# Quiz 6: Probability

Statistics

Q 1Q 1

The relative frequency approach to probability uses long term relative frequencies, often based on past data.

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True False

True

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True False

True

Q 3Q 3

You think you have a 90% chance of passing your next advanced financial accounting exam.This is an example of subjective approach to probability.

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True False

True

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True False

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True False

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True False

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True False

Q 8Q 8

If either event A or event B must occur, then A and B are mutually exclusive and collectively exhaustive events.

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True False

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True False

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True False

Q 11Q 11

Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is
A) 0.10
B) 0.90
C) 0.50
D) None of these choices.

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Multiple Choice

Q 12Q 12

If A and B are mutually exclusive events with P(A) = 0.75, then P(B):
A) can be any value between 0 and 1.
B) can be any value between 0 and 0.75.
C) cannot be larger than 0.25.
D) equals 0.25.

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Multiple Choice

Q 13Q 13

If you roll a balanced die 50 times, you should expect an even number to appear:
A) on every other roll.
B) exactly 50 times out of 100 rolls.
C) 25 times on average, over the long term.
D) All of these choices are true.

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Multiple Choice

Q 14Q 14

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the:
A) subjective approach
B) objective approach
C) classical approach
D) relative frequency approach

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Multiple Choice

Q 15Q 15

The collection of all possible outcomes of an experiment is called:
A) a simple event
B) a sample space
C) a sample
D) a population

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Multiple Choice

Q 16Q 16

Which of the following is an approach to assigning probabilities?
A) Classical approach
B) Relative frequency approach
C) Subjective approach
D) All of these choices are true.

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Multiple Choice

Q 17Q 17

A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5.Which of the following is a simple event?
A) At least 3
B) At most 2
C) 3
D) 15

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Multiple Choice

Q 18Q 18

Which of the following is a requirement of the probabilities assigned to outcome O

_{i}? A) P(O_{i}) 0 for each i B) P(O_{i}) 1 for each i C) 0 P(O_{i}) 1 for each i D) P(O_{i}) = 1 for each iFree

Multiple Choice

Q 19Q 19

If an experiment consists of five outcomes with P(O

_{1}) = 0.10, P(O_{2}) = 0.20, P(O_{3}) = 0.30, P(O_{4}) = 0.25, then P(O_{5}) is A) 0.75 B) 0.15 C) 0.50 D) Cannot be determined from the information given.Free

Multiple Choice

Q 20Q 20

If two events are collectively exhaustive, what is the probability that one or the other occurs?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 21Q 21

If two events are collectively exhaustive, what is the probability that both occur at the same time?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 22Q 22

If two events are mutually exclusive, what is the probability that one or the other occurs?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 23Q 23

If two events are mutually exclusive, what is the probability that both occur at the same time?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 24Q 24

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 25Q 25

If the two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 26Q 26

If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
A) 0.25
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 27Q 27

If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

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Multiple Choice

Q 28Q 28

If event A and event B cannot occur at the same time, then A and B are said to be
A) mutually exclusive
B) independent
C) collectively exhaustive
D) None of these choices.

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Multiple Choice

Q 29Q 29

The collection of all possible events is called
A) an outcome
B) a sample space
C) an event
D) None of these choices.

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Multiple Choice

Q 30Q 30

A random experiment is an action or process that leads to one of several possible ____________________.

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Essay

Q 31Q 31

The outcomes of a sample space must be ____________________, which means that all possible outcomes must be included.

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Q 32Q 32

The outcomes of a sample space must be ____________________, which means that no two outcomes can occur at the same time.

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Q 33Q 33

A(n) ____________________ of a random experiment is a list of all possible outcomes of the experiment.

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Q 35Q 35

There are ____________________ requirements of probabilities for the outcomes of a sample space.

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Q 37Q 37

A(n) ____________________ is a collection or set of one or more simple events in a sample space.

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Q 38Q 38

The probability of an event is the ____________________ of the probabilities of the simple events that constitute the event.

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Q 39Q 39

No matter which approach was used to assign probability (classical, relative frequency, or subjective) the one that is always used to interpret a probability is the ____________________ approach.

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Q 40Q 40

Alana, Eva, and Stephanie, three candidates for the presidency of a college's student body, are to address a student forum.The forum's organizer is to select the order in which the candidates will give their speeches, and must do so in such a way that each possible order is equally likely to be selected.
a.
What is the random experiment?
b.
List the outcomes in the sample space.
c.
Assign probabilities to the outcomes.
d.
What is the probability that Stephanie will speak first?
e.
What is the probability that Alana will speak before Stephanie does?

