Deck 4: Basic Probability

Question 1

If two equally likely events A and B are mutually exclusive, what is the probability that event A
Occurs?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Answer 1

D

Question 2

If event A and event B cannot occur at the same time, then events A and B are said to be

A) mutually exclusive.
B) independent.
C) collectively exhaustive.
D) None of the above.

Answer 2

A

Question 3

If two events are mutually exclusive and collectively exhaustive, what is the probability that one
Or the other occurs?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Answer 3

C

Question 4

Selection of raffle tickets from a large bowl is an example of

A) simple probability.
B) sampling without replacement.
C) subjective probability.
D) None of the above.

Question 5

If either event A or event B must occur, then events A and B are said to be

A) mutually exclusive.
B) independent.
C) collectively exhaustive.
D) None of the above.

Question 6

If two events are collectively exhaustive, what is the probability that both occur at the same time?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 7

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.

Question 8

If two events are mutually exclusive and collectively exhaustive, what is the probability that both
Occur?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 9

A business venture can result in the following outcomes (with their corresponding chance of
Occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%),
Disappointing (20%), and Highly Disappointing (?).If these are the only outcomes possible for
The business venture, what is the chance that the business venture will be considered Highly
Disappointing?

A) 10%
B) 15%
C) 20%
D) 25%

Question 10

If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is
The probability that event A occurs?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 11

When using the general multiplication rule, P(A and B)is equal to

Question 12

The collection of all possible events is called

A) a simple probability.
B) a sample space.
C) a joint probability.
D) the null set.

Question 13

All the events in the sample space that are not part of the specified event are called

A) simple events.
B) joint events.
C) the sample space.
D) the complement of the event.

Question 14

If events A and B are mutually exclusive and collectively exhaustive, what is the probability that
Event A occurs?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 15

If two events are mutually exclusive, what is the probability that both occur at the same time?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 16

If two equally likely events A and B are collectively exhaustive, what is the probability that event
A occurs?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 17

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 the above.

Question 18

If two events are collectively exhaustive, what is the probability that one or the other occurs?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 19

Simple probability is also called

A) marginal probability.
B) joint probability.
C) conditional probability.
D) Bayes' theorem.

Question 20

If two events are mutually exclusive, what is the probability that one or the other occurs?

A) 0.
B) 0.50.
C) 1.00.
D) Cannot be determined from the information given.

Question 21

A survey of banks revealed the following distribution for the interest rate being charged on a
Home loan (based on a 30-year mortgage with a 10% down payment)on a certain date in the past.
If a bank is selected at random from this distribution, what is the chance that the interest rate charged
On a home loan will exceed 3.49%?

A) 0.06
B) 0.41
C) 0.59
D) 1.00

Question 22

The probability that a new advertising campaign will increase sales is assessed as being 0.80.The
Probability that the cost of developing the new ad campaign can be kept within the original
Budget allocation is 0.40.Assuming that the two events are independent, the probability that
Neither the cost is kept within budget nor the campaign will increase sales is:

A) 0.12
B) 0.32
C) 0.68
D) 0.88

Question 23

A company has 2 machines that produce widgets.An older machine produces 23% defective
Widgets, while the new machine produces only 8% defective widgets.In addition, the new
Machine produces 3 times as many widgets as the older machine does.Given that a widget was
Produced by the new machine, what is the probability it is not defective?

A) 0.06
B) 0.50
C) 0.92
D) 0.94

Question 24

According to a survey of American households, the probability that the residents own 2 cars if
Annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars.The probability that annual household income is over $50,000
If the residents of a household do not own 2 cars is:

A) 0.12
B) 0.18
C) 0.40
D) 0.70

Question 25

The probability that a new advertising campaign will increase sales is assessed as being 0.80.The
Probability that the cost of developing the new ad campaign can be kept within the original
Budget allocation is 0.40.Assuming that the two events are independent, the probability that the
Cost is kept within budget or the campaign will increase sales is:

A) 0.20
B) 0.32
C) 0.68
D) 0.88

Question 26

A company has 2 machines that produce widgets.An older machine produces 23% defective
Widgets, while the new machine produces only 8% defective widgets.In addition, the new
Machine produces 3 times as many widgets as the older machine does.Given a randomly chosen
Widget was tested and found to be defective, what is the probability it was produced by the new
Machine?

