Deck 7: Randomness and Probability

Question 1

The option to buy extended warranties is commonplace with most electronics purchases.But does the type of purchase affect a consumer's willingness to pay extra for
An extended warranty? Data for 420 consumers who purchased digital cameras and
Laptop computers from a leading electronics retailer are summarized in the table.Which
Of the following statement is true?

A)The decision to purchase an extended warranty and type of electronics (digital
B)The decision to purchase an extended warranty and type of electronics (digital
C)The decision to purchase an extended warranty and type of electronics (digital
D)The decision to purchase an extended warranty and type of electronics (digital
E)The decision to purchase an extended warranty and type of electronics (digital

Answer 1

A

Question 2

A small manufacturing company recently instituted Six Sigma training for its
employees.Two methods of training were offered: online and traditional classroom.
Management was interested in whether the division in which employees worked affected
their choice of method.Below is a table summarizing the data. a.What is the probability that an employee chose online training?
b.What is the probability that an employee is in the quality division and chose online
training?
c.What is the probability that an employee chose online training given that he/she is in
the sales division?

Answer 2

a..75 (102/136)
b..17 (23/136)
c..69 (35/51)

Question 3

During its grand opening week, Stickler's bicycle shop offers a "wheel of discount savings." After customers select the items they wish to purchase, they spin the wheel to
Determine the discount they will receive.The wheel is divided into 12 slices.Six slices
Are red and award a 10% discount, three slices are white and award a 20% discount, and
Two slices are blue and award a 40% discount.The remaining slice is gold and awards a
100% discount! The probability that a customer gets a 10% or 20% discount is

A)3/12
B)2/12
C).0625
D)9/12
E)10/12

Answer 3

D

Question 4

A recent survey of local cell phone retailers showed that of all cell phones sold last
month, 64% had a camera, 28% had a music player and 22% had both.
a.What is the probability that a cell phone sold last month had a camera or a music
player?
b.What is the probability that a cell phone sold last month did not have either a camera
or a music player?
c.Is a cell phone having a camera and a music player mutually exclusive? Explain.

Question 5

During its grand opening week, Stickler's bicycle shop offers a "wheel of discount
savings." After customers select the items they wish to purchase, they spin the wheel to
determine the discount they will receive.The wheel is divided into 12 slices.Six slices
are red and award a 10% discount, three slices are white and award a 20% discount, and
two slices are blue and award a 40% discount.The remaining slice is gold and awards a
100% discount! a.What is the probability that a customer gets at least a 40% discount?
b.What is the probability that a customer does not get at least a 40% discount?
c.What is the probability that a customer gets a 10% or 20% discount?
d.What is the probability that two customers in a row get a 20% discount?

Question 6

A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both.The probability
That a cell phone sold last month had a camera or a music player is

A).22
B).70
C).92
D).30
E).08

Question 7

The option to buy extended warranties is commonplace with most electronics purchases.But does the type of purchase affect a consumer's willingness to pay extra for
An extended warranty? Data for 420 consumers who purchased digital cameras and
Laptop computers from a leading electronics retailer are summarized in the table.The
Probability that a consumer does not purchase an extended warranty is

A).07
B).42
C).58
D).17
E).83

Question 8

As an incentive to get new customers, the local branch of a bank launched "bouncing for bucks." During this week long event, any customer opening a new checking account
With the bank would have the opportunity to throw a bouncy rubber ball into a large box
Divided into squares.Each square was labeled with a dollar amount that would be
Deposited into his/her new checking account.The way the box was labeled is shown
Below.What is the probability that a customer gets $50?

A)0.10
B)0.01
C)0.50
D)0.05
E)0.20

Question 9

Does it appear that choice of instructional method (traditional or online) and division
(sales, quality and operations) are independent? Explain.

