- Probability Chapter.4 Verified Test Bank

CHAPTER 4

TRUE/FALSE

1. A probability near 1 for an event indicates that the event is very unlikely to occur.
2. A probability near 0 for an event indicates that the event is very likely to occur.

1. Probability is defined as the numerical measure of the likelihood that an event will occur and is always between 0 and 1.
2. Probability is a number between 0 and 1 that measures the chance or likelihood that some event or set of events will occur.

Each individual outcome of an experiment is called a sample point.

1. When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the subjective method.
2. Two events are mutually exclusive if the probability of their intersection is 0.5.
3. Two events A and B are said to be mutually exclusive if the occurrence of one event means that the other event cannot or will not occur; that is P(A ∩ B) = 0.
4. If events A and B are mutually exclusive, then P(A or B) = P(A)+P(B).

1. If events A and B are independent, then P(A and b) = P(A)*P(B).
2. If events A and B are independent, then P(A) = P(A|B).
3. A graphical method of representing the sample points or outcomes of a multiple step experiment is a Venn diagram.

1. In constructing a probability tree, probabilities beyond the first stage are conditional probabilities and the multiplication rule is used to get end node probabilities.
2. In a multi-stage experiment, if there are two outcomes per stage and there are three stages, then the total number of outcomes is six.

MULTIPLE CHOICE

1. For the cases listed below, in which one would you most likely use the classical approach to assign probability?

a. the probability that at least one of the ten orders you placed on Amazon will be delivered late.

b. the probability that you will become famous.

c. the probability that you roll a five on one roll of two dice.

d. the probability that you it will snow be cloudy tomorrow.

e. the probability that you will pass the exam today.

1. For the cases listed below, in which one would you most likely use the subjective approach to assign probability?

a. the probability of being chosen randomly from your class of 30 students to lead today’s class discussion.

b. the probability that your friend Kyle will pick up the check for lunch.

c. the probability that you will guess the right answer on a multiple choice test question.

d. the probability that you produce at least ten heads when you flip a quarter 20 times.

e. the probability that you will an ace of spades from a 52-card deck of cards.

1. When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the:

a. relative frequency method

b. subjective method

c. classical method

d. posterior method

e. none of the above

1. Drew is a long-time employee at your coffee shop. Which would be the most appropriate method for estimating the probability that Drew will be on time to work next Monday morning?

a. the classical approach

b. the relative frequency approach

c. the subjective approach

d. the experimental method

e. none of the above

1. One of the basic requirements of probability is:

a. for each experimental outcome E_i, we must have P(E_i) ≥ 1

b. P(A) = P(A^’) - 1

c. if there are k experimental outcomes, then P(E₁) + P(E₂) + … + P(E_k) = 1

d. both b and c

e. all of the above

1. Which of the following is NOT one of the basic requirements of probability?

a. for each experimental outcome E_i, then 0 < P(E_i) < 1 for all i

b. P(A) = P(A^’) - 1

c. if there are k experimental outcomes, then P(E₁) + P(E₂) + … + P(E_k) = 1

d. both b and c

e. all of the above

1. An experiment consists of four outcomes with P(E₁) = 0.2, P(E₂) = 0.3, and P(E₃) = 0.4. The probability of P(E₄) is:

a. 0.50

b. 0.90

c. 0.02

d. 0.10

e. none of the above

1. An experiment consists of four outcomes with P(E₁) = 0.2, P(E₂) = 0.25, and P(E₃) = 0.35. The probability of P(E₄) is:

a. 0.50

b. 0.90

c. 0.20

d. 0.10

e. none of the above

1. The union of events A and B is the event containing:

a. all the sample points common to both A and B

b. all the sample points belonging to A or B

c. all the sample points belonging to A or B or both

d. all the sample points belonging to A or B, but not both

e. none of the above

1. The conditional probability of A given B:

a. will always be less than the simple probability of A.

b. will always be greater than the simple probability of A.

c. will always be equal to or less than the simple probability of A.

d. will always be 0 if A and B are mutually exclusive.

e. will always be equal to the simple probability of B.

1. The joint probability of A and B is determined by:

a. adding the probabilities of A and B.

b. multiplying the probability of A by the probability of B.

c. multiplying the probability of A by the conditional probability of A given B.

d. multiplying the probability of A by the conditional probability of B given A.

e. dividing the conditional probability of B given A by the probability of B

1. A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial:

a. tails cannot appear

b. heads has a larger chance of appearing than tails

c. tails has a better chance of appearing than heads

d. heads and tails both have an equal chance of appearing

e. none of the above

1. If two events A and B are statistically independent, then:

a. A’s occurrence makes it less likely that B will occur.

b. A’s occurrence makes it more likely that B will occur.

c. A’s occurrence makes it impossible that B will occur.

d. A’s occurrence has no effect on the probability of B occurring.

e. B’s occurrence has minimal effect on the probability of A occurring.

1. If two events are independent, then:

a. they must be mutually exclusive

b. the sum of their probabilities must be equal to one

c. the probability of their intersection must be zero

d. all of the above

e. none of the above

1. Which of the following illustrates the concept of statistically independent?

a. P(A|B) = P(A)

b. P(A ∩ B) = P(A)*P(B)

c. P(A ∪ B) = P(A) + P(B)

d. a and b only

e. all of the above

1. Which of the following pairs of events would seem to be mutually exclusive?

a. Vacationing next week in Hawaii and vacationing next week in Paris.

b. Ordering a hamburger for dinner and ordering French fries for dinner.

c. Enrolling in a math class and enrolling in a Spanish class next quarter.

d. Majoring in economics and playing on the soccer team.

e. Eating a sandwich for lunch and drinking a glass of milk for lunch.

1. Which of the following event pair would seem to be mutually exclusive?

a. A = studying 12 hours a day. B = sleeping 15 hours a day.

b. A = swimming a mile each day. B = having a full-time job.

c. A = playing professional basketball. B = making a million dollars.

d. A = playing Angry Birds. B = playing Minecraft.

e. A = exercising regularly. B = listening to classical music.