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Q 41Q 41

There are three approaches to determining the probability that an outcome will occur: classical, relative frequency, and subjective.For each situation that follows, determine which approach is most appropriate.
a.
A Russian will win the French Open Tennis Tournament next year.
b.
The probability of getting any single number on a balanced die is 1/6.
c.
Based on the past, it's reasonable to assume the average book sales for a certain textbook is 6,500 copies per month.

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Q 42Q 42

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.
-{Hobby Shop Sales Narrative} Define the random experiment of interest to the store.

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Q 43Q 43

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.
-{Hobby Shop Sales Narrative} List the outcomes in the sample space.

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Q 44Q 44

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.
-{Hobby Shop Sales Narrative} What approach would you use in determining the probabilities for next week's sales? Assign probabilities to the outcomes.

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Q 45Q 45

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.
-{Hobby Shop Sales Narrative} What is the probability of selling at least two trucks in any given week?

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Q 46Q 46

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.
-{Hobby Shop Sales Narrative} What is the probability of selling between 1 and 3 (inclusive) trucks in any given week?

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Q 47Q 47

Mutual Fund Price
An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks, based on past data.
-{Mutual Fund Price Narrative} Which approach was used to produce this figure?

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Essay

Q 48Q 48

Mutual Fund Price
An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks, based on past data.
-{Mutual Fund Price Narrative} Interpret the 75% probability.

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Q 49Q 49

The sample space of the toss of a balanced die is S = {1, 2, 3, 4, 5, 6}.If the die is balanced, each simple event (outcome) has the same probability.Find the probability of the following events:
a.
Rolling an odd number
b.
Rolling a number less than or equal to 3
c.
Rolling a number greater than or equal to 5
d.
Rolling a number between 2 and 5, inclusive.

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Essay

Q 50Q 50

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records.
-{Equity Loan Rates Narrative} If a bank is selected at random from this distribution, what is the probability that the interest rate charged on a home loan exceeds 7.0%?

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Q 51Q 51

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records.
-{Equity Loan Rates Narrative} What is the most common interest rate?

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Essay

Q 52Q 52

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records.
-{Equity Loan Rates Narrative} What approach was used in estimating the probabilities for the interest rates?

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True False

Q 54Q 54

Two or more events are said to be independent when the occurrence of one event has no effect on the probability that another will occur.

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True False

Q 55Q 55

The union of events A and B is the event that occurs when either A or B or both occur.It is denoted as 'A or B'.

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True False

Q 56Q 56

If A and B are independent events with P(A) = 0.35 and P(B) = 0.55, then P(A|B) is 0.35/0.55 = .64.

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True False

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True False

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True False

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True False

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True False

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True False

Q 62Q 62

The union of events A and B is the event that occurs when either A or B occurs but not both.

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True False

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True False

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True False

Q 65Q 65

Suppose the probability that a person owns both a cat and a dog is 0.10.Also suppose the probability that a person owns a cat but not a dog is 0.20.The marginal probability that someone owns a cat is 0.30.

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True False

Q 66Q 66

The probability of the intersection of two events A and B is denoted by P(A and B) and is called the:
A) marginal probability
B) joint probability
C) conditional probability of A given B
D) conditional probability of B given A

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Multiple Choice

Q 67Q 67

The intersection of events A and B is the event that occurs when:
A) either A or B occurs but not both
B) neither A nor B occur
C) both A and B occur
D) All of these choices are true.

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Multiple Choice

Q 68Q 68

The probability of event A given event B is denoted by
A) P(A and B)
B) P(A or B)
C) P(A|B)
D) P(B|A)

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Multiple Choice

Q 69Q 69

Which of the following is equivalent to P(A|B)?
A) P(A and B)
B) P(B|A)
C) P(A)/P(B)
D) None of these choices.

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Multiple Choice

Q 70Q 70

Which of the following best describes the concept of marginal probability?
A) It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.
B) It is a measure of the likelihood that a particular event will occur, if another event has already occurred.
C) It is a measure of the likelihood of the simultaneous occurrence of two or more events.
D) None of these choices.