A) 0.08
B) 0.15
C) 0.489
D) 0.511

Question 27

The probability that a new advertising campaign will increase sales is assessed as being 0.80.The
Probability that the cost of developing the new ad campaign can be kept within the original
Budget allocation is 0.40.Assuming that the two events are independent, the probability that the
Cost is kept within budget and the campaign will increase sales is:

A) 0.20
B) 0.32
C) 0.40
D) 0.88

Question 28

According to a survey of American households, the probability that the residents own 2 cars if
Annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars.The probability that the residents of a household own 2 cars
And have an income over $50,000 a year is:

A) 0.12
B) 0.18
C) 0.22
D) 0.48

Question 29

According to a survey of American households, the probability that the residents own 2 cars if
Annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars.The probability that the residents of a household do not own 2
Cars and have an income over $50,000 a year is:

A) 0.12
B) 0.18
C) 0.22
D) 0.48

Question 30

A company has 2 machines that produce widgets.An older machine produces 23% defective
Widgets, while the new machine produces only 8% defective widgets.In addition, the new
Machine produces 3 times as many widgets as the older machine does.What is the probability
That a randomly chosen widget produced by the company is defective?

A) 0.078
B) 0.1175
C) 0.156
D) 0.310

Question 31

According to a survey of American households, the probability that the residents own 2 cars if
Annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars.The probability that annual household income is over $50,000
If the residents of a household own 2 cars is:

A) 0.42
B) 0.48
C) 0.50
D) 0.69

Question 32

The employees of a company were surveyed on questions regarding their educational background
(college degree or no college degree)and marital status (single or married).Of the 600
Employees, 400 had college degrees, 100 were single, and 60 were single college graduates.The
Probability that an employee of the company is married and has a college degree is:

A) 0.0667
B) 0.567
C) 0.667
D) 0.833

Question 33

According to a survey of American households, the probability that the residents own 2 cars if
Annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars.The probability that the residents do not own 2 cars if annual
Household income is not over $50,000 is:

A) 0.12
B) 0.18
C) 0.45
D) 0.70

Question 34

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, what proportion of accidents involved alcohol and a single vehicle?

A) 25/400 or 6.25%
B) 50/400 or 12.5%
C) 195/400 or 48.75%
D) 245/400 or 61.25%

Question 35

According to a survey of American households, the probability that the residents own 2 cars if
Annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars.The probability that the residents of a household own 2 cars
And have an income less than or equal to $50,000 a year is:

A) 0.12
B) 0.18
C) 0.22
D) 0.48

Question 36

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, given alcohol was involved, what proportion of accidents involved a
Single vehicle?

A) 50/75 or 66.67%
B) 50/170 or 29.41%
C) 120/170 or 70.59%
D) 120/400 or 30%

Question 37

The employees of a company were surveyed on questions regarding their educational background
(college degree or no college degree)and marital status (single or married).Of the 600
Employees, 400 had college degrees, 100 were single, and 60 were single college graduates.The
Probability that an employee of the company is single or has a college degree is:

A) 0.10
B) 0.25
C) 0.667
D) 0.733

Question 38

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, what proportion of accidents involved more than one vehicle?

A) 50/400 or 12.5%
B) 75/400 or 18.75%
C) 275/400 or 68.75%
D) 325/400 or 81.25%

Question 39

The probability that a new advertising campaign will increase sales is assessed as being 0.80.The
Probability that the cost of developing the new ad campaign can be kept within the original
Budget allocation is 0.40.Assuming that the two events are independent, the probability that the
Cost is not kept within budget or the campaign will not increase sales is:

A) 0.12
B) 0.32
C) 0.68
D) 0.88

Question 40

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, what proportion of accidents involved alcohol or a single vehicle?