1. The probability of the intersection of two mutually exclusive events:

a. can be any value between 0 and 1.

b. must always be equal to 1.

c. must always be equal to 0.

d. can be any positive value.

e. none of the above.

1. The addition law is potentially helpful when we are interested in computing the probability of:

a. independent events.

b. the intersection of two events.

c. the union of two events.

d. conditional events.

e. complimentary events.

1. If two events A and B are complementary,

a. they must also be mutually exclusive.

b. they must also be statistically independent.

c. the probabilities of the two events must sum to one.

c. both a and b are true.

d. none of the above.

1. In a Venn diagram, if the circles representing the probability of A and the probability of B overlap,

a. A and B are not statistically independent.

b. A and B are not mutually exclusive.

c. the multiplication rule can be used to find the joint probability.

d. both a and b are true.

e. none of the above.

1. Which of the following statements is TRUE concerning a probability tree?
2. it is especially helpful when the experiment involves multiple steps/stages.

b. branches extend from each node.

c. each branch represents a possible outcome.

d. beyond the first step/stage, the branch probabilities are conditional probabilities.

e. all of the above.

1. A useful counting method that enables us to count the number of experimental outcomes when x objects are to be selected from a set of n objects, where the order of selection is NOT important is:

a. a combination

b. a permutation

c. the multiplication method

d. joint probability table

e. none of the above

1. A useful counting method that enables us to count the number of experimental outcomes when x objects are to be selected from a set of n objects, where the order of selection does matter is:

a. a combination

b. a permutation

c. the multiplication method

d. joint probability table

e. none of the above

FILL IN THE BLANK

1. When the results of experimentation or historical data are used to assign probability values, the is used to assign probabilities.

a. relative frequency method

b. subjective method

c. classical method

d. posterior method

e. none of the above

1. The is potentially helpful when we are interested in computing the probability of the union of two events.

a. multiplication rule

b. the complimentary rule

c. addition rule

d. joint probability rule

e. the joint over simple rule

1. A can be used to show elements of basic probability and provide an effective visual basis for solving a wide range of probability problems.

a. probability tree

b. Venn diagram

c. scatter diagram

d. histogram

e. bar chart

1. A is a visual method that is especially helpful when the probability experiment involves multiple steps/stages.

a. probability tree

b. Venn diagram

c. scatter diagram

d. histogram

e. bar chart

1. The method enables us to count the number of experimental outcomes when x objects are to be selected from a set of n objects, where the order of selection is important.

a. combination

b. permutation

c. multiplication method

d. joint probability table

e. probability tree

PROBLEMS

1. Below is a table showing the five department heads in Carlton-Manning’s San Jose (CA) and Utica (NY) regional offices, along with each department head’s forecast of sales in the upcoming quarter. One person from the group will be randomly chosen to make a sales presentation. Determine the simple probability of randomly selecting a person who forecasts a decrease in sales.

a. .4

b. .6

c. .125

d. .25

e. .3

1. Below is a table showing the five department heads in Carlton-Manning’s San Jose and Utica (N.Y.) regional offices, along with each department head’s forecast of sales in the upcoming quarter. One person from the group will be randomly chosen to make a sales presentation. Determine the simple probability of selecting a person from the Utica Office.

a. .2

b. .5

c. .25

d. .125

e. ..4

1. The table below shows six companies that were established within the last two years, along with each company’s classification and current financial status (profitable or unprofitable). If one company will be randomly selected for closer study, what is the conditional probability that the company selected is unprofitable, given that the company is classified as low tech.

a. .333

b. .667

c. .5

d. .125

e. .25

1. The table below shows six companies that were established within the last two years, along with each company’s classification and current financial status (profitable or unprofitable). If one company will be randomly selected for closer study, what is the conditional probability that the company selected is a Hi Tech company, given that the company is profitable?

a. .333

b. .5

c. .25

d. .667

e. .4

1. Below is a table showing the five department heads in Carlton-Manning’s San Jose and Utica (N.Y.) regional offices, along with each department head’s forecast of sales in the upcoming quarter. One person from the group will be randomly chosen to make a sales presentation. Determine the conditional probability that the person selected is from the San Jose office, given that the person forecasts a decrease in sales.

a. .5

b. .333

c. .667

d. .4

e. .125

1. Below is a table showing the five department heads in Carlton-Manning’s San Jose (CA) and Utica (NY) regional offices, along with each department head’s forecast of sales in the upcoming quarter. One person from the group will be randomly chosen to make a sales presentation. Determine the conditional probability that the person selected is from the San Jose office, given that the person forecasts an increase in sales.

a. 1.0

b. .333

c. .5

d. .667

e. .00

1. The table below shows six companies that were established within the last two years, along with each company’s classification and current financial status (profitable or unprofitable). If one company will be randomly selected for closer study, what is the joint probability that the company selected is a Hi Tech company and is currently profitable?

a. 1.0

b. .333

c. .167

d. .667

e. .00

1. Below is a table showing the five department heads in Carlton-Manning’s San Jose and Utica (N.Y.) regional offices, along with each department head’s forecast of sales in the upcoming quarter. One person from the group will be randomly chosen to make a sales presentation. Are the events “choosing someone from the Utica office” and “choosing someone who forecasts a decrease in sales” statistically independent.

a. Yes, since P(San Jose given increase) is equal to P(increase).

b. Yes, since P(San Jose given increase) is equal to P(San Jose).

c. No, since P(San Jose given increase) is not equal to P(San Jose).

d. No, since P(San Jose given increase) is not equal to P(increase).

e. No, since P(San Jose given decrease) is not equal to P(decrease)

1. The table below shows six companies that were established within the last two years, along with each company’s classification and current financial status (profitable or unprofitable). One company from the group will be randomly chosen for closer study. Are the events “choosing a Lo Tech company” and “choosing an unprofitable company” statistically independent?

a. Yes, since P(Lo Tech given unprofitable) is equal to P(unprofitable).

b. Yes, since P(unprofitable given Lo Tech) is equal to P(Lo Tech).

c. Yes, since P(Lo Tech given unprofitable) is equal to P(Lo Tech).

d. No, since P(unprofitable given Lo Tech) is not equal to P(Lo Tech).

e. No, since P(profitable given Lo Tech) is not equal to P(Lo Tech).