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Multiple Choice

Q 71Q 71

If two events are independent, what is the probability that they both occur?
A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given

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Multiple Choice

Q 72Q 72

If the outcome of event A is not affected by event B, then events A and B are said to be
A) mutually exclusive
B) independent
C) collectively exhaustive
D) None of these choices.

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Multiple Choice

Q 73Q 73

If A and B are disjoint events with P(A) = 0.70, then P(B):
A) can be any value between 0 and 1
B) can be any value between 0 and 0.70
C) cannot be larger than 0.30
D) cannot be determined with the information given

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Multiple Choice

Q 74Q 74

If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is:
A) 1.23
B) 0.47
C) 0.18
D) 0.11

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Multiple Choice

Q 75Q 75

Suppose P(A) = 0.60, P(B) = 0.85, and A and B are independent.The probability of the complement of the event (A and B) is:
A) .4 .15 = .060
B) 0.40 + .15 = .55
C) 1 (.40 + .15) = .45
D) 1 (.6 .85) = .490

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Multiple Choice

Q 76Q 76

Which of the following statements is correct if the events A and B have nonzero probabilities?
A) A and B cannot be both independent and disjoint
B) A and B can be both independent and disjoint
C) A and B are always independent
D) A and B are always disjoint

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Multiple Choice

Q 77Q 77

A and B are disjoint events, with P(A) = 0.20 and P(B) = 0.30.Then P(A and B) is:
A) 0.50
B) 0.10
C) 0.00
D) 0.06

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Multiple Choice

Q 78Q 78

If P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.25, then P(A|B) is:
A) 1.4
B) 1.8
C) 0.714
D) 0.556

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Multiple Choice

Q 79Q 79

If A and B are independent events with P(A) = 0.60 and P(A|B) = 0.60, then P(B) is:
A) 1.20
B) 0.60
C) 0.36
D) cannot be determined with the information given

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Multiple Choice

Q 80Q 80

If A and B are independent events with P(A) = 0.20 and P(B) = 0.60, then P(A|B) is:
A) 0.20
B) 0.60
C) 0.40
D) 0.80

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Multiple Choice

Q 81Q 81

If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is:
A) 0.25
B) 0.40
C) 0.90
D) cannot be determined from the information given

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Multiple Choice

Q 82Q 82

Cars
Suppose X = the number of cars owned by a family in the U.S.The probability distribution of X is shown in the table below.
-{Car Narrative}What is the chance that a family owns more than one car?
A) 0.23
B) 0.21
C) 0.44
D) None of these choices.

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Multiple Choice

Q 83Q 83

Cars
Suppose X = the number of cars owned by a family in the U.S.The probability distribution of X is shown in the table below.
-{Cars Narrative} Suppose you choose two families at random.What is the chance that they each own one car? (That means family A owns a car and family B owns a car.)
A) 0.23
B) 0.23 + 0.23 = 0.46
C) 0.23 + 0.23 (0.23)*(0.23) = .4071
D) (0.23)*(0.23) = 0.0529

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Multiple Choice

Q 84Q 84

The ____________________ of events A and B is the event that occurs when both A and B occur.

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Essay

Q 85Q 85

The probability of an intersection of two events is called a(n) ____________________ probability.

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Q 86Q 86

Suppose two events A and B are related.The ____________________ probability of A is the probability that A occurs, regardless of whether event B occurred or not.

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Q 88Q 88

A conditional probability of A given B is written in probability notation as ____________________.

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Q 90Q 90

The ____________________ of two events A and B is the event that occurs when either A or B or both occur.

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Q 94Q 94

Tea and Seltzer
Suppose 55 percent of adults drink tea, 45 percent drink seltzer, and 10 percent drink both.
-{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult does not drink seltzer?

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Essay

Q 95Q 95

Tea and Seltzer
Suppose 55 percent of adults drink tea, 45 percent drink seltzer, and 10 percent drink both.
-{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult drinks seltzer or tea or both?

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Essay

Q 96Q 96

Tea and Seltzer
Suppose 55 percent of adults drink tea, 45 percent drink seltzer, and 10 percent drink both.
-{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult doesn't drink tea or seltzer?

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Q 97Q 97

Club Members
A survey of a club's members indicates that 50% own a home, 80% own a car, and 90% of the homeowners who subscribe also own a car.
-{Club Members Narrative} What is the probability that a subscriber owns both a car and a house?

