Deck 7: Randomness and Probability

Question 1

Use conditional probability.
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

Answer 1

B

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

Determine if two events are disjoint or independent.
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 camera or laptop computer) purchased are independent.
B) The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are mutually exclusive.
C) The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are disjoint events.
D) The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are not independent.
E) The decision to purchase an extended warranty and type of electronics (digital

Answer 3

A

Question 4

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.
a. What is the probability that a customer gets $20 or more?
b. What is the probability that a customer gets less than $20?
c. What is the probability that a customer gets $20 or $30?
d. What is the probability that two customers in a row get $50?

Question 5

Does it appear that the decision to purchase an extended warranty and type of
electronics (digital camera or laptop computer) purchased are independent? Explain.

Question 6

Use the appropriate probability model (Poisson).
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 7

Use the basic rules and definitions of probability.

-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? $$\begin{array} { | l | l | l | l | l | } \hline 10 & 30 & 10 & 30 & 10 \\\hline 20 & 10 & 50 & 10 & 20 \\\hline\end{array}$$

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

Question 8

Use the addition rule or multiplication rule for probability.
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 9

Use the appropriate probability model (Poisson).
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.

Question 10

A major airline keeps track of data on how their passengers redeem frequent flyer
miles. They found that in the last year 58% of passengers redeemed them to purchase
tickets for domestic travel, 44% redeemed them to purchase tickets for international
travel, and that 16% redeemed them to purchase tickets for both domestic and
international travel.
a. What is the probability that in the last year a passenger redeemed frequent flyer miles
to purchase a ticket for domestic or international travel?
b. What is the probability that in the last year a passenger did not redeem frequent flyer
miles to purchase a ticket for domestic or international travel?
c. Is redeeming frequent flyer miles to purchase a ticket for domestic and international
travel mutually exclusive? Explain) general addition rule

Question 11

Use a contingency table.
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 12

Use the basic rules and definitions of probability.

-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? $$\begin{array} { | l | l | l | l | l | } \hline 10 & 30 & 10 & 30 & 10 \\\hline 20 & 10 & 50 & 10 & 20 \\\hline\end{array}$$

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

Question 13

Use the addition rule or multiplication rule for probability.
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 14

Use a contingency table.
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 15

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.
a. What is the probability that a consumer purchases an extended warranty?
b. What is the probability that a consumer purchases a digital camera and an extended
warranty?
c. What is the probability that a consumer purchases an extended warranty given that
he / she has purchased a digital camera?

Question 16

Determine if two events are disjoint or independent.
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 17

Use the basic rules and definitions of probability.
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 18

Use the addition rule or multiplication rule for probability.
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 19

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

Question 20

It has been reported that men are more likely than women to participate in online
auctions. A recent study found that 52% of Internet shoppers are women and that 35% of

Question 21

Use the addition rule or the multiplication rule for probability.

-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? $$\begin{array} { | l | l | l | l | l | } \hline 10 & 30 & 10 & 30 & 10 \\\hline 20 & 10 & 50 & 10 & 20 \\\hline\end{array}$$

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

Question 22

Use a contingency table.

-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? $$\begin{array} { | l | l | l | l | } \hline \text { Problem Resolved? } & \text { HD cable TV } & \text { Internet } & \text { Phone } \\\hline \text { Yes } & 123 & 350 & 77 \\\hline \text { No } & 115 & 122 & 63 \\\hline\end{array}$$

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

Question 23

Use the basic rules and definitions of probability. .

-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? $$\begin{array} { | l | l | l | l | } \hline \text { Problem Resolved? } & \text { HD cable TV } & \text { Internet } & \text { Phone } \\\hline \text { Yes } & 123 & 350 & 77 \\\hline \text { No } & 115 & 122 & 63 \\\hline\end{array}$$

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

Question 24

Use the addition rule or the multiplication rule for probability.
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 25

Use conditional probability.
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 26

Use a contingency table.

-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? $$\begin{array} { | l | l | l | l | } \hline \text { Problem Resolved? } & \text { HD cable TV } & \text { Internet } & \text { Phone } \\\hline \text { Yes } & 123 & 350 & 77 \\\hline \text { No } & 115 & 122 & 63 \\\hline\end{array}$$

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

Question 27

Use the addition rule or the multiplication rule for probability.

-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? $$\begin{array} { | l | l | l | l | l | } \hline 10 & 30 & 10 & 30 & 10 \\\hline 20 & 10 & 50 & 10 & 20 \\\hline\end{array}$$

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

Question 28

Determine if two events are disjoint or independent.
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.