1. Josh has been given two assignments, assignment A and assignment B. He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%. Assuming that assignment grades are statistically independent, how likely is it that Josh gets a passing grade on both assignments?

a. 20%

b. 50%

c. 30%

d. 10%

e. 70%

1. Josh has been given two assignments, assignment A and assignment B. He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%. If Josh gets a passing grade on assignment A, he figures his chances of getting a passing grade on assignment B increase to 70%. How likely is it that Josh gets a passing grade on assignment A but not on assignment B?

a. .30

b. .42

c. .18

d. .49

e. .85

1. Josh has been given two assignments, assignment A and assignment B. He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%. If Josh gets a passing grade on assignment A, he figures his chances of getting a passing grade on assignment B increase to 70%. How likely is it that Josh does NOT get a passing grade on either assignment?

a. .85

b. .32

c. .20

d. .18

e. .15

1. Josh has been given two assignments, assignment A and assignment B. He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%. If Josh gets a passing grade on assignment A, he figures his chances of getting a passing grade on assignment B increase to 70%. How likely is it that Josh gets a passing grade on assignment B but NOT on assignment A?

a. .08

b. .32

c. .20

d. .18

e. .15

1. Tobrix Corporation plans to introduce two new games this year. Analysts estimate a 60% probability that Teletron will be successful and a 50% probability that Monstroids will be successful. They agree that there is a 30% probability that both will be successful. How likely is it that either Teletron or Monstroids (or both) will be successful?

a. .2

b. .8

c. .3

d. .7

e .5

1. Eryn has just bought two stocks: A and B. She estimates that stock A has an 80% chance of increasing in value. She estimates that stock B has a 70% chance of increasing in value. She also estimates that if stock A increases in value, the chance that stock B will increase jumps to 75%. What’s the probability that both stocks increase in value?

a. .60

b. .56

c. .665

d. .74

e. .65

1. Eryn has just bought two stocks: A and B. She estimates that stock A has an 80% chance of increasing in value. She estimates that stock B has a 70% chance of increasing in value. She also estimates that if stock A increases in value, the chance that stock B will increase jumps to 75%. What’s the probability that at least one of the stocks will increase in value?

a. .24

b. .20

c. .26

d. .90

e. .56

1. Marcus works as a waiter on the weekends and in the evenings after classes. 7% of the time he gets a customer’s food order wrong. 3% of the time he gets a customer’s drink order wrong. 2% of the time, he gets both orders wrong. According to these numbers, if Marcus gets the food order wrong for a customer, how likely is it that he gets the drink order wrong, as well?

a. .210

b. .286

c. .140

d. .060

e. .568

1. Marcus works as a waiter on the weekends and in the evenings after classes. 7% of the time he gets a customer’s food order wrong. 3% of the time he gets a customer’s drink order wrong. Two percent of the time, he gets both orders wrong. According to these numbers, if Marcus gets a customer’s drink order wrong, how likely is it that he gets the customer’s food order wrong, as well?

a. .333

b. .060

c. .667

d. .210

e. .014

1. Marcus works as a waiter on the weekends and in the evenings after classes. 7% of the time he gets a customer’s food order wrong. 3% of the time he gets a customer’s drink order wrong. Two percent of the time, he gets both orders wrong. According to these numbers, are the two events—getting the drink order wrong and getting the food order wrong— statistically independent?

a. Yes, since P(wrong food given wrong drink) is equal to P(wrong food).

b. No, since P(wrong food given wrong drink) is not equal to P(wrong drink).

c. No, since P(wrong food given wrong drink) is not equal to P(wrong food).

d. Yes, P(wrong food given wrong drink) is equal to P(wrong drink).

e. Yes, P(wrong food given wrong drink) is equal to P(wrong food).

1. According to studies, 62% percent of online teenagers are Facebook users, while 51% are users of Twitter. If 43% are both Facebook and Twitter users, what proportion of Facebook users are Twitter users?

a. .694

b. .267

c. .733

d. .843

e. .167

1. According to studies, 62% percent of online teenagers are Facebook users, while 51% are users of Twitter. If 43% are both Facebook and Twitter users, what percent of Twitter users are Facebook users?

a. .167

b. .694

c. .733

d. .267

e. .843

1. According to studies, 62% percent of online teenagers are Facebook users, while 51% are use Twitter. 43% are both Facebook and Twitter users. Are the two events—uses Facebook and uses Twitter—statistically independent?

a. Yes, since P(Facebook given Twitter) is equal to P(Facebook).

b. Yes, since P(Facebook given Twitter) is equal to P(Twitter).

c. No, since P(Facebook given Twitter) is not equal to P(Twitter).

d. No, since P(Facebook given Twitter) is not equal to P(Facebook).

e. No, since P(Twitter given Facebook) is not equal to P(Facebook).