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Q 98Q 98

Club Members
A survey of a club's members indicates that 50% own a home, 80% own a car, and 90% of the homeowners who subscribe also own a car.
-{Club Members Narrative} What is the probability that a club member owns a car or a house, or both?

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Q 99Q 99

Club Members
A survey of a club's members indicates that 50% own a home, 80% own a car, and 90% of the homeowners who subscribe also own a car.
-{Club Members Narrative} What is the probability that a club member owns neither a car nor a house?

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Q 100Q 100

Business Majors
Suppose 30% of business majors major in accounting.You take a random sample of 3 business majors.
-{Business Majors Narrative} What is the chance that they all major in accounting?

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Q 101Q 101

Business Majors
Suppose 30% of business majors major in accounting.You take a random sample of 3 business majors.
-{Business Majors Narrative} What is the chance that at least one majors in accounting?

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Q 102Q 102

Business Majors
Suppose 30% of business majors major in accounting.You take a random sample of 3 business majors.
-{Business Majors Narrative} What is the chance that exactly one majors in accounting?

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Q 103Q 103

Business Majors
Suppose 30% of business majors major in accounting.You take a random sample of 3 business majors.
-{Business Majors Narrative} What is the chance that none of them major in accounting?

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Q 104Q 104

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} What proportion of accidents involved more than one vehicle?

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Essay

Q 105Q 105

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} What proportion of accidents involved alcohol and single vehicle?

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Q 106Q 106

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} What proportion of accidents involved alcohol or a single vehicle?

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Q 107Q 107

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} Given alcohol was involved, what proportion of accidents involved a single vehicle?

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Q 108Q 108

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} If multiple vehicles were involved, what proportion of accidents involved alcohol?

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Q 109Q 109

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} If 3 vehicles were involved, what proportion of accidents involved alcohol?

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Q 110Q 110

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} If alcohol was not involved, what proportion of the accidents were single vehicle?

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Q 111Q 111

Drunk Drivers
Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below:
-{Drunk Drivers Narrative} If alcohol was not involved, what proportion of the accidents were multiple vehicle?

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Essay

Q 112Q 112

Suppose A and B are two independent events for which P(A) = 0.20 and P(B) = 0.60.
a.
Find P(A|B).
b.
Find P(B|A).

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Essay

Q 113Q 113

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} If the student selected is in the upper class, what is the probability that her GPA is between 2.0 and 3.0?

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Essay

Q 114Q 114

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} If the GPA of the student selected is over 3.0, what is the probability that the student is in the lower class?

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Essay

Q 115Q 115

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} What is the probability that the student is in the upper class?

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Essay

Q 116Q 116

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} What is the probability that the student has GPA over 3.0?

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Q 117Q 117

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} What is the probability that the student is in the lower class?

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Q 118Q 118

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} What is the probability that the student is in the lower class and has GPA over 3.0?

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Q 119Q 119

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} What is the probability that the student is in the upper class and has GPA under 2.0?

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Essay

Q 120Q 120

GPA and Class
A college professor classifies his students according to their grade point average (GPA) and their class rank.GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors).One student is selected at random.
-{GPA and Class Narrative} Are being in the upper class and having a GPA over 3.0 related? Explain.

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Q 121Q 121

Marital Status
An insurance company has collected the following data on the gender and marital status of 570 customers.
Suppose that a customer is selected at random.
-{Marital Status Narrative} Develop the joint probability table.

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Q 122Q 122

Marital Status
An insurance company has collected the following data on the gender and marital status of 570 customers.
Suppose that a customer is selected at random.
-{Marital Status Narrative} Find the probability that the customer selected is a married female.

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Q 123Q 123

Marital Status
An insurance company has collected the following data on the gender and marital status of 570 customers.
Suppose that a customer is selected at random.
-{Marital Status Narrative} Find the probability that the customer selected is
a.
female and single
b.
married if the customer is male.
c.
not single

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Essay

Q 124Q 124

Financial Consultants
A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-{Financial Consultants Narrative} Find the following probabilities:
a.
P(A)
b.
P(B)

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Q 125Q 125

Financial Consultants
A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-{Financial Consultants Narrative} Express each of the following events in words:
a.
A or B
b.
A and B

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Essay

Q 126Q 126

Financial Consultants
A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-{Financial Consultants Narrative} Find P(A and B).

