Deck 4: Introduction to Probability

Question 1

When a patient arrives at a clinic complaining of several specific symptoms,the doctor who makes the diagnosis says that he is 80 percent certain that the patient has a particular problem.It is likely that he is basing this assessment on relative frequency of occurrence.

Answer 1

True

Question 2

If a manager were interested in assessing the probability that a new product will be successful in a New Jersey market area,she would most likely use relative frequency of occurrence as the method for assessing the probability.

Answer 2

False

Question 3

Suppose a coin is flipped twice.The event of getting heads on the first toss and the event of getting heads on the second toss could be said to be mutually exclusive.

Answer 3

False

Question 4

Two football teams play in the Super Bowl.The event of team A winning and the event of team B winning can be said to be mutually exclusive.

Question 5

A car salesman has noted that the probability that the dealership sells a car on a Saturday morning is .30.Then the probability of the dealership not selling a car on Saturday morning is .70.

Question 6

Classical probability assessment is likely to be the most common method of probability assessment used in business decision making.

Question 7

At a potato processing plant in the state of Washington,400 potatoes have been examined for disease.Of these,four were diseased.Based on this,the plant manager has stated that the probability of finding a diseased potato is 0.01.He is applying subjective probability to arrive at this 0.01 value.

Question 8

If the probability of one event occurring is .40 and the probability of a second event occurring is 0.60,then the probability that both events will occur must be 1.0 since that is the maximum value a probability can be.

Question 9

If you were planning to take a small group out to dinner on a Thursday evening and you were considering whether to call ahead for a reservation,the method of probability assessment you would most likely use to assess the chances of being able to get in for dinner without having a reservation would be subjective assessment.

Question 10

In playing the game Monopoly,the probability of a player landing on Park Place would be assessed using classical probability assessment.

Question 11

A car salesman states that the probability that the dealership sells a car on a Saturday morning is .30.The method of probability assessment that he has used is most likely classical assessment.

Question 12

If a company has the opportunity to bid on three contracts,A,B,and C,then the number of these contracts that are awarded to the company would be considered an elementary event.

Question 13

Suppose a player is dealt 2 cards from a standard deck of 52 playing cards.To determine the probability of having a blackjack would involve classical probability.

Question 14

A manufacturing company makes three types of products.Each time it makes a product,the item can be either good or defective and it can be either customized or standard.The events consisting of customized and defective would be considered mutually exclusive since they apply to different attributes of the product.

Question 15

One of the difficulties in using the relative frequency of occurrence method for assessing probabilities in business situations is getting a large enough set of examples that match the one in question.

Question 16

The owners of Greg's Department Store have reason to believe that one of their employees has been stealing from the store.In an interview with the police,the owner says that she is 75 percent sure that the employee is stealing.This probability is an example of one that was assessed using classical probability.

Question 17

If two events are mutually exclusive,it is possible for them to also be independent of each other.

Question 18

Suppose a single die (a 6-sided cube with sides numbered 1 through 6)is rolled once.The event of interest is defined as rolling an even number.This can be said to be an elementary event.

Question 19

In most situations,there is no difference between the events and the elementary events.

Question 20

A product that is produced at Ramsey Manufacturing goes through three steps to be built.At step one,the components are assembled by technicians.At step two,the product is sanded,and at step three the product is painted.The product can become defective if any of these three steps is performed incorrectly.The three steps are done by different people in different locations.We let D₁ = defect introduced at step 1,D₂ = defect introduced at step 2,and D₃ = defect introduced at step three.Based on this situation these three events would be considered to be mutually exclusive.

Question 21

The following probability distribution was subjectively assessed for the number of sales a salesperson would make if he or she made five sales calls in one day.
Given this distribution,the probability that the number of sales is 2 or 3 is 0.50.

Question 22

When customers come to a bank,there are three primary locations they may select to go to: teller,loan officer,or escrow department.Based on past experience,the following probability distribution applies:
Seventy percent of customers are males.The probability that the next two customers to enter the bank are males and go to the Loan Officer is 0.42.