1. If the probability of an economic recovery next year is 0.55, what is the probability that there won’t be a recovery?

a. .45

b. .25

c. .015

d. .50

e. .75

1. If the probability that either the Microsoft or Intel (or both) will have a significant growth in profits next year is 0.75, what is the probability that neither will?

a. .25

b. .176

c. .125

d. .15

e. .475

1. If the probability that both Microsoft and Intel will have a significant growth in profits next year is 0.4, what is the probability that at least one of them will not?

a. .4

b. .6

c. .667

d. .333

e. .5

1. The price of Chrysler stock increased on 30% of the trading days over the past year. The price of Ford stock increased on 40% of the trading days over the past year. On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well. On what proportion of the days did both stocks increase in price?

a. .18

b. .12

c. .36

d. .24

e. .70

1. The price of Chrysler stock increased on 30% of the trading days. The price of Ford stock increased on 40% of the trading days over the past year. On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well. On what proportion of the days did neither stock increase in price?

a. .82

b. .46

c. .54

d. .30

e. .88

1. The price of Chrysler stock increased on 30% of the trading days over the past year. The price of Ford stock increased on 40% of the trading days over the past year. On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well. On what proportion of the days did exactly one of the stocks increase in price?

a. .22

b. .88

c. .40

d. .12

e. .24

1. The price of Chrysler stock increased on 30% of the trading days over the past year. The price of Ford stock increased on 40% of the trading days over the past year. On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well. On what proportion of the days did at least one stock increase in price?

a. .54

b. .46

c. .12

d. .88

e. .22

1. Antonia and Bethany played in the same 50 tennis matches last year. Antonia made the finals in 20 of those matches. Bethany made the finals in 15 of the matches. In 12 of the matches, they both made the final. Determine the proportion of the matches in which Bethany made the final, but Antonia did not.

a. .10

b. .24

c. .18

d. .06

e. .76

1. Antonia and Bethany played in the same 50 tennis matches last year. Antonia made the finals in 20 of those matches. Bethany made the finals in 15 of the matches. In 12 of the matches, they both made the final. In what proportion of the matches did neither player make it to the final match?

a. .24

b. .82

c. .90

d. .88

e. .54

1. Antonia and Bethany played in the same 50 tennis matches last year. Antonia made the finals in 20 of those matches. Bethany made the finals in 15 of the matches. In 12 of the matches, they both made it to the finals. In what proportion of the matches where Antonia made the final did Bethany also make the final?

a. .54

b. .06

c. .12

d. .88

e. .60

1. Antonia and Bethany played in the same 50 tennis matches last year. Antonia made the finals in 20 of those matches. Bethany made the finals in 15 of the matches. In 12 of the matches, they both made it to the finals. Are the events “Antonia makes it to the finals” and “Bethany makes it to the finals” statistically independent?

a. No, since P(Antonia given Bethany) is not equal to P(Bethany)

b. No, since P(Antonia given Bethany) is not equal to P(Antonia)

c. Yes, since P(Antonia given Bethany) is equal to P(Bethany)

d. Yes, since P(Antonia given Bethany) is equal to P(Antonia)

e. Yes, since P(Bethany given Antonia) is equal to P(Antonia)

1. K-Tone Marketing has just launched two new products: Product A and Product B. The probability that A will become a market leader is put at .60. The probability that B will become a market leader is .20 of the time. Assuming that the success of one product is independent of the success of the other, what is the probability that at least one of the products will end up being a market leader?

a. .68

b. .48

c. .12

d. .32

e. .50

1. Your investment club plans to buy three stocks this semester and has narrowed the choice of stocks to a final ten— six US companies and four EU companies. From the ten finalists, you now plan to randomly select the three stocks to buy. Determine the probability that you would end up with all three choices being US stocks.

a. .1823

b. .2472

c. .1667

d. .1258

e. .2205

1. Your investment club plans to buy three stocks this semester and has narrowed the choice of stocks to a final ten— six US companies and four EU companies. From the ten finalists, you now plan to randomly select the three stocks to buy. What is the probability that you end up buying one US stock and two EU stocks?

a. .30

b. .80

c. .20

d. .70

e. .25

1. Your investment club plans to buy three stocks this semester and has narrowed the choice of stocks to a final ten— six US companies and four EU companies. From the ten finalists, you now plan to randomly select the three stocks to buy. What is the probability that you end up buying no US stocks?

a. .064

b. .127

c. .056

d. .129

e. .033

1. As project manager at Gonzaga Contracting, you currently have a major project nearing completion, but are concerned about the delivery of the roofing materials needed to complete the project. Ace roofing, your main supplier, may need to first deliver materials to another of its clients. You put the chance of that happening at 30%. You believe that if Ace has to first deliver to its other client, there’s a 60% chance that you will not get your delivery in time to complete your project on schedule. If Ace does not have to first deliver to its other client, you estimate that the chance that you will not get your delivery in time to finish on schedule falls to 10%. Determine the likelihood that you will not get the roofing delivery in time to finish on schedule.

a. .50

b. .18

c. .06

d. .25

e. .03

1. As project manager at Gonzaga Contracting, you currently have a major project nearing completion, but are concerned about the delivery of the roofing materials needed to complete the project. Ace roofing, your main supplier, may need to first deliver materials to another of its clients. You put the chance of that happening at 30%. You believe that if Ace has to first deliver to its other client, there’s a 60% chance that you will not get your delivery in time to complete your project on schedule. If Ace does not have to first deliver to its other client, you estimate that the chance that you will not get your delivery in time to finish on schedule falls to 10%. Suppose you now learn that Ace will not be able to deliver your roofing materials in time. How likely is that they had to first deliver to their other client?

a. .18

b. .28

c. .09

d. .56

e. .72

1. Randall Realty has two rental properties available. The agent assesses a 0.6 probability that property A will be rented by the end of the month, and a probability of 0.8 that property B will be rented by the end of the month. She also believes there is a 0.5 probability that both properties will be rented by the end of the month. What is the probability that at least one of the properties is rented by the end of the month

a. .75

b. .40

c. .60

d. .90

e. 1.40

1. Randall Realty has two rental properties available. The agent assesses a 0.6 probability that property A will be rented by the end of the month, and a probability of 0.8 that property B will be rented by the end of the month. She also believes there is a 0.5 probability that both properties will be rented by the end of the month. What is the probability that property A is rented if property B is rented?

a. .125

b. .625

c. .325

d. .525

e. .475

1. Randall Realty has two rental properties available. The agent assesses a 0.6 probability that property A will be rented by the end of the month, and a probability of 0.8 that property B will be rented by the end of the month. She also believes there is a 0.5 probability that both properties will be rented by the end of the month. What is the probability that both properties fail to be rented by the end of the month?

a. .1

b. .8

c. .4

d. .48

e. .32

1. Randall Realty has two rental properties available. The agent assesses a 0.6 probability that property A will be rented by the end of the month, and a probability of 0.8 that property B will be rented by the end of the month. She also believes there is a 0.5 probability that both properties will be rented by the end of the month. Is the renting of property A independent of the renting of property B?

a. Yes, since P(A rents given B rents) is equal to P(A rents).

b. No, since P(A rents given B rents) is not equal to P(B rents).

c. No, since P(A rents given B rents) is not equal to P(A rents).

d. Yes, since P(A rents given B rents) is equal to P(B rents).

e. Yes, since P(B rents given A rents) is equal to P(B rents).