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Q 127Q 127

Financial Consultants
A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-{Financial Consultants Narrative} Express each of the following probabilities in words:
a.
P(A|B)
b.
P(B|A)

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Essay

Q 128Q 128

Financial Consultants
A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-{Financial Consultants Narrative} Find the following probabilities:
a.
P(A|B)
b.
P(B|A)

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Essay

Q 129Q 129

Julius and Gabe go to a show during their Spring break and toss a balanced coin to see who will pay for the tickets.The probability that Gabe will pay three days in a row is 0.125.

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True False

Q 130Q 130

If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.

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True False

Q 131Q 131

If the event of interest is A, the probability that A will not occur is the complement of A.

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True False

Q 132Q 132

Assume that A and B are independent events with P(A) = 0.30 and P(B) = 0.50.The probability that both events will occur simultaneously is 0.80.

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True False

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True False

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True False

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True False

Q 136Q 136

If A and B are two independent events with P(A) = 0.9 and P(B|A) = 0.5, then P(A and B) = 0.45.

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True False

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True False

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True False

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True False

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True False

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True False

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True False

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True False

Q 144Q 144

If the events A and B are independent with P(A) = 0.35 and P(B) = 0.45, then the probability that both events will occur simultaneously is:
A) 0
B) 0.16
C) 0.80
D) Not enough information to tell.

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Multiple Choice

Q 145Q 145

Two events A and B are said to be mutually exclusive if:
A) P(A|B) = 1
B) P(A|B) = P(A)
C) P(A and B) =1
D) P(A and B) = 0

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Multiple Choice

Q 146Q 146

If P(A) = 0.84, P(B) = 0.76, and P(A or B) = 0.90, then P(A and B) is:
A) 0.06
B) 0.14
C) 0.70
D) 0.83

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Multiple Choice

Q 147Q 147

Which of the following statements is always correct?
A) P(A and B) = P(A) * P(B)
B) P(A or B) = P(A) + P(B)
C) P(A) = 1 P(A

^{c}) D) None of these choices.Free

Multiple Choice

Q 148Q 148

If P(A) = 0.20, P(B) = 0.30, and P(A and B) = 0, then A and B are:
A) dependent events
B) independent events
C) mutually exclusive events
D) complementary events

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Multiple Choice

Q 149Q 149

If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is:
A) 1.23
B) 0.47
C) 0.24
D) None of these choices.

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Multiple Choice

Q 150Q 150

Suppose P(A) = 0.30.The probability of the complement of A is:
A) 0.30
B) 0.70
C) 0.30
D) None of these choices.

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Multiple Choice

Q 151Q 151

If events A and B are independent then:
A) P(A and B) = P(A) * P(B)
B) P(A and B) = P(A) + P(B)
C) P(B|A) = P(A)
D) None of these choices.

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Multiple Choice

Q 152Q 152

If A and B are mutually exclusive events, with P(A) = 0.20 and P(B) = 0.30, then the probability that both events will occur simultaneously is:
A) 0.50
B) 0.06
C) 0
D) None of these choices.

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Multiple Choice

Q 153Q 153

If A and B are independent events with P(A) = 0.60 and P(B) = 0.70, then P(A or B) equals:
A) 1.30
B) 0.88
C) 0.42
D) Cannot tell from the given information.

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Multiple Choice

Q 154Q 154

If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is:
A) 0.10
B) 0.12
C) 0.70
D) None of these choices

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Multiple Choice

Q 155Q 155

If A and B are any two events with P(A) = .8 and P(B|A) = .4, then P(A and B) is:
A) .40
B) .32
C) 1.20
D) None of these choices.

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Multiple Choice

Q 156Q 156

If A and B are any two events with P(A) = .8 and P(B|A

^{c}) = .7, then P(A^{c}and B) is A) 0.56 B) 0.14 C) 1.50 D) None of these choices.Free

Multiple Choice

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Essay

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Essay

Q 159Q 159

If A and B are ____________________ events, the joint probability of A and B is the product of the probabilities of those two events.

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Essay

Q 160Q 160

The ____________________ rule is used to calculate the probability of the union of two events.

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Essay

Q 161Q 161

If A and B are ____________________ then the probability of the union of A and B is the sum of their individual probabilities.

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Essay

Q 162Q 162

The first set of branches of a probability tree represent ____________________ probabilities.

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Essay

Q 163Q 163

The second set of branches of a probability tree represent ____________________ probabilities.