Question 23

When the salesperson makes a sale,there are three possible sales levels: large,medium,and small.The probability of a large sale is 0.20 and the chance of a medium sale is 0.60.Thus,when a sale is made,the chance of it being a small sale is 0.20.

Question 24

Suppose 10 students are enrolled in a class and the probability of at least 8 showing up on a given day is 90 percent.Then the probability of 7 or fewer showing that day is 10 percent.

Question 25

Sometime it is necessary to assign probabilities based on a person's belief that an outcome will occur.

Question 26

Mutually exclusive means that the occurrence of event A has no effect on the probability of the occurrence of event B,and independent means the occurrence of event A prevents the occurrence of event B.

Question 27

When customers come to a bank,there are three primary locations they may select to go to: teller,loan officer,or escrow department.Based on past experience,the following probability distribution applies:
Seventy percent of customers are males.The probability that three consecutive customers all go to a teller is approximately 0.22.

Question 28

When customers come to a bank,there are three primary locations they may select to go to: teller,loan officer,or escrow department.Based on past experience,the following probability distribution applies:
Seventy percent of customers are males.Thus,the probability that the next customer to enter the bank is a male who goes to the teller is 1.30.

Question 29

A dam on a river that holds back a water reservoir begins to leak.Engineers say that there is a 10 percent chance of the dam breaking if repairs are not made.This is an example of classical probability.

Question 30

Assume P(A)= 0.4 and P(B)= 0.2 and P(A andB)= 0.1,then the probability of P(A orB)= 0.7.

Question 31

A used car lot has 15 cars.Five of these cars were manufactured in the United States and the others were made in other countries.If one car is purchased at random from this car lot,the probability that it is a U.S.car is 0.33.

Question 32

During the past week,of the 250 customers at the Dairy Queen who ordered a Blizzard,50 ordered strawberry.This means that of the next five Blizzard customers,exactly one will order strawberry.

Question 33

The following probability distribution was subjectively assessed for the number of sales a salesperson would make if he or she made five sales calls in one day.
Given this distribution,the probability that the number of sales is less than 2 is 0.15.

Question 34

The following probability distribution was subjectively assessed for the number of sales a salesperson would make if he or she made five sales calls in one day.
When the salesperson makes a sale,there are three possible sales levels: large,medium,and small.The probability of a large sale is 0.20 and the chance of a medium sale is 0.60.The probability on a given day that the salesperson will make one sale and that it is medium is 0.09.

Question 35

It is correct to say that subjective probability assessments are neither right nor wrong,but are merely reflections of the state of mind of the individual making the probability assessment.

Question 36

When a construction company bids on a contract,the events will be win or lose.The closer the probability is to 0.50,the greater the uncertainty about whether the company will win or lose the bid.

Question 37

The following probability distribution was subjectively assessed for the number of sales a salesperson would make if he or she made five sales calls in one day.
Given this distribution,the probability that the number of sales is more than 2 is 0.80.

Question 38

A New Jersey company relies on a steady supply of power to keep its manufacturing going.Recently at a planning meeting,the general manager stated that the chance of a rolling blackout affecting production is 0.15.She most likely made this assessment using subjective probability assessment.

Question 39

If a single die is rolled (a cube where the sides are numbered 1 through 6),the probability of rolling at least a 3 is 0.33.

Question 40

When the salesperson makes a sale,there are three possible sales levels: large,medium,and small.The probability of a large sale is 0.20 and the chance of a medium sale is 0.60.If a salesperson makes two sales,the probability that at least one is large is 0.36.

Question 41

An event is:

A)the list of possible outcomes that can occur from a selection or decision.
B)a collection of elementary events.
C)similar to an experiment but not controlled by the decision maker.
D)more frequently found in business than in other disciplines.