1. In a recent survey of local businessmen and businesswomen, 40% of the respondents belong to the Rotary Club, 70% belong to the Chamber of Commerce. 30% were members of both. What proportion of the respondents are members of at least one of the groups?

a. .12

b. .28

c. .9

d. .7

e. .8

1. In a recent survey of local businessmen and businesswomen, 40% of the respondents belong to the Rotary Club, 70% belong to the Chamber of Commerce. 30% were members of both. What proportion belong to neither group?

a. .12

b. .2

c. .98

d. .4

e. .75

1. In a recent survey of local business owners, 40% of the respondents belong to the Rotary Club, 70% belong to the Chamber of Commerce. 30% were members of both. 30% said that they read both. What proportion belong to the Chamber of Commerce but not the Rotary Club?

a. .5

b. .12

c. .4

d. .88

e. .25

1. In a recent survey of local business owners, 40% of the respondents belong to the Rotary Club, 70% belong to the Chamber of Commerce. 30% were members of both. If a respondent is selected at random, and it turns out that that person is a member of the Chamber of Commerce, how likely is it that that person is also a member of the Rotary Club?

a. .5422

b. .6617

c. .2500

d. .4286

e. .3624

1. In a recent survey of local business owners, 40% of the respondents belong to the Rotary Club and 70% belong to the Chamber of Commerce. 30% were members of both. Are the events "member of Chamber" and "member of Rotary" statistically independent?

a. Yes, since P(Chamber given Rotary) is equal to P(Rotary)

b. Yes, since P(Chamber given Rotary) is equal to P(Chamber)

c. Yes, since P(Rotary given Chamber) is equal to P(Chamber)

d. No, since P(Chamber given Rotary) is not equal to P(Rotary)

e. No, since P(Chamber given Rotary) is not equal to P(Chamber)

1. In a recent survey of local business owners, 40% of the respondents belong to the Rotary Club and 70% belong to the Chamber of Commerce. 30% were members of both. Are the events "member of Chamber" and "member of Rotary" mutually exclusive?

a. Yes, since P(Chamber and Rotary) is equal to 0

b. No, since P(Chamber and Rotary) is not equal to P(Chamber)

c. No, since P(Chamber and Rotary) is not equal to 0

d. Yes, since P(Chamber and Rotary) is not equal to P(Chamber)

d. Yes, since P(Rotary and Chamber) is not equal to P(Chamber)

1. When a machine is working properly only 4% of the units it produces are defective. When it slips out of adjustment, the rate jumps to 25% and the machine has to be shut down and adjusted. On 90% of the mornings when production restarts, the machine is in proper adjustment. You turn on the machine this morning and produce the first unit. How likely is it that the first unit is defective?

a. .057

b. .061

c. .10

d. .126

e. .04

1. When a machine is working properly only 4% of the units it produces are defective. When it slips out of adjustment, the rate jumps to 25% and the machine has to be shut down and adjusted. On 90% of the mornings when production restarts, the machine is in proper adjustment. You turn on the machine this morning and produce the first unit. If the first unit is defective, what is the probability that the machine is in adjustment?

a. .563

b. .360

c. .10

d. .536

e. .618

1. When a machine is working properly only 4% of the units it produces are defective. When it slips out of adjustment, the rate jumps to 25% and the machine has to be shut down and adjusted. On 90% of the mornings when production restarts, the machine is in proper adjustment. You turn on the machine this morning and produce the first unit. If the first unit is not defective, what is the probability that the machine is out of adjustment?

a. .10

b. .360

c. .080

d. .536

e. .618

1. The probability that Omaha will be struck by a severe tornado during the year is 60%. The probability that Omaha will be struck by a severe blizzard is 30%. The likelihood that Omaha will be hit by both is put at 10%. What is the probability that at least one of the weather events occurs this year?

a. .2

b. .5

c. .75

d. .25

e. .8

1. The probability that Oklahoma will be struck by a severe tornado during the year is 60%. The probability that Oklahoma will be struck by a severe blizzard is 30%. The likelihood that Oklahoma will be hit by both is put at 10%. What is the probability that neither weather event will occur this year?

a. .8

b. .5

c. .2

d. .4

e. .7

1. The probability that Oklahoma will be struck by a severe tornado during the year is 60%. The probability that Oklahoma will be struck by a severe blizzard is 30%. The likelihood that Oklahoma will be hit by both is put at 10%. If Oklahoma is struck by a severe blizzard this year, how likely is it that it will also be struck by a severe tornado?

a. .333

b. .667

c. .5

d. .4

e. .18

1. On any given morning, the probability that Alex catches his 8 AM train into the city is .5. What is the likelihood that Alex will miss the train on five consecutive mornings?

a. .0014

b. .03125

c. .0658

d. .0871

e. .0026

1. According to a recent survey, 90% of all American CEO’s favor a general lowering of tariffs between the US and the EU, while only 20% of EU CEO’s favor such a move. At a conference of American and EU CEOs, 70% of those in attendance are American and the remaining 30% are from the EU. You choose a CEO at random and discover that the person you have chosen is a supporter of a general lowering of tariffs. What is the probability that the person is from the EU?