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Essay

Q 164Q 164

When you multiply a first level branch with a second level branch on a probability tree you get a(n) ____________________ probability.

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Essay

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Essay

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Essay

Q 167Q 167

Suppose A and B are two independent events for which P(A) = 0.20 and P(B) = 0.60.
a.
Find P(A and B).
b.
Find P(A or B).

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Essay

Q 168Q 168

College Professorship
A Ph.D.graduate has applied for a job with two colleges: A and B.The graduate feels that she has a 60% chance of receiving an offer from college A and a 50% chance of receiving an offer from college B.If she receives an offer from college B, she believes that she has an 80% chance of receiving an offer from college A.Let A = receiving an offer from college A, and let B = receiving an offer from college B.
-{College Professorship Narrative} What is the probability that both colleges will make her an offer?

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Essay

Q 169Q 169

College Professorship
A Ph.D.graduate has applied for a job with two colleges: A and B.The graduate feels that she has a 60% chance of receiving an offer from college A and a 50% chance of receiving an offer from college B.If she receives an offer from college B, she believes that she has an 80% chance of receiving an offer from college A.Let A = receiving an offer from college A, and let B = receiving an offer from college B.
-{College Professorship Narrative} What is the probability that at least one college will make her an offer?

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Essay

Q 170Q 170

College Professorship
A Ph.D.graduate has applied for a job with two colleges: A and B.The graduate feels that she has a 60% chance of receiving an offer from college A and a 50% chance of receiving an offer from college B.If she receives an offer from college B, she believes that she has an 80% chance of receiving an offer from college A.Let A = receiving an offer from college A, and let B = receiving an offer from college B.
-{College Professorship Narrative} If she receives an offer from college B, what is the probability that she will not receive an offer from college A?

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Essay

Q 171Q 171

Suppose P(A) = 0.50, P(B) = 0.40, and P(B|A) = 0.30.
a.
Find P(A and B).
b.
Find P(A or B).
c.
Find P(A|B).

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Essay

Q 172Q 172

A survey of a magazine's subscribers indicates that 50% own a house, 80% own a car, and 90% of the homeowners also own a car.What proportion of subscribers:
a.
own both a car and a house?
b.
own a car or a house, or both?
c.
own neither a car nor a house?

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Essay

Q 173Q 173

Suppose A and B are two mutually exclusive events for which P(A) = 0.30 and P(B) = 0.40.
a.
Find P(A and B).
b.
Find P(A or B).
c.
Are A and B independent events? Explain using probabilities.

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Essay

Q 174Q 174

Suppose P(A) = 0.30, P(B) = 0.50, and P(B|A) = 0.60.
a.
Find P(A and B).
b.
Find P(A or B).
c.
Find P(A|B).

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Essay

Q 175Q 175

Is it possible to have two events for which P(A) = 0.40, P(B) = 0.50, and P(A or B) = 0.30? Explain.

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Essay

Q 176Q 176

A pharmaceutical firm has discovered a new diagnostic test for a certain disease that has infected 1% of the population.The firm has announced that 95% of those infected will show a positive test result, while 98% of those not infected will show a negative test result.
a.
What proportion of people don't have the disease?
b.
What proportion who have the disease test negative?
c.
What proportion of those who don't have the disease test positive?
d.
What proportion of test results are incorrect?
e.
What proportion of test results are correct?

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Essay

Q 177Q 177

Construction Bids
A construction company has submitted bids on two separate state contracts, A and B.The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B.Furthermore, the company believes that it has an 80% chance of winning contract A if it wins contract B.
-{Construction Bids Narrative} What is the probability that the company will win both contracts?

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Essay

Q 178Q 178

Construction Bids
A construction company has submitted bids on two separate state contracts, A and B.The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B.Furthermore, the company believes that it has an 80% chance of winning contract A if it wins contract B.
-{Construction Bids Narrative} What is the probability that the company will win at least one of the two contracts?

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Essay

Q 179Q 179

Construction Bids
A construction company has submitted bids on two separate state contracts, A and B.The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B.Furthermore, the company believes that it has an 80% chance of winning contract A if it wins contract B.
-{Construction Bids Narrative} If the company wins contract B, what is the probability that it will not win contract A?

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Essay

Q 180Q 180

Construction Bids
A construction company has submitted bids on two separate state contracts, A and B.The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B.Furthermore, the company believes that it has an 80% chance of winning contract A if it wins contract B.
-{Construction Bids Narrative} What is the probability that the company will win at most one of the two contracts?