Question 42

A study was recently done in which 500 people were asked to indicate their preferences for one of three products.The following table shows the breakdown of the responses by gender of the respondents. Suppose one person is randomly chosen.Based on this data,what is the probability that the person chosen is a female who prefers product C?

A)0.24
B)0.86
C)0.92
D)0.31

Question 43

The Baker Oil and Gas Company has four retail locations,code-named A,B,C,and D.The following table illustrates the percentage of total company sales at each store and also the percentage of customers at that store who make purchases with debit cards:
Based on this information,given that a customer has used a debit card to make the purchase,the sale was most likely made at store D.

Question 44

The Baker Oil and Gas Company has four retail locations,code-named A,B,C,and D.The following table illustrates the percentage of total company sales at each store and also the percentage of customers at that store who make purchases with debit cards:
Based on this information,the probability that a customer who used a debit card shopped at store C is 0.0738.

Question 45

The method of probability assessment that is least likely to be used by business decision makers is:

A)subjective assessment.
B)relative frequency of occurrence.
C)classical assessment.
D)None of the above is used by decision makers.

Question 46

The Crystal Window Company makes windows at three locations: Reno,Las Vegas,and Boise.Some windows made by the company contain a visible defect and must be replaced.Each defect costs the company $45.00.The Reno plant makes 40 percent of all windows while the Las Vegas and Boise plants split the remaining production evenly.A recent quality study shows that 8 percent of the Reno windows contain a defect,11 percent of the Las Vegas windows contain a defect,while 4 percent of the windows made in Boise have a defect.Once the windows are made,they are shipped to a central warehouse where they are commingled and the location where they were made is lost.
Based on this information,the percentage of the defective cost that should be allocated to the Reno plant is approximately 42 percent.

Question 47

The Baker Oil and Gas Company has four retail locations,code-named A,B,C,and D.The following table illustrates the percentage of total company sales at each store and also the percentage of customers at that store who make purchases with debit cards:
Based on this information,the probability that a customer will use a debit card is just slightly greater than 0.23.

Question 48

The Crystal Window Company makes windows at three locations: Reno,Las Vegas,and Boise.Some windows made by the company contain a visible defect and must be replaced.Each defect costs the company $45.00.The Reno plant makes 40 percent of all windows while the Las Vegas and Boise plants split the remaining production evenly.A recent quality study shows that 8 percent of the Reno windows contain a defect,11 percent of the Las Vegas windows contain a defect,while 4 percent of the windows made in Boise have a defect.Once the windows are made,they are shipped to a central warehouse where they are commingled and the location where they were made is lost.
Based on this information the probability that a defective window was made by the Boise plant is approximately 0.16.

Question 49

Assume P(A)= 0.6,P(B)= 0.7,and P(A andB)= 0.42,which means that events A and B are independent of each other.

Question 50

A study was recently done in which 500 people were asked to indicate their preferences for one of three products.The following table shows the breakdown of the responses by gender of the respondents. Based on these data,the probability that a person in the population will prefer product A can be assessed as:

A)0.18
B)0.56
C)0.286
D)0.16

Question 51

When customers come to a bank,there are three primary locations they may select to go to: teller,loan officer,or escrow department.Based on past experience,the following probability distribution applies:
Seventy percent of customers are males.The probability that the next customer will be male and will go to either the teller or the escrow department is 0.49.

Question 52

There are three general locations that a taxi can go to: the airport,downtown,and elsewhere.When a taxi driver starts in the downtown location,there is a 0.40 chance that his first call will take him to the airport and a 0.40 chance of going to another downtown location.Once a taxi is at the airport,there is a 0.80 probability that the next fare will take him downtown and a 0.20 chance of going elsewhere.The probability of a call from anywhere except downtown taking him to the airport is 0.20.Therefore,the probability that the taxi is at the airport when the third call arrives after going on shift is 0.20.

Question 53

At gambling casinos all over the country,a popular dice game is called craps.The probability of a player winning at this game can be assessed using:

A)subjective assessment.
B)classical probability.
C)relative frequency of occurrence.
D)None of the above

Question 54

When a pair of dice are rolled,the outcome for each die can be said to be:

A)mutually exclusive.
B)mutually inclusive.
C)dependent.
D)independent.