a. .132

b. .087

c. .023

d. .198

e. .154

1. You plan a conference call to present your new marketing proposal to two of your partners in China—Arthur Tang and Barbara Liu. You decide that the probability of Arthur endorsing the proposal is 0.6 and probability of Barbara endorsing the proposal is 0.4. The probability that both will endorse the proposal is put at 0.1. Determine the probability that at least one of the partners will endorse your proposal.

a. .8

b. .64

c. .9

d. .81

e. .75

1. You plan a conference call to present your new marketing proposal to two of your partners in China—Arthur Tang and Barbara Liu. You decide that the probability of Arthur endorsing the proposal is 0.6 and probability of Barbara endorsing the proposal is 0.4. The probability that both will endorse the proposal is put at 0.1. Determine the probability that Barbara will endorse your proposal given that Arthur does not.

a. .5

b. .25

c. .2

d. .75

e. .8

1. You plan a conference call to present your new marketing proposal to two of your partners in China—Arthur Tang and Barbara Liu. You decide that the probability of Arthur endorsing the proposal is 0.6 and probability of Barbara endorsing the proposal is 0.4. The probability that both will endorse the proposal is put at 0.1. Determine the probability that Arthur will not endorse the proposal given that Barbara does.

a. .833

b. .167

c. .75

d. .25

e. .50

1. You plan a conference call to present your new marketing proposal to two of your partners in China—Arthur Tang and Barbara Liu. You decide that the probability of Arthur endorsing the proposal is 0.6 and probability of Barbara endorsing the proposal is 0.4. The probability that both will endorse the proposal is put at 0.1. Determine the probability that only Arthur endorses the proposal.

a. .75

b. .5

c. .25

d. .8

e. .2

1. In a recent survey of 600 Belkin employees (240 in the US, 210 in Europe, and the remainder in Asia), each employee was asked the question, “Is the company doing enough to support you in your work?” Overall, 64% of the survey participants said yes. The remaining 36% said no. You note that 38% of the participants were US employees who said yes. You also note that 80% of the European employees in the survey said no. What proportion of employees in the survey are employees in Asia who answered no?

a. .12

b. .06

c. .24

d. .04

e. .2

1. In a recent survey of 600 Belkin employees (240 in the US, 210 in Europe, and the remainder in Asia), each employee was asked the question, “Is the company doing enough to support you in your work?” Overall, 64% of the survey participants said yes. The remaining 36% said no. You note that 38% of the participants were US employees who said yes. You also note that 80% of the European employees in the survey said no. What proportion of those who responded no are European employees?

a. .109

b. .063

c. .044

d. .128

e. .246

1. In a recent survey of 600 Belkin employees (240 in the US, 210 in Europe, and the remainder in Asia), each employee was asked the question, “Is the company doing enough to support you in your work?” Overall, 64% of the survey participants said yes. The remaining 36% said no. You note that 38% of the participants were US employees who said yes. You also note that 80% of the European employees in the survey said no. If you randomly choose a US employee from the survey, how likely is it that he/she responded no?

a. .05

b. .75

c. .06

d. .12

e. .04

1. In a survey of 1000 college freshmen, 60% indicated that they took at least one AP class in high school, while 40% did not. 45% of the students who took at least one AP class said they were admitted to the college of their choice. 15% of the students who did not take at least one AP class said they were admitted to the college of their choice. What proportion of the students were admitted to the college of their choice?

a. .46

b. .24

c. .39

d. .33

e. .45

1. In a survey of 1000 college freshmen, 60% indicated that they took at least one AP class in high school, while 40% did not. 45% of the students who took at least one AP class said they were admitted to the college of their choice. 15% of the students who did not take at least one AP class said they were admitted to the college of their choice. According to the study, what is the probability that a student took at least one AP class if that student was admitted to the college of his/her choice?

a. .723

b. .818

c. .542

d. .876

e. .769

1. The following table lists the world’s five largest employers, along with their industry and nationality (BBC News, March 19, 2012). If one of the five employers is chosen at random, what is the probability that it is headquartered in China?

a. 20%

b. 20.5%

c. 25%

d. 80%

e. 40%

1. The following table lists the world’s five largest employers, along with their industry and nationality (BBC News, March 19, 2012). You plan to randomly choose one employer from the group. Find the conditional probability that the employer you select is in the defense industry, given that the employer is headquartered in the US.

a. 20%

b. 33%

c. 50%

d. 60%

e. 40%

1. The following table lists the world’s five largest employers, along with their industry and nationality (BBC News, March 19, 2012). You plan to randomly choose one employer from the group. Find the conditional probability that the employer you select is in the defense industry, given that the employer is headquartered in the US.

a. 20%

b. 33%

c. 40%

d. 50%

e. 100%

1. The following table lists the world’s five largest employers, along with their industry and nationality (BBC News, March 19, 2012). You plan to randomly choose one employer from the group. Are the events “choosing an employer in the defense industry” and “choosing an employer headquartered in the US” statistically independent?

a. Yes, the two events are statistically independent.

b. No, the two events are not statically independent.

c. Statistical independence cannot be determined based on the information given.

1. The following table lists the world’s five largest employers, along with their industry and nationality (BBC News, March 19, 2012). You plan to randomly choose one employer from the group. Are the events “choosing an employer in the health care industry” and “choosing an employer headquartered in the UK” statistically independent?

a. Yes, the two events are statistically independent.

b. No, the two events are not statically independent.

c. Statistical independence cannot be determined based on the information given.