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Essay

Q 181Q 181

Construction Bids
A construction company has submitted bids on two separate state contracts, A and B.The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B.Furthermore, the company believes that it has an 80% chance of winning contract A if it wins contract B.
-{Construction Bids Narrative} What is the probability that the company will win neither contract?

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Essay

Q 182Q 182

Condo Sales and Interest Rates
The probability that condo sales will increase in the next 6 months is estimated to be 0.30.The probability that the interest rates on condo loans will go up in the same period is estimated to be 0.75.The probability that condo sales or interest rates will go up during the next 6 months is estimated to be 0.90.
-{Condo Sales and Interest Rates Narrative} What is the probability that both condo sales and interest rates will increase during the next six months?

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Essay

Q 183Q 183

Condo Sales and Interest Rates
The probability that condo sales will increase in the next 6 months is estimated to be 0.30.The probability that the interest rates on condo loans will go up in the same period is estimated to be 0.75.The probability that condo sales or interest rates will go up during the next 6 months is estimated to be 0.90.
-{Condo Sales and Interest Rates Narrative} What is the probability that neither condo sales nor interest rates will increase during the next six months?

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Essay

Q 184Q 184

Condo Sales and Interest Rates
The probability that condo sales will increase in the next 6 months is estimated to be 0.30.The probability that the interest rates on condo loans will go up in the same period is estimated to be 0.75.The probability that condo sales or interest rates will go up during the next 6 months is estimated to be 0.90.
-{Condo Sales and Interest Rates Narrative} What is the probability that condo sales will increase but interest rates will not during the next six months?

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Essay

Q 185Q 185

Bayes' Law is a formula for revising an initial subjective (prior) probability value on the basis of new results, thus obtaining a new (posterior) probability value.

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True False

Q 186Q 186

Although there is a formula defining Bayes' law, you can also use a probability tree to conduct calculations.

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True False

Q 187Q 187

Bayes' Law allows us to compute conditional probabilities from other forms of probability.

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True False

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True False

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True False

Q 190Q 190

In applying Bayes' Law, as the prior probabilities increase, the posterior probabilities decrease.

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True False

Q 191Q 191

Prior probability of an event is the probability of the event before any information affecting it is given.

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True False

Q 192Q 192

Bayes' Law can be used to calculate posterior probabilities, prior probabilities, as well as new conditional probabilities.

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True False

Q 193Q 193

Posterior probability of an event is the revised probability of the event after new information is available.

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True False

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True False

Q 195Q 195

In general, a posterior probability is calculated by adding the prior and likelihood probabilities.

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True False

Q 196Q 196

We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

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True False

Q 197Q 197

In problems where the joint probabilities are given, we can compute marginal probabilities by adding across rows and down columns.

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True False

Q 198Q 198

If joint, marginal, and conditional probabilities are available, only joint probabilities can be used to determine whether two events are dependent or independent.

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True False

Q 199Q 199

Suppose we have two events A and B.We can apply the addition rule to compute the probability that at least one of these events occurs.

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True False

Q 200Q 200

Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

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True False

Q 201Q 201

Prior probabilities can be calculated using the multiplication rule for mutually exclusive events.

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True False

Q 202Q 202

We can apply the multiplication rule to compute the probability that two events occur at the same time.

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True False

Q 203Q 203

Which of the following statements is false?
A) Thomas Bayes first employed the calculation of conditional probability in the eighteenth century.
B) There is no formula defining Bayes' Law.
C) We use a probability tree to conduct all necessary calculations for Bayes' Law.
D) None of these choices.

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Multiple Choice

Q 204Q 204

A posterior probability value is a prior probability value that has been:
A) modified on the basis of new information.
B) multiplied by a conditional probability value.
C) divided by a conditional probability value.
D) added to a conditional probability value.

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Multiple Choice

Q 205Q 205

Initial estimates of the probabilities of events are known as:
A) joint probabilities
B) posterior probabilities
C) prior probabilities
D) conditional probabilities

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Multiple Choice

Q 206Q 206

Which of the following statements is false regarding a scenario using Bayes' Law?
A) Prior probabilities are called likelihood probabilities.
B) Conditional probabilities are called posterior probabilities.
C) Posterior probabilities are calculated by using prior probabilities that have been modified based on new information.
D) None of these choices.