Question 55

If a six-sided die is tossed two times and "4" shows up both times,the probability of "4" on the third trial is much larger than any other outcome.

Question 56

The Crystal Window Company makes windows at three locations: Reno,Las Vegas,and Boise.Some windows made by the company contain a visible defect and must be replaced.Each defect costs the company $45.00.The Reno plant makes 40 percent of all windows while the Las Vegas and Boise plants split the remaining production evenly.A recent quality study shows that 8 percent of the Reno windows contain a defect,11 percent of the Las Vegas windows contain a defect,while 4 percent of the windows made in Boise have a defect.Once the windows are made,they are shipped to a central warehouse where they are commingled and the location where they were made is lost.
Based on this information,if a defective window is discovered,it was most likely made by the Las Vegas plant.

Question 57

A study was recently done in which 500 people were asked to indicate their preferences for one of three products.The following table shows the breakdown of the responses by gender of the respondents. If the people conducting the study wish to assess the probability that product A will be preferred by members of the target population,the method of assessment to be used would most likely be:

A)classical probability assessment.
B)subjective assessment.
C)relative frequency of occurrence.
D)independent events.

Question 58

A consumer products company is planning to introduce a new product.The method that is least likely to be used to assess the probability of the product being successful is:

A)classical probability assessment.
B)subjective assessment.
C)relative frequency of occurrence.
D)elementary events.

Question 59

When a customer enters a store there are three outcomes that can occur: buy nothing,buy a small amount,or buy a large amount.In this situation,if a customer buys a large amount,he or she cannot also buy a small amount or buy nothing.Thus the events are:

A)independent.
B)mutually exclusive.
C)all inclusive.
D)dependent events.

Question 60

The method of probability assessment that relies on an examination of historical data from similar situations is:

A)relative frequency of occurrence.
B)classical assessment.
C)historical assessment.
D)subjective assessment.

Question 61

Long-time friends,Pat and Tom,agree on many things,but not the outcome of the American League pennant race and the World Series.Pat is originally from Boston,and Tom is from New York.They have a steak dinner bet on next year's race,with Pat betting on the Red Sox and Tom on the Yankees.Both are convinced they will win.What probability assessment technique is being used by the two friends?

A)Subjective probability
B)Classical probability
C)Relative frequency probability
D)Independent probability

Question 62

The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap.A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data,the probability of a golfer having a handicap less than 10 is:

A)0.52
B)0.10
C)0.34
D)None of the above

Question 63

Of the last 100 customers entering a computer shop,25 have purchased a computer.If the classical probability assessment for computing probability is used,the probability that the next customer will purchase a computer is:

A)0.25
B)0.50
C)1.00
D)0.75

Question 64

Students who live on campus and purchase a meal plan are randomly assigned to one of three dining halls: the Commons,Northeast,and Frazier.What is the probability that the next student to purchase a meal plan will be assigned to the Commons?

A)0.66
B)0.5
C)0.25
D)0.33

Question 65

An inventory of appliances contains four white washers and one black washer.If a customer selects one at random,what is the probability that the black washer will be selected?

A)0.5
B)0.4
C)0.2
D)0.8

Question 66

The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap.A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data,the probability of someone using a Strata ball and having a handicap under 2 is:

A)0.05
B)0.38
C)0.25
D)None of the above

Question 67

What method of probability assessment would most likely be used to assess the probability that a customer will return a purchase for a refund?