1. Suppose that 1% of all tax returns are audited by the IRS. If two tax returns are randomly selected, what is the probability that both will be audited? (Assume that they are selected with replacement; that is, it is possible for the same tax return to be selected twice).

a. 0.01%

b. .1%

c. 1%

d. 2%

e. 5%

1. Nationally, 46% of applicants to medical school are accepted to at least one school. If two medical school applicants are selected at random, what is the probability that neither of the two was accepted by any medical school? (Assume that the two applicants are selected with replacement; that is, it is possible for the same applicant to be selected twice).

a. 21%

b. 29%

c. 46%

d. 54%

e. 87%

1. Of the 50 European countries (includes Eurasian countries), 52% are members of North Atlantic Treaty Organization (NATO) and 56% are member states of the European Union (EU). Forty-four percent of European countries are members of both NATO and the EU. If a European nation is chosen at random, what is the probability that it belongs to at least one of the two organizations?

a. 29%

b. 64%

c. 78%

d. 96%

e. 108%

1. Of the 50 European countries (includes Eurasian countries), 52% are members of North Atlantic Treaty Organization (NATO) and 56% are member states of the European Union (EU). Forty-four percent of European countries are members of both NATO and the EU. If a European nation is a member of NATO, what is the probability that it is also a member of the EU?

a. 44%

b. 56%

c. 79%

d. 85%

e. 100%

1. Kim eats out with friends on 70% of all Friday evenings. She goes to see a film on 15% of all Friday evenings. On 10 percent of all Friday evenings, she eats out with friends and goes to see a film. On any Friday, what is the probability that Kim eats out with friends, goes to see a film, or both?

a. 10.5%

b. 25%

c. 75%

d. 85%

e. 100%

1. Kim eats out with friends on 70% of all her Friday evenings. She goes to see a film on 15% of all her Friday evenings. On 10% of all her Friday evenings, she both eats out with friends and goes to see a film. If Kim goes out to eat with friends on a given Friday, what is that probability that she also goes to see a film?

a. 10%

b. 14%

c. 67%

d. 75%

e. 90%

1. Each year, on Groundhog’s Day, February 2nd, everyone awaits the appearance of the groundhog. As the story has it, if he emerges from his hole and if it is sunny, he will be startled by his own shadow and quickly retreat back into his hole. This signals six more weeks of winter. However, if it is a cloudy day and he sees no shadow, spring-like weather will come early.

There is a 25% chance that the groundhog will see his shadow on February 2. The probability of spring coming early if the groundhog sees his shadow is 20%; the probability of spring coming early if the groundhog does not see his shadow is 60%. Suppose that spring comes early this year. What is the probability that the groundhog saw his shadow on February 2?

a. 50%

b. 12%

c. 10%

d. 5%

e. 2%

1. There is a 25% chance that Seattle will build a new basketball stadium in the next five years. If the stadium is built, there is a 60% chance that Seattle will get a new expansion NBA team. If the stadium is not built, there is only a 15% chance that Seattle will get a new expansion NBA team. Using a probability tree, determine the probability that Seattle will get a new expansion NBA team.

a. 15%

b. 26%

c. 60%

d. 70%

e. 90%

1. You have an important test tomorrow morning and want to be sure to wake up at 6:00 AM to study. Without an alarm to wake you up, you know you have no chance. You have an alarm clock that works 80% of the time. To be on the safe side, you decide to set both your alarm clock and your roommate’s alarm clock—also 80% reliable. How likely is it you’ll be awakened at the proper time? (Assume statistical independence.)

a. .04

b. .64

c. .36

d. .96

e..16

1. You have an important test tomorrow morning and want to be sure to wake up at 6:00 AM to study. Without an alarm to wake you up, you know you have no chance. You have an alarm clock that works 80% of the time. To be on the safe side, you decide to set your alarm clock plus your two roommates’ alarm clocks—each of which is also 80% reliable. With the three clocks set, how likely is it that you will be awakened at the time you want? (Assume statistical independence.)

a. .64

b. .001

c. .992

d. .512

e. .488

1. You have an important test tomorrow morning and want to be sure to wake up at 6:00 AM to study. Without an alarm to wake you up, you know you have no chance. You have an alarm clock that works 80% of the time. To be on the safe side, you decide to set your alarm clock plus the alarm clocks that you borrow from some of your friends in the dorm. Assuming that each of these borrowed clocks is also 80% reliable, how many clocks should you borrow if you want to ensure that there is no more than 1 chance in a thousand that you will not be awakened at the proper time? (Assume statistical independence.)

a. 6

b. 4

c. 3

d. 5

e. 2

1. Gomez Office Supply has installed three smoke detectors in its stockroom. The installer asserts that each detector is 90% likely to detect a fire within 30 seconds of ignition. Assuming the three detectors function independently, how likely is it that a fire will be detected within 30 seconds?

a. .100

b. .001

c. .300

d. .999

e. .270

1. Juliana estimates that there’s a 50% probability that the construction of her company’s new data storage facility will be completed within the next month. However, she believes that it is 30% likely that the construction will take two months, and 20% likely it will take a full three months. She also believes that if the construction is completed within one month, there is a 65% likelihood that she can have the facility fully staffed and operational by summer. If the construction takes two months, the chances of meeting the summer deadline drops to 40%; and if the construction takes three months, there is only a 10% probability meeting the summer deadline. How likely is it that Juliana will not meet the summer deadline?

a. .200

b. .346

c. .685

d. .282

e. .535

1. The management team at Colston.com predicts that if the economy continues to grow at the current rate, there is a 95% probability that the company will see at least a 40% increase in revenue this year. If the economy slows, that probability drops to 30%, but if it accelerates, the probability increases to 99%. The Wall Street Journal believes that there is a 60% chance that the economy will continue to grow at the current rate, a 25% chance that it will slow, and a 15% chance that it will accelerate. Use this information to estimate the likelihood that Colston.com will show at least a 40% increase in profits this year.

a. .6652

b. .5597

c. .8447

d. .6132

e. .7935

1. A survey of 500 consumers was conducted. One of the questions asked was “Have you purchased a new cell phone or a tablet PC within the past six months?” Responses are reported in the joint probability table below. Based on the numbers in the table, if a consumer is selected from the survey at random, how likely is it that that consumer either purchased a cell phone or purchased a tablet or did both?