A) 25/400 or 6.25%
B) 50/400 or 12.5%
C) 195/400 or 48.75%
D) 245/400 or 61.25%

Question 41

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, given that alcohol was not involved, what proportion of the accidents
Were multiple vehicle?

A) 50/170 or 29.41%
B) 120/170 or 70.59%
C) 205/230 or 89.13%
D) 25/230 or 10.87%

Question 42

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, given that multiple vehicles were involved, what proportion of
Accidents involved alcohol?

A) 120/170 or 70.59%
B) 120/230 or 52.17%
C) 120/325 or 36.92%
D) 120/400 or 30%

Question 43

True or False: If either A or B must occur they are called collectively exhaustive.

Question 44

True or False: If P(A or B)= 1.0, then A and B must be mutually exclusive.

Question 45

True or False: If P(A or B)= 1.0, then A and B must be collectively exhaustive.

Question 46

True or False: If A and B cannot occur at the same time they are called mutually exclusive.

Question 47

SCENARIO 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to
ask them whether they went bar hopping the weekend before the midterm or spent the weekend
studying, and whether they did well or poorly on the midterm.The following result was obtained.
Referring to Scenario 4-2, what is the probability that a randomly selected student did well on the
Midterm or went bar hopping the weekend before the midterm?

A) 30/200 or 15%
B) (80+30) /200 or (30+80) /200 or 55%
C) (30+70) /200 or (70+30) /200 or 50%
D) (80+30+70) /200 or (110+100-30) /200 or 90%

Question 48

SCENARIO 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to
ask them whether they went bar hopping the weekend before the midterm or spent the weekend
studying, and whether they did well or poorly on the midterm.The following result was obtained.
Referring to Scenario 4-2, what is the probability that a randomly selected student who went bar
Hopping did well on the midterm?

A) 30/100 or 30%
B) 30/110 or 27.27%
C) 30/200 or 15%
D) (100/200) *(110/200) or 27.50%

Question 49

SCENARIO 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to
ask them whether they went bar hopping the weekend before the midterm or spent the weekend
studying, and whether they did well or poorly on the midterm.The following result was obtained.
Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

A) not dependent.
B) not mutually exclusive.
C) collective exhaustive.
D) None of the above.

Question 50

True or False: The collection of all the possible events is called a sample space.

Question 51

True or False: When A and B are mutually exclusive, P(A or B)can be found by adding P(A)and
P(B).

Question 52

True or False: If either A or B must occur they are called mutually exclusive.

Question 53

True or False: If P(A and B)= 0, then A and B must be mutually exclusive.

Question 54

SCENARIO 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to
ask them whether they went bar hopping the weekend before the midterm or spent the weekend
studying, and whether they did well or poorly on the midterm.The following result was obtained.
Referring to Scenario 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are

A) dependent.
B) mutually exclusive.
C) collective exhaustive.
D) All of the above.

Question 55

SCENARIO 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to
ask them whether they went bar hopping the weekend before the midterm or spent the weekend
studying, and whether they did well or poorly on the midterm.The following result was obtained.
Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

A) dependent.
B) mutually exclusive.
C) collective exhaustive.
D) None of the above.

Question 56

True or False: If P(A)= 0.4 and P(B)= 0.6, then A and B must be collectively exhaustive.

Question 57

SCENARIO 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to
ask them whether they went bar hopping the weekend before the midterm or spent the weekend
studying, and whether they did well or poorly on the midterm.The following result was obtained.
Referring to Scenario 4-2, what is the probability that a randomly selected student did well on the
Midterm and also went bar hopping the weekend before the midterm?

A) 30/200 or 15%
B) (80+30) /200 or 55%
C) (30+70) /200 or 50%
D) (80+30+70) /200 or 90%

Question 58

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, given that alcohol was not involved, what proportion of the accidents
Were single vehicle?

A) 50/75 or 66.67%
B) 25/230 or 10.87%
C) 50/170 or 29.41%
D) 25/75 or 33.33%

Question 59

SCENARIO 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public
about the harm caused by drunk drivers.A study was recently done that emphasized the problem we
all face with drinking and driving.Four 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:
-
Referring to Scenario 4-1, given that 3 vehicles were involved, what proportion of accidents
Involved alcohol?