Question 10

During its grand opening week, Stickler's bicycle shop offers a "wheel of discount savings." After customers select the items they wish to purchase, they spin the wheel to
Determine the discount they will receive.The wheel is divided into 12 slices.Six slices
Are red and award a 10% discount, three slices are white and award a 20% discount, and
Two slices are blue and award a 40% discount.The remaining slice is gold and awards a
100% discount! The probability that a customer gets at least a 40% discount is

A)3/12
B)2/12
C).0625
D)9/12
E)10/12

Question 11

Suppose you visit Stickler's bicycle shop in the hopes of getting a 100% discount on
your purchases.As you wait your turn in line, there are three gold winners in a row.The
two customers in line behind you begin to discuss what's happened.One believes that
the streak of three gold winners has killed anyone else's chances of getting a 100%
discount, while the other says just the opposite… that the wheel's "hot streak" increases
their chances of getting a 100% discount.Comment on these opinions.
7-4 Chapter 7 Randomness and Probability

Question 12

During its grand opening week, Stickler's bicycle shop offers a "wheel of discount savings." After customers select the items they wish to purchase, they spin the wheel to
Determine the discount they will receive.The wheel is divided into 12 slices.Six slices
Are red and award a 10% discount, three slices are white and award a 20% discount, and
Two slices are blue and award a 40% discount.The remaining slice is gold and awards a
100% discount! The probability that two customers in a row get a 20% discount is

A)3/12
B)2/12
C).0625
D)9/12
E)10/12

Question 13

As an incentive to get new customers, the local branch of a bank launched "bouncing for bucks." During this week long event, any customer opening a new checking account
With the bank would have the opportunity to throw a bouncy rubber ball into a large box
Divided into squares.Each square was labeled with a dollar amount that would be
Deposited into his/her new checking account.The way the box was labeled is shown
Below.What is the probability that three customers in a row do not get $50?

A)0.125
B)0.001
C)0.729
D)0.970
E)0.300

Question 14

As accounts manager in your company, you classify 75% of your customers as "good credit" and the rest as "risky credit" depending on their credit rating.Customers in the
"risky" category allow their accounts to go overdue 50% of the time on average, whereas
Those in the "good" category allow their accounts to become overdue only 10% of the
Time.What percentage of overdue accounts are held by customers in the "risky credit"
Category?

A)20%
B)12.5%
C)93.75%
D)62.5%

Question 15

A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both.Which of the
Following statements about cell phones sold last month is true?

A)Having a camera and having a music player are mutually exclusive events.
B)The intersection of having a camera and having a music player is zero.
C)Having a camera and having a music player are independent events.
D)Having a camera and having a music player are disjoint events.
E)Having a camera and having a music player are not mutually exclusive events.

Question 16

As an incentive to get new customers, the local branch of a bank launched "bouncing for bucks." During this week long event, any customer opening a new checking account
With the bank would have the opportunity to throw a bouncy rubber ball into a large box
Divided into squares.Each square was labeled with a dollar amount that would be
Deposited into his/her new checking account.The way the box was labeled is shown
Below.What is the probability that a customer does not get $50?

A)0.90
B)0.99
C)0.50
D)0.95
E)0.80

Question 17

One explanation put forth for the dearth of women CEO's in the high tech industry is
that there are a lack of mentoring opportunities for women.A recent survey of CEO's in
that industry found that 80% were men.Moreover, 75% had been mentored while only
15% were women and had been mentored.
a.Construct the contingency table.
b.Are gender and mentoring independent? Explain.

Question 18

A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both.The probability
That a cell phone sold last month did not have either a camera or a music player is

A).22
B).70
C).92
D).30
E).08

Question 19

The option to buy extended warranties is commonplace with most electronics purchases.But does the type of purchase affect a consumer's willingness to pay extra for
An extended warranty? Data for 420 consumers who purchased digital cameras and
Laptop computers from a leading electronics retailer are summarized in the table.The
Probability that a consumer purchases a digital camera and an extended warranty is

