Deck 5: Randomness and Probability

Question 1

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

Answer 1

.30

Question 2

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

Answer 2

.58

Question 3

As you enter the bank, you watch four persons in front of you all win $50. The local
branch manager tells you how lucky you are to be throwing the ball while it is on a hot
streak but the friend with you says that you're unlucky because the streak can't continue.
Comment on their statements.

Answer 3

Question 4

During a promotion, Christina's department store offers a mailing "scratch a winner - discount savings." After customers select the items they wish to purchase, they scratch
Their discount sticker from the mailing to determine the discount they will receive. The
Scratch 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 if the customer
Scratches that slice! 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 5

Suppose you visit Christina's department store 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 6

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 big screen TVs 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 big screen TV and an extended
warranty?
c. What is the probability that a consumer purchases an extended warranty given that
he/she has purchased a big screen TV?

Question 7

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 8

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 9

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

Question 10

During a promotion, Christina's department store offers a mailing "scratch a winner - discount savings." After customers select the items they wish to purchase, they scratch Their discount sticker from the mailing to determine the discount they will receive. The Scratch 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 if the customer Scratches that slice! The probability that a customer gets at least a 40% discount is

A)
B)
C)
D)
E)

Question 11

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 12

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 13

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
Internet shoppers have participated in online auctions. Moreover, 25% of online
shoppers were men and had participated in online auctions.
A. Construct the contingency table.
b. Are gender and participation in online auctions independent? Explain.

Question 14

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.

Question 15

During a promotion, Christina's department store offers a mailing "scratch a winner - discount savings." After customers select the items they wish to purchase, they scratch Their discount sticker from the mailing to determine the discount they will receive. The Scratch 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 if the customer Scratches that slice! The probability that a customer gets a 10% or 20% discount is

A)
B)
C)
D)
E)

Question 16

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?

Question 17

A recent survey of local cell phone retailers showed that of all smart phones sold last
month, 64% of buyers also owned a tablet of laptop, 28% also owned an iPod type music
player and 22% owned both.
A. What is the probability that a smart phone buyer also owned a tablet/ laptop or a music
player?
5-1

Question 18

During a promotion, Christina's department store offers a mailing "scratch a winner -
discount savings." After customers select the items they wish to purchase, they scratch
their discount sticker from the mailing to determine the discount they will receive. The
scratch 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 if the customer
scratches that slice!
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 19

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 20

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 21

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 22

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 23

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 24

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 big screen TVs 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 (big screen TV
Or laptop computer) purchased are independent.
B) The decision to purchase an extended warranty and type of electronics (big screen TV
Or laptop computer) purchased are mutually exclusive.
C) The decision to purchase an extended warranty and type of electronics (big screen TV
Or laptop computer) purchased are disjoint events.
D) The decision to purchase an extended warranty and type of electronics (big screen TV
Or laptop computer) purchased are not independent.
E) The decision to purchase an extended warranty and type of electronics (big screen TV
Or laptop computer) purchased are related.

Question 25

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 26

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 27

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 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. 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 29

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 30

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 31

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

Question 32

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 33

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 34

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