Deck 2: Probability Concepts and Applications

Question 1

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

Answer 1

True

Question 2

Given the following distribution:
The expected value is 3.

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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 8

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 9

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

Question 10

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

Question 11

A posterior probability is a revised probability.

Question 12

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

Question 13

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

Question 14

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 15

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 16

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 17

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 18

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

Question 19

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

Question 20

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

Question 21

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 22

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 23

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 24

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 25

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

Question 26

Bayes' theorem is used to calculate

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

Question 27

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

Question 28

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

Question 29

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.

Question 30

The standard deviation equals the square of the variance.

Question 31

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.

Question 32

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

Question 33

If P(A)= 0.3, P(B)= 0.2, P(A and B)= 0.0, what can be said about events A and B?

A)They are independent.
B)They are mutually exclusive.
C)They are posterior probabilities.
D)They are collectively exhaustive.

Question 34

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 35

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.

Question 36

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

Question 37

Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same.Six of the entrants are female and two of those are engineering majors.Three of the men are engineers.What is the probability that the winner will be either female or majoring in something other than engineering?

A)0.10
B)0.30
C)0.70
D)0.90

Question 38

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 39

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

Question 40

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 40 percent.
D)be unrelated.

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same.Six of the entrants are female and two of those are engineering majors.Three of the men are engineers.What is the probability that the winner will be either a non-engineering major or a male?

A)0.20
B)0.40
C)0.60
D)0.80

Question 46

Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same.Six of the entrants are female and two of those are engineering majors.Three of the men are engineers.What is the probability that the winner will be a male engineering major?

A)0.10
B)0.30
C)0.70
D)0.90

Question 47

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

Question 48

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.

Question 49

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

Question 50

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

Question 51

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.

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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

Question 57

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

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

Question 58

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

Question 59

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

Question 60

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)0.480

Question 61

A discrete random variable has a mean of 400 and a variance of 64.What is the standard deviation?

A)64
B)8
C)20
D)400

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 actually is successful?

A)0.90
B)0.54
C)0.60
D)0.63

Question 63

A company is considering producing two new electronic games designed for the popular Gameboy toy.Based on market data, management believes that there is a 60 percent chance that a "cops and robbers" game will be successful and a 40 percent chance that a "let's play house" game will be successful.As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other.If two products are introduced to the market, what is the probability that both are successful?

A)0.12
B)0.60
C)0.36
D)0.24

Question 64

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

Question 65

Properties of the normal distribution include

A)a continuous bell-shaped distribution.
B)a discrete probability distribution.
C)the number of trials is known and is either 1, 2, 3, 4, 5, etc.
D)the random variable can assume only a finite or limited set of values.

Question 66

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

Question 67

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

Question 68

The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, 2, 3, 4, 5, or 6.The probabilities are the same for each of these (1/7).If X is the number of calls arriving in a five-minute time period, what is the mean of X?

A)2
B)3
C)4
D)5

Question 69

The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, or 2.The probabilities are the same for each of these (1/3).If X is the number of calls arriving in a five-minute time period, what is the mean of X?

A)1/3
B)2/3
C)1
D)4/3

Question 70

The expected value of a probability distribution is

A)the measure of the spread of the distribution.
B)the variance of the distribution.
C)the average value of the distribution.
D)the probability density function.

Question 71

Historical data indicates that only 20% of cable customers are willing to switch companies.If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that between 2 and 5 (inclusive)customers are willing to switch companies?

A)0.1369
B)0.1746
C)0.0377
D)0.7350

Question 72

Which of the following is not true for discrete random variables?

A)The expected value is the weighted average of the values.
B)They can assume only a countable number of values.
C)The probability of each value of the random variable must be 0.
D)The probability values always sum up to 1.

Question 73

Which distribution is helpful in testing hypotheses about variances?

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

Question 74

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

Question 75

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses fewer than 600 minutes?

A)0
B)0.023
C)0.841
D)0.977

Question 76

Historical data indicates that only 20% of cable customers are willing to switch companies.If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that exactly 2 customers would be willing to switch their cable?

A)0.1
B)0.04
C)0.137
D)0.206

Question 77

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses fewer than 400 minutes?

A)0
B)0.023
C)0.159
D)0.977

Question 78

Which of the following is not true about continuous random variables?

A)They have an infinite set of values.
B)The area under each of the curves represents probabilities.
C)The entire area under each of the curves equals 1.
D)They can only be integer values.

Question 79

A company is considering producing two new electronic games designed for the popular Gameboy toy.Based on market data, management believes that there is a 60 percent chance that a "cops and robbers" game will be successful and a 40 percent chance that a "let's play house" game will be successful.As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other.If two products are introduced to the market, what is the probability that both are failures?

A)0.16
B)0.24
C)0.80
D)0.36

Question 80

Historical data indicates that only 20% of cable customers are willing to switch companies.If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that no more than 3 customers would be willing to switch their cable?

A)0.85
B)0.15
C)0.20
D)0.411