a. 1.0

b. .25

c. .20

d. .50

e. .80

1. A survey of 500 consumers was conducted. One of the questions asked was “Have you purchased a new cell phone or a new tablet PC within the past six months?” Responses are reported in the joint probability table below. Based on the numbers in the table, if a consumer is selected from the survey at random, how likely is it that the person purchased a cell phone?

a. .7

b. .3

c. .5

d. .4

e. .25

1. A survey of 500 consumers was conducted. One of the questions asked was “Have you purchased a new cell phone or a tablet PC within the past six months?” Responses are reported in the joint probability table below. If a randomly selected consumer in the study purchased a cell, how likely is it that he/she purchased a tablet?

a. .4

b. .5

c. .625

d. .6

e. .3

1. A survey of 500 consumers was conducted. One of the questions asked was “Have you purchased a new cell phone or a tablet PC within the past six months?” Responses are reported in the joint probability table below. If a randomly selected consumer in the study didn’t purchase a cell phone, how likely is it that he/she purchased a tablet?

a. .4

b. .167

c. .625

d. .6

e. .3

1. A survey of 500 consumers was conducted. One of the questions asked was “Have you purchased a new cell phone or a tablet PC within the past six months?” Responses are reported in the joint probability table below. If a randomly selected consumer in the study didn’t purchase a tablet, how likely is it that he/she didn’t purchase a cell phone?

a. .4

b. .167

c. .714

d. .6

e. .3

1. The cross-tabulation table below shows partial results from a study done at the Mt. Bachelor ski area. Patrons were asked whether they preferred snowboarding or skiing. If a person is randomly selected from the study and the person selected prefers snowboarding, how likely is it that the person selected is 25 to 40 years old?

a. .420

b. .311

c. .566

d. .332

e. .664

1. The cross-tabulation table below shows partial results from a study done at the Mt. Bachelor ski area. Patrons were asked whether they preferred snowboarding or skiing. If a person is randomly selected from the study and the person selected is over 40 years of age, how likely is it that the person selected prefers skiing?

a. .420

b. .311

c. .667

d. .125

e. .50

1. The cross-tabulation table below shows partial results from a study done at the Mt. Bachelor ski area. Patrons were asked whether they preferred snowboarding or skiing. If a person is randomly selected from the study, how likely is it that the person selected is under 25 years old and prefers skiing?

a. .420

b. .272

c. .680

d. .128

e. .664

1. The cross-tabulation table below shows partial results from a study done at the Mt. Bachelor ski area. Patrons were asked whether they preferred snowboarding or skiing. In the study, are preference and age statistically independent?

a. No, since P(under 25 given skiing) not equal to P(under 25).

b. Yes, since P(under 25 given skiing) is equal to P(skiing).

c. Yes, since P(under 25 given skiing) is equal to P(under 25).

d. Yes, since P(skiing given under 25) is equal to P(under 25).

e. No, since P(under 25 given skiing) is not equal to P(skiing).

1. The Bank of Chicago conducted a study of 332 individuals who had recently requested mortgage relief. In one part of the report, the individuals in the study were grouped by market value of the home and the number of years the individual had been making payments. The table shows the results. If you select an individual at random from the study, how likely is that the individual had made payments for at least 10 years and had a home valued at $500,000 or more?

a. .152

b. .224

c. .108

d. .252

e. .468

1. The Bank of Chicago conducted a study of 332 individuals who had recently requested mortgage relief. In one part of the report, the individuals in the study were grouped by market value of the home and the number of years the individual had been making payments. The table shows the results. What proportion of the individuals in the study who had made payments for less than 10 years had a home valued between $200,000 and $300,000?

a. .2165

b. .0876

c. .1643

d. .3622

e. .2815

1. The Bank of Chicago conducted a study of 332 individuals who had recently requested mortgage relief. The individuals in the study were grouped by market value of the home and the number of years the individual had been making payments. The table shows the results. If you select someone at random from the study and find they had a home valued at $100,000 or less, how likely is it that they had been making payments for less than 10 years?”

a. .6352

b. .9843

c. .5466

d. .6439

e. .7742

1. Twelve new accounts have recently been added to your area of responsibility. You plan to meet with five of the new accounts this week. How many different groups of five could you form from the group of 12 new accounts?

a. .721

b. .663

c. .883

d. 792

e. .697

1. Dobson and Company’s chances for survival depend on three factors: customer reaction to its new product, the state of the economy, and the entry of new competitors into the marketplace. If Dobson foresees 5 possible customer reactions, 6 possible economic conditions, and 3 different possibilities for competitors entering the marketplace, how many different sets of possibilities are there?

a. 33

b. 14

c. 90

d. 45

e. 36

1. Johnson Products needs to hire a new team consisting of a marketing director, an HR manager, an office supervisor and an IT specialist. You’ve narrowed your choices to 6 marketing directors, 10 HR managers, 4 office supervisors and 3 IT specialists. How many team possibilities are there to choose from?

a. 550

b. 436

c. 680

d. 720

e. 966

1. Ten project managers are available for assignment to six upcoming projects at Crosslands Development. How many subgroups of size six could be formed from the list of ten project managers?

a. 1020

b. 360

c. 440

d. 210

e. 582

1. Ten project managers are available for assignment to six upcoming projects at Crosslands Development. Three of the project managers are women and seven are men. From the list of ten project managers, how many subgroups of size six could be formed containing exactly two women and four men?

a. 105

b. 88

c. 24

d. 156

e. 212

1. Nine customer service technicians are available today for service calls. As of 9:00 AM, only six service calls are scheduled. How many different assignments of technicians to service calls are possible?

a. 60,480

b. 40,260

c. 120,400

d. 80,290

e. 110,800

1. Twelve new accounts have recently been added to your area of responsibility. Four of the accounts are local and the remaining eight are international. You plan to meet with five of the new accounts this week. How many different groups of five could you form that would include exactly two local and three international accounts?

a. 422

b. 336

c. 648

d. 524

e. 980