A) 20/30 or 66.67%
B) 20/50 or 40%
C) 20/170 or 11.77%
D) 20/400 or 5%

Question 60

True or False: If P(A)= 0.4 and P(B)= 0.6, then A and B must be mutually exclusive.

Question 61

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, the probability that a randomly selected individual is a child or prefers
hamburger is __________.

Question 62

SCENARIO 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large
companies, 40 offered stock options to their board members as part of their non-cash compensation
packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock
options as part of their noncash compensation packages to their board members.
Referring to Scenario 4-9, set up a contingency table.

Question 63

SCENARIO 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large
companies, 40 offered stock options to their board members as part of their non-cash compensation
packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock
options as part of their noncash compensation packages to their board members.
Referring to Scenario 4-9, is the size of the company independent of whether stock options are
offered to their board members and why?

Question 64

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, the probability that a randomly selected individual is an adult or a child
is __________.

Question 65

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, the probability that a randomly selected individual is a child and
prefers chicken is __________.

Question 66

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, the probability that a randomly selected individual is an adult and
prefers chicken is __________.

Question 67

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, assume we know that a person prefers hamburger.The probability that
this individual is a child is __________.

Question 68

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, the probability that a randomly selected individual is an adult is
__________.

Question 69

True or False: If P(A and B)= 0, then A and B must be collectively exhaustive.

Question 70

SCENARIO 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large
companies, 40 offered stock options to their board members as part of their non-cash compensation
packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock
options as part of their noncash compensation packages to their board members.
Referring to Scenario 4-9, if a company is selected at random, what is the probability that the
company is small to mid-sized and did not offer stock options to their board members?

Question 71

You know that the probability of a randomly selected student will cheat on an exam is 1%.You
Also know that the probability of a randomly selected student will cheat on an exam knowing that
His/her fellow classmate is cheating on the exam is also 1%.Which of the following is true about
The event of "the randomly selected student cheating on an exam" and "his/her classmate is
Cheating on the exam"?

A) They are mutually exclusive.
B) They are collectively exhaustive.
C) They are independent.
D) None of the above.

Question 72

True or False: If P(A and B)= 1, then A and B must be collectively exhaustive.

Question 73

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, assume we know the person is a child.The probability that this
individual prefers hamburger is __________.

Question 74

SCENARIO 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large
companies, 40 offered stock options to their board members as part of their non-cash compensation
packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock
options as part of their noncash compensation packages to their board members.
Referring to Scenario 4-9, if a randomly selected company offered stock options to their board
members, what is the probability that it is a large company?

Question 75

SCENARIO 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger
and 80 preferred chicken.55 of the children preferred hamburger.
Referring to Scenario 4-3, assume we know that a person prefers chicken.The probability that
this individual is an adult is __________.

Question 76

True or False: To ethically advertise a school lottery scheme to try to raise money for the
athletic department, the organizer of the lottery does not need to explicitly specify the probability
of each of the prize in the lottery.

Question 77

SCENARIO 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large
companies, 40 offered stock options to their board members as part of their non-cash compensation
packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock
options as part of their noncash compensation packages to their board members.
Referring to Scenario 4-9, if a randomly selected company is a large company, what is the
probability that it offered stock options to their board members?

Question 78

SCENARIO 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large
companies, 40 offered stock options to their board members as part of their non-cash compensation
packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock
options as part of their noncash compensation packages to their board members.
Referring to Scenario 4-9, if a company is selected at random, what is the probability that the
company offered stock options to their board members?

Question 79

True or False: If P(A and B)= 1, then A and B must be mutually exclusive.

Question 80

SCENARIO 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large
companies, 40 offered stock options to their board members as part of their non-cash compensation
packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock
options as part of their noncash compensation packages to their board members.
Referring to Scenario 4-9, if a company is selected at random, what is the probability that the
company is small to mid-sized or offered stock options to their board members?