A).07
B).42
C).58
D).17
E).83

Question 20

The option to buy extended warranties is commonplace with most electronics purchases.But does the type of purchase affect a consumer's willingness to pay extra for
An extended warranty? Data for 420 consumers who purchased digital cameras and
Laptop computers from a leading electronics retailer are summarized in the table.The
Probability that a consumer purchases an extended warranty given that he/she has
Purchased a digital camera is

A).07
B).42
C).58
D).17
E).83

Question 21

Suncast Cable offers high definition (HD) cable TV, Internet and phone services to its customers.For those service issues that can be resolved by calling its technical support
Center, Suncast's goal is to have the problem solved within 30 minutes.In order to
Determine how well it is achieving this goal, they monitored calls to its technical support
Center over the last three months.The data compiled is shown in the table below.What
Is the probability that a call to the technical support center involved an issue with Internet
Service?

A)0.56
B)0.41
C)0.74
D)0.26
E)0.35

Question 22

It has been reported that men are more likely than women to participate in online auctions.In a recent survey, 65% of respondents reported that they had participated in an
Online auction.In this same survey, 45% of respondents were men and 38% were men
Who had participated in online auctions.What is the probability that a respondent had
Participated in an online auction given that he is male?

A)0.38
B)0.84
C)0.62
D)0.45
E)0.55

Question 23

A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time.Further, 15% of all steroid-free
Individuals also test positive.10% of the rugby team members use steroids.Your friend
On the rugby team has just tested positive.The correct probability tree looks like

Question 24

As an incentive to get new customers, the local branch of a bank launched "bouncing for bucks." During this week long event, any customer opening a new checking account
With the bank would have the opportunity to throw a bouncy rubber ball into a large box
Divided into squares.Each square was labeled with a dollar amount that would be
Deposited into his/her new checking account.The way the box was labeled is shown
Below.Out of the next three customers that come into the bank and play the game, what
Is the probability that at least one gets $50?

A)0.001
B)0.271
C)0.729
D)0.300
E)0.125

Question 25

Suncast Cable offers high definition (HD) cable TV, Internet and phone services to its customers.For those service issues that can be resolved by calling its technical
Support center, Suncast's goal is to have the problem solved within 30 minutes.In order
To determine how well it is achieving this goal, they monitored calls to its technical
Support center over the last three months.The data compiled is shown in the table below.
What is the probability that a call to the technical support center involved an issue with
Internet service or was not resolved within 30 minutes?

A)0.91
B)0.55
C)0.35
D)0.76
E)0.14

Question 26

It has been reported that men are more likely than women to participate in online auctions.In a recent survey, 65% of respondents reported that they had participated in an
Online auction.In this same survey, 45% of respondents were men and 38% were men
Who had participated in online auctions.Which of the following is true?

A)Gender and participation in online auctions are independent.
B)Gender and participation in online auctions are disjoint.
C)The intersection of being male and participating in online auctions is zero.
D)Gender and participation in online auctions are not related.
E)Gender and participation in online auctions are dependent.

Question 27

A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time.Further, 15% of all steroid-free
Individuals also test positive.10% of the rugby team members use steroids.Your friend
On the rugby team has just tested positive.The probability that he uses steroids is

A)0.4130
B)0.8636
C)0.0950
D)0.2300

Question 28

It has been reported that men are more likely than women to participate in online auctions.In a recent survey, 65% of respondents reported that they had participated in an
Online auction.In this same survey, 45% of respondents were men and 38% were men
Who had participated in online auctions.What is the probability that a respondent
Selected at random is female and has never participated in an online auction?

A)0.62
B)0.72
C)0.38
D)0.28
E)0.07

Question 29

Suncast Cable offers high definition (HD) cable TV, Internet and phone services to its customers.For those service issues that can be resolved by calling its technical support
Center, Suncast's goal is to have the problem solved within 30 minutes.In order to
Determine how well it is achieving this goal, they monitored calls to its technical support
Center over the last three months.The data compiled is shown in the table below.If
Suncast wished to determine probabilities using these data, what type of probability
Would it be calculating?

A)Personal
B)Theoretical
C)Empirical
D)Model-based
E)Subjective