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Multiple Choice

Q 207Q 207

Bayes' Law is used to compute:
A) prior probabilities.
B) joint probabilities.
C) union probabilities.
D) posterior probabilities.

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Multiple Choice

Free

Essay

Q 209Q 209

Bayes' Law involves three different types of probabilities: 1) prior probabilities; 2) likelihood probabilities; and 3) ____________________ probabilities.

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Essay

Q 210Q 210

Bayes' Law involves three different types of probabilities: 1) ____________________ probabilities; 2) likelihood probabilities; and 3) posterior probabilities.

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Essay

Q 211Q 211

Bayes' Law involves three different types of probabilities: 1) prior probabilities; 2) ____________________ probabilities; and 3) posterior probabilities.

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Essay

Q 212Q 212

There are situations where we witness a particular event and we need to compute the probability of one of its possible causes.____________________ is the technique we use to do this.

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Essay

Q 213Q 213

In the scenario of Bayes' Law, P(A|B) is a(n) ____________________ probability, while P(B|A) is a posterior probability.

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Essay

Q 214Q 214

In the scenario of Bayes' Law, P(A|B) is a posterior probability, while P(B|A) is a(n) ____________________ probability.

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Essay

Q 215Q 215

____________________ can find the probability that someone with a disease tests positive by using (among other things) the probability that someone who actually has the disease tests positive for it.

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Essay

Q 216Q 216

Certification Test
A standard certification test was given at three locations.1,000 candidates took the test at location A, 600 candidates at location B, and 400 candidates at location C.The percentages of candidates from locations A, B, and C who passed the test were 70%, 68%, and 77%, respectively.One candidate is selected at random from among those who took the test.
-{Certification Test Narrative} What is the probability that the selected candidate passed the test?

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Essay

Q 217Q 217

Certification Test
A standard certification test was given at three locations.1,000 candidates took the test at location A, 600 candidates at location B, and 400 candidates at location C.The percentages of candidates from locations A, B, and C who passed the test were 70%, 68%, and 77%, respectively.One candidate is selected at random from among those who took the test.
-{Certification Test Narrative} If the selected candidate passed the test, what is the probability that the candidate took the test at location B?

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Essay

Q 218Q 218

Certification Test
A standard certification test was given at three locations.1,000 candidates took the test at location A, 600 candidates at location B, and 400 candidates at location C.The percentages of candidates from locations A, B, and C who passed the test were 70%, 68%, and 77%, respectively.One candidate is selected at random from among those who took the test.
-{Certification Test Narrative} What is the probability that the selected candidate took the test at location C and failed?

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Essay

Q 219Q 219

Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient.
-{Cysts Narrative} In the absence of any test, what is the probability that the cyst is malignant?

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Essay

Q 220Q 220

Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient.
-{Cysts Narrative} In the absence of any test, what is the probability that the cyst is benign?

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Essay

Q 221Q 221

Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient.
-{Cysts Narrative} What is the probability that the patient will test positive?

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Essay

Q 222Q 222

Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient.
-{Cysts Narrative} What is the probability that the patient will test negative?

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Essay

Q 223Q 223

Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient.
-{Cysts Narrative} What is the probability that the patient has a benign tumor if he or she tests positive?

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Essay

Q 224Q 224

Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient.
-{Cysts Narrative} What is the probability that the patient has a malignant cyst if he or she tests negative?

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Essay

Q 225Q 225

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} Calculate P(A and O).

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Essay

Q 226Q 226

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} Calculate P(B and O).

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Essay

Q 227Q 227

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} Calculate P(C and O).

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Essay

Q 228Q 228

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} Calculate the probability that a package was delivered on time.

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Essay

Q 229Q 229

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} If a package was delivered on time, what is the probability that it was service A?

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Essay

Q 230Q 230

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} If a package was delivered on time, what is the probability that it was service B?

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Essay

Q 231Q 231

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} If a package was delivered on time, what is the probability that it was service C?

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Essay

Q 232Q 232

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} If a package was delivered 40 minutes late, what is the probability that it was service A?

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Essay

Q 233Q 233

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} If a package was delivered 40 minutes late, what is the probability that it was service B?

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Essay

Q 234Q 234

Messenger Service
Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively.Define event O as a service delivers a package on time.
-{Messenger Service Narrative} If a package was delivered 40 minutes late, what is the probability that it was service C?

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Essay