected as they come off the production line,what is the probability that the second item will be defective?

A)0.05
B)0.005
C)0.18
D)0.20
E)None of the above

Question 79

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge.Management believes 60 percent of the existing customers will take advantage of this service.They are also considering offering customers the option of opening an account and receiving monthly bills.They believe 60 percent of customers (regardless of whether or not they use the pick-up service)will use the account service.If the two services are introduced to the market,what is the probability that a customer uses only one of these services?

A)0.40
B)0.60
C)0.48
D)0.24
E)None of the above

Question 80

Suppose that when the temperature is between 35 and 50 degrees,it has historically rained 40% of the time.Also,historically,the month of April has had a temperature between 35 and 50 degrees on 25 days.You have scheduled a golf tournament for April 12.What is the probability that players will experience rain and a temperature between 35 and 50 degrees?

A)0.333
B)0.400
C)0.833
D)1.000
E)0.480