Preliminary Edition of Statistics Learning from Data 1st Edition by Roxy Peck - Test Bank

Preliminary Edition of Statistics Learning from Data 1st Edition by Roxy Peck – Test Bank

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Sample Questions Are Posted Below

Chapter 5, Concept Quiz
Page 1 of 1
Chapter 5: Probability
Concept Quiz
Name _________________________
The following questions are in a True / False format. The answers to these questions will
frequently depend on remembering facts, understanding of the concepts, and knowing the
statistical vocabulary. Before answering these questions, be sure to read them carefully!
T F 1. A chance experiment is the process of making an observation when there
is uncertainty concerning which of two or more possible outcomes will
result.
T F 2. The collection of possible outcomes of a chance experiment is called the
sample space of the experiment.
T F 3. An event, by definition, consists of exactly one outcome.
T F 4. The event “A or B” consists of all of the outcomes that are in both of the
events.
T F 5. Two events are said to be mutually exclusive if they can’t occur at the
same time.
T F 6. The probability of an event E can always be computed using the formula,  number of outcomes favorable to E
number of outcomes in the sample space
P E 
T F 7. If two events, A and B, are mutually exclusive, then     A and BP P A P B 
.
T F 8. It is possible for two mutually exclusive events to be independent.
T F 9. The Multiplication Rule states that for any two events,     E F |P P E F P F  
.
T F 10. The Addition Rule states that for any two events,       E FP P E P F P E F    
.
T F 11. Two events, E and F, are independent if   | |P E F P F E .
Chapter 5, Concept Quiz Answer Key
1. T
2. T
3. F
4. F
5. T
6. F
7. F
8. F
9. T
10. T
11. F
Chapter 5, Concept Quiz Answer Key Page 1 of 1
Chapter 5: Probability
Section 5.1-5.2
Name ___________________________
1. In a few sentences, define the following terms:
a) Event
b) Chance experiment
2. As discussed in the text, the classical approach to probability has a serious limitation
that is overcome by the relative frequency approach. What is the limitation?
Chapter 5, Quiz 1, Form A
Page 1 of 2
3. Arctic Plains Planes Airlines flies in Alaska between Prudhoe Bay and Deadhorse.
APPA has only one small plane, and passengers have a choice between sitting in one
of two first class seats, one of four second class seats, and the co-pilot’s seat. (APPA
airlines also has only one pilot.) If the seats are assigned at random, what is the
probability that a passenger will be assigned a second class seat?
4. Anna is a child who has just turned 2 years old, and she has entered the “terrible
two’s” stage of human development. She has discovered that if she drops her spoon
on the floor, her parents will pick it up and return it to her. By actual count halfway
through her second year, there have been 900 spoon retrievals. Out of these, 315
times the spoon has landed in the “up” position on the floor. Based on this long series
of observations, what is the estimated probability that her 901st spoon drop will land
in the “up” position?
Chapter 5, Quiz 1, Form A
Page 2 of 2
Chapter 5, Quiz 1, Form A Answer Key
1.
a) An event is any collection of outcomes from the sample space of a chance
experiment.
b) A chance experiment is the process of making an observation when there is
uncertainty about which of two or more possible outcomes will result.
2. The classical approach is only appropriate when the outcomes of the experiment are
equally likely outcomes.
3. 4 0.5714
7 =
4. 315 0.35
900 =
Chapter 5, Quiz 1, Form A Answer Key Page 1 of 1
Chapter 5: Probability
Section 5.1-5.2
Name ___________________________
1. In a few sentences, define the following terms:
a) Simple event
b) Sample space
2. As discussed in the text, the classical approach to probability has a serious limitation
that is overcome by the relative frequency approach. What is the limitation?
Chapter 5, Quiz 1, Form B
Page 1 of 2
3. Anna is an engineer on vacation with a problem. S he is driving in Halifax, Nova
Scotia, and is stopped at an intersection. She could drive to Wolfville, Truro, or
Antigonish. She does not have a preference, and decides make her decision by
flipping two coins. If two heads appear, she will go to Wolfville, if two tails she will
go to Antigonish. What is the probability she will go to Truro?
4. Moosy-Woosy Airlines flies between Moose Bay and Moose Lake Alaska. In many
airports, nearby flocking birds can present problems during takeoffs and landings. In
Alaska, the problem is moose. If a moose is spotted in the immediate area of the
runway, a takeoff or landing must be delayed until the moose is very carefully
escorted away. Of the 1200 takeoffs and landings in a recent 12-month period at
Moose Bay, there were 75 moose delays. Based on this long series of observations,
what is the estimated probability that the 1201st takeoff or landing attempt will be
delayed by a moose sighting?
Chapter 5, Quiz 1, Form B
Page 2 of 2
Chapter 5, Quiz 1, Form B Answer Key
1.
a) A simple event is an event consisting of exactly one outcome.
b) The sample space for an experiment is the collection of all possible outcomes.
2. The classical approach is only appropriate when the outcomes of the experiment are
equally likely outcomes.
3. 2 0.5
4 =
4. 75 0.0625
1200 =
Chapter 5, Quiz 1, Form B Answer Key Page 1 of 1
Chapter 5: Probability
Section 5.3
Name ___________________________
1. In a few sentences, describe the difference between the intersection of two events and
the union of two events
2. Experimental studies in psychology use blinding to prevent researchers from biasing
their measurements of subjects in the study. In a study of a psychotherapeutic
intervention, a blinded clinician was asked to guess what treatment each subject
received. Data from that experiment are shown below. Suppose a subject is to be
chosen at random from the subjects in this study.
Frequencies for Blinding Experiment
a) What is the probability that the clinician made a correct guess for the selected
subject?
b) What is the probability the selected subject will have had therapy?
Correct
Guess
Incorrect
Guess
Therapy 30 6
Placebo 26 11
Chapter 5, Quiz 2, Form A
Page 1 of 4
c) What is the probability the selected subject will be one for whom the clinician
correctly guessed had therapy?
d) What is the probability the selected subject will be one for whom the clinician
guessed correctly or who received the placebo treatment?
e) What is the probability the selected subject will be one for whom the clinician
guessed correctly and who received the placebo treatment?
f) In a few sentences, explain why the probabilities calculated in parts (d) and (e)
differ.
Chapter 5, Quiz 2, Form A
Page 2 of 4
3. For a special report in the Cedar Rapids, IA, Gazette, reporters used a radar gun to
check the speeds of 1,239 drivers in two counties. They were shocked (!) to discover
that some drivers were driving at a speed greater than the posted limits. They
reported the following information in their story:
Speeding data for cities in Linn and Johnson Counties
Suppose that one of these drivers is selected at random. Define the following events:
F = the event that a randomly selected driver was in the fast lane (speed limit
above 25 mph)
S = the event that a randomly selected driver is speeding.
a) The table below shows the possible combinations of F and S. For each
combination, calculate the probability that the combination would be observed for
a randomly selected driver. Enter these probabilities into the corresponding cell in
the table.
Speed Limit
> 25mph
(Fast lane)
Speed Limit
25mph or less
(Slow lane)
Driver speeding
Driver not speeding
City City
Speed
Limit
Drivers
Observed
Over
Limit
%Over
Limit
Cedar Rapids 25 241 233 96.7
Iowa City 35 292 124 42.5
Iowa City 20 203 203 100.0
Marion 30 329 268 81.5
Coralville 25 174 161 92.5
Chapter 5, Quiz 2, Form A
Page 3 of 4
b) Using the information in your table from part (a), calculate  P F S .
c) Using the information in your table from part (a), calculate  C
P S
Chapter 5, Quiz 2, Form A
Page 4 of 4
Chapter 5, Quiz 2, Form A Answer Key
1. The intersection of two events consists of outcomes common to both events; the
union of two events consists of outcomes that are in either or both events.
2.
a) 56 0.7671
73 =
b) 36 0.4932
73 =
c) 30 0.4110
73 =
d) 67 0.9178
73 =
e) 26 0.3562
73 =
f) The probabilities differ because (d) asks about a union of two events and (e) asks
about the intersection of the same two events.
3.
a)
( ) 392Driver speeding in fast lane 0.3164
1239
P = =
( ) 597Driver speeding in slow lane 0.4818
1239
P = =
( ) 229Driver not speeding in fast lane 0.1848
1239
P = =
( ) 21Driver not speeding in slow lane 0.0169
1239
P = =
Chapter 5, Quiz 2, Form A Answer Key Page 1 of 2
b) ( ) 0.3164 0.1848 0.4818 0.9830P F S∪ = + + =
c) ( ) 0.1848 0.0169 0.2017C
P S = + =
Chapter 5, Quiz 2, Form A Answer Key Page 2 of 2
Chapter 5: Probability
Section 5.3
Name ___________________________
1. In a few sentences, explain the difference between an event, A, and the complement of
event A.
2. Experimental studies use blinding to prevent researchers from biasing their
measurements of the subjects. In a study of a drug intervention, a clinician who was
“blinded” was asked to guess what treatment each subject received. Data from that
experiment are shown below. Suppose a person is to be chosen at random from the
subjects in this study.
Frequencies for Blinding Experiment
a) What is the probability that the clinician made a correct guess for the selected
subject?
b) What is the probability the selected subject received the drug treatment?
Correct Guess Incorrect Guess
Drug 23 12
Standard treatment 32 6
Chapter 5, Quiz 2, Form B
Page 1 of 4
c) What is the probability the selected subject will be one for whom the clinician
correctly guessed as having received drug treatment?
d) What is the probability the selected subject will be one for whom the clinician
guessed correctly or who received the standard treatment?
e) What is the probability the selected subject will be one for whom the clinician
guessed correctly and who received the standard treatment?
f) In a few sentences, explain why the probabilities calculated in parts (d) and (e)
differ.
Chapter 5, Quiz 2, Form B
Page 2 of 4
3. For a special report in the Cedar Rapids, IA, Gazette, reporters used a radar gun to
check the speeds of 1,239 drivers in two counties. They were shocked (!) to discover
that some drivers were driving at a speed greater than the posted limits. They
reported the following information in their story:
Some Speeding data for cities in Linn and Johnson Counties
Suppose we randomly select one of these drivers for interview by our reporter.
Consider the following events:
IC = the event that a randomly selected driver is driving in Iowa City.
S = the event that a randomly selected driver is speeding.
a) The table below shows the possible combinations of IC and S. For each
combination, calculate the probability that the combination would be observed for
a randomly selected driver. Enter these probabilities into the corresponding cell in
the table.
Driving in
Iowa City
Driving other
than in Iowa City
Driver speeding
Driver not speeding
City City
Speed
Limit
Drivers
Observed
Over
Limit
%Over
Limit
Cedar Rapids 25 241 233 96.7
Iowa City 35 292 124 42.5
Iowa City 20 203 203 100.0
Marion 30 329 268 81.5
Coralville 25 174 161 92.5
Chapter 5, Quiz 2, Form B
Page 3 of 4
b) Using the information in your table from part (a), calculate  P IC S .
c) Using the information in your table from part (a), calculate  C
P S
Chapter 5, Quiz 2, Form B
Page 4 of 4
Chapter 5, Quiz 2, Form B Answer Key
1. The complement of event A consists of those outcomes not in event A.
2.
a) 55 0.7534
73 =
b) 35 0.4795
73 =
c) 23 0.3151
73 =
d) 61 0.8356
73 =
e) 32 0.4384
73 =
f) The probabilities differ because (d) asks about a union of two events and (e) asks
about the intersection of the same two events.
3.
a)
( ) 327Driver speeding and in Iowa City 0.2640
1239
P = =
( ) 662Driver speeding and not in Iowa City 0.5343
1239
P = =
( ) 168Driver not speeding and in Iowa City 0.1356
1239
P = =
( ) 82Driver not speeding and not in Iowa City 0.0662
1239
P = =
Chapter 5, Quiz 2, Form B Answer Key Page 1 of 2
b) ( ) 0.2640 0.1356 0.5343 0.9339P IC S∪ = + + =
c) ( ) 0.1356 0.0662 0.2018C
P S = + =
Chapter 5, Quiz 2, Form B Answer Key Page 2 of 2
Chapter 5: Probability
Section 5.4
Name ___________________________
Understanding attitudes of humans towards wildlife is an important step in learning how
to work with people on wildlife issues. Coyotes have expanded their range throughout the
continental United States, even in the Washington, DC area. The data below are from a
survey of George Mason University undergraduate students.
“How much do you like coyotes?”
Gender Dislike
Very
much
Dislike
Somewhat Neutral
Like
Somewhat
Like
Very
much
Total
Male 8 12 186 49 25 280
Female 27 45 330 52 26 480
Total 35 57 516 101 51 760
Suppose a newspaper decides to select one of these students at random for an interview.
1. What is the probability that the selected student dislikes coyotes somewhat?
2. What is the probability that the selected student is male?
3. What is the probability that the selected student is male, given that he likes coyotes
very much?
4. What is the probability that the selected student dislikes coyotes very much, given
that she is a female?
Chapter 5, Quiz 3, Form A
Page 1 of 1
Chapter 5, Quiz 3, Form A Answer Key
1. 57 0.0750
760 =
2. 280 0.3684
760 =
3. 25 0.4902
51 =
4. 27 0.0563
480 =
Chapter 5, Quiz 3, Form A Answer Key Page 1 of 1
Chapter 5: Probability
Section 5.4
Name ___________________________
In the Athenian democracy of Classical Greece, some officials (Strategoi) were elected,
and some (Tamiai) were selected at random. While selection at random would tend to
result in representative samples of the population (of course!), it is possible that elections
might give a different pattern. The table below shows the numbers of officials known to
be from the metropolitan area of Athens and the rest of Attica, the region that
encompasses Athens.
Strategoi and Tamiai from Athens and the rest of Attica
Officials Metro Athens
Attica,
Outside
Metro Athens
Total
Strategoi 41 70 111
Tamiai 67 183 250
Total 108 253 361
Suppose the ancient Athenian newspaper, the Papyrus Times Gazette, had decided to
select one of these officials at random for an interview.
1. What is the probability that the selected official is from the Strategoi?
2. What is the probability that the selected official is from Metro Athens?
3. What is the probability that the selected official is from Metro Athens, given that this
person is a Tamaiai?
4. What is the probability that the selected official is a Strategoi, given that this person
lives outside Metro Athens?
Chapter 5, Quiz 3, Form B
Page 1 of 1
Chapter 5, Quiