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Chapter 5: Randomness and Probability – Quiz A
Name_____________________________________
5.4.1 Find probabilities and/or determine independence.
1. 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?
5.4.1 Use and understand the concepts and definitions of probability.
2. 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.
5.4.1 Find probabilities and/or determine independence.
3. 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?
5-2 Chapter 5 Randomness and Probability
b. What is the probability that a smart phone buyer did not also own either a tablet/ laptop
or a music player?
c. Is a smart phone buyer owning a tablet/laptop in addition to a music player mutually
exclusive? Explain.
5.5.2 Find probabilities and/or determine independence.
4. 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?
5.5.2 Find probabilities and/or determine independence.
5. Does it appear that choice of instructional method (traditional or online) and division
(sales, quality and operations) are independent? Explain.
5.5.2 Find probabilities and/or determine independence.
6. 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.
Sales Quality Operations Total
Traditional 16 10 8 34
Online 35 23 44 102
Total 51 33 52 136
Quiz A 5-3
Chapter 5: Randomness and Probability – Quiz A – Key
5-4 Chapter 5 Randomness and Probability
Quiz A 5-5
5-6 Chapter 5 Randomness and Probability
Chapter 5: Randomness and Probability – Quiz B
Name_____________________________________
5.4.1 Find probabilities and/or determine independence.
1. 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.
10 30 10 30 10
20 10 50 10 20
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?
5.4.1 Use and understand the concepts and definitions of probability.
2. 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.
5.4.1 Find probabilities and/or determine independence.
3. 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.
Quiz B 5-7
5.5.2 Find probabilities and/or determine independence.
4. 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?
5.5.2 Find probabilities and/or determine independence.
5. 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.
5.5.2 Find probabilities and/or determine independence.
6. 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.
Purchased Warranty?
Yes No Total
Big Screen TV 30 42 72
Laptop Computer 145 203 348
Total 175 245 420
5-8 Chapter 5 Randomness and Probability
Chapter 5: Randomness and Probability – Quiz B – Key
Quiz B 5-9
5-10 Chapter 5 Randomness and Probability
Quiz C 5-11
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Chapter 5: Randomness and Probability – Quiz C – Multiple Choice
Name_____________________________________
5.4.1 Find probabilities and/or determine independence.
1. 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. 3/12
B. 2/12
C. .0625
D. 9/12
E. 10/12
5.1. Use and understand the concepts and definitions of probability.
2. 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. 3/12
B. 2/12
C. .0625
D. 9/12
E. 10/12
5-12 Chapter 5 Randomness and Probability
5.3.2 Find probabilities and/or determine independence.
3. 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
5.3.2 Find probabilities and/or determine independence.
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. 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
5.3.2 Find probabilities and/or determine independence.
5. 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
Quiz C 5-13
5.3.2 Find probabilities and/or determine independence.
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. 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.
5.5.2 Find probabilities and/or determine independence.
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
Purchased Warranty?
Yes No Total
Digital Camera 30 42 72
Laptop Computer 145 203 348
Total 175 245 420
5-14 Chapter 5 Randomness and Probability
5.5.2 Find probabilities and/or determine independence.
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 a digital camera and an extended warranty is
A. .07
B. .42
C. .58
D. .17
E. .83
5.5.2 Find probabilities and/or determine independence.
9. 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
Purchased Warranty?
Yes No Total
Digital Camera 30 42 72
Laptop Computer 145 203 348
Total 175 245 420
Purchased Warranty?
Yes No Total
Digital Camera 30 42 72
Laptop Computer 145 203 348
Total 175 245 420
Quiz C 5-15
5.5.2 Find probabilities and/or determine independence.
10. 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.
5.3.2 Find probabilities and/or determine independence.
11. 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%
Purchased Warranty?
Yes No Total
Big Screen TV 30 42 72
Laptop Computer 145 203 348
Total 175 245 420
5-16 Chapter 5 Randomness and Probability
Chapter 5: Randomness and Probability – Quiz C – Key
Quiz D 5-17
Chapter 5: Randomness and Probability – Quiz D – Multiple Choice
Name_____________________________________
5.4.1 Find probabilities and/or determine independence.
1. 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?
10 30 10 30 10
20 10 50 10 20
A. 0.10
B. 0.01
C. 0.50
D. 0.05
E. 0.20
5.4.1 Find probabilities and/or determine independence.
2. 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?
10 30 10 30 10
20 10 50 10 20
A. 0.90
B. 0.99
C. 0.50
D. 0.95
E. 0.80
5-18 Chapter 5 Randomness and Probability
5.4.1 Find probabilities and/or determine independence.
3. 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?
10 30 10 30 10
20 10 50 10 20
A. 0.125
B. 0.001
C. 0.729
D. 0.970
E. 0.300
5.4.1 Find probabilities and/or determine independence.
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. 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?
10 30 10 30 10
20 10 50 10 20
A. 0.001
B. 0.271
C. 0.729
D. 0.300
E. 0.125
5.4.1 Find probabilities and/or determine independence.
5. 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.
Quiz D 5-19
5.4.1 Find probabilities and/or determine independence.
6. 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
5.4.1 Find probabilities and/or determine independence.
7. 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
5.3.2 Use and understand the concepts and definitions of probability.
8. 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?
Problem Resolved? HD cable TV Internet Phone
Yes 123 350 77
No 115 122 63
A. Personal
B. Theoretical
C. Empirical
D. Model-based
E. Subjective
5-20 Chapter 5 Randomness and Probability
5.3.2 Use and understand the concepts and definitions of probability.
9. 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?
Problem Resolved? HD cable TV Internet Phone
Yes 123 350 77
No 115 122 63
A. 0.56
B. 0.41
C. 0.74
D. 0.26
E. 0.35
5.3.2 Use and understand the concepts and definitions of probability.
10. 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?
Problem Resolved? HD cable TV Internet Phone
Yes 123 350 77
No 115 122 63
A. 0.91
B. 0.55
C. 0.35
D. 0.76
E. 0.14
Quiz D 5-21
5.8.3 Construct and use probability trees.
11. 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
5.8.3 Construct and use probability trees.
12. 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
5-22 Chapter 5 Randomness and Probability
Chapter 5: Randomness and Probability – Quiz D – Key