A)Classical probability based on the ratio of the number of ways the event can occur
B)Relative frequency based on previous history
C)Subjective probability based on expert opinion
D)Independent probability based on two unrelated outcomes

Question 68

The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap.A joint frequency table for the 100 golfers covered in the survey is shown below: If a player comes to the course using a Nike golf ball,the probability that he or she has a handicap of at least 10 is:

A)0.22
B)0.48
C)slightly greater than 0.45
D)0.10

Question 69

The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap.A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data,if a player has a handicap that is 10 or more,the probability that he or she will use a Nike golf ball is:

A)0.21
B)0.10
C)0.45
D)0.48

Question 70

A special roulette wheel,which has an equal number of red and black spots,has come up red four times in a row.Assuming that the roulette wheel is fair,what concept allows a player to know that the probability the next spin of the wheel will come up black is 0.5?

A)Concept of independent events
B)Concept of mutually exclusive events
C)Concept of dependent events
D)Concept of mutually inclusive events

Question 71

The Anderson Lumber Company has three sawmills that produce boards of different lengths.The following table is a joint frequency distribution based on a random sample of 1,000 boards selected from the lumber inventory. Based on these data,if a board is selected that is 12 feet long,the probability that it was made at sawmill A is:

A)0.08
B)0.41
C)0.24
D)0.20

Question 72

In a survey,respondents were asked to indicate their favorite brand of cereal (Post or Kellogg's).They were allowed only one choice.What is the probability concept that implies it is not possible for a single respondent to state both Post and Kellogg's to be the favorite cereal?

A)Concept of independent events
B)Concept of mutually exclusive events
C)Concept of dependent events
D)Concept of mutually inclusive events

Question 73

Harrison Water Sports has three retail outlets: Seattle,Portland,and Phoenix.The Seattle store does 50 percent of the total sales in a year,while the Portland store does 35 percent of the total sales.Further analysis indicates that of the sales in Seattle,20 percent are in boat accessories.The percentage of boat accessories at the Portland store is 30 and the percentage at the Phoenix store is 25.Overall,the probability that a sale by Harrison Water Sports will be for a boat accessory is:

A)0.105
B)0.2425
C)0.75
D)None of the above

Question 74

The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap.A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data,the probability that a player will use a Strata golf ball is:

A)0.15
B)0.20
C)0.18
D)None of the above

Question 75

What method of probability assessment would most likely be used to assess the probability that a major earthquake will occur in California in the next three years?

A)Classical probability based on the ratio of the number of ways the event can occur
B)Relative frequency based on previous history
C)Subjective probability based on expert opinion
D)Independent probability based on two unrelated outcomes

Question 76

The results of a census of 2,500 employees of a mid-sized company with 401(k)retirement accounts are as follows: Suppose researchers are going to sample employees from the company for further study.
Based on the relative frequency assessment method,what is the probability that a randomly selected employee will be a female?

A)0.1580
B)0.1040
C)0.6160
D)0.4040

Question 77

The Anderson Lumber Company has three sawmills that produce boards of different lengths.The following table is a joint frequency distribution based on a random sample of 1000 boards selected from the lumber inventory. Based on these data,if three boards are selected at random,the probability that all three were made at sawmill A is:

A)0.037
B)0.334
C)1.00
D)0.556

Question 78

The Anderson Lumber Company has three sawmills that produce boards of different lengths.The following table is a joint frequency distribution based on a random sample of 1,000 boards selected from the lumber inventory. Based on these data,the probability of selecting a board from inventory that is 10 feet long is:

A)0.196
B)0.450
C)0.084
D)0.170

Question 79

If two events are independent,then

A)they must be mutually exclusive.
B)the sum of their probabilities must be equal to one.
C)their intersection must be zero.
D)None of the above

Question 80

Harrison Water Sports has three retail outlets: Seattle,Portland,and Phoenix.The Seattle store does 50 percent of the total sales in a year,while the Portland store does 35 percent of the total sales.Further analysis indicates that of the sales in Seattle,20 percent are in boat accessories.The percentage of boat accessories at the Portland store is 30 and the percentage at the Phoenix store is 25.If a sales dollar is recorded as a boat accessory,the probability that the sale was made at the Portland store is:

A)slightly greater than 0.43
B)0.35
C)0.2425
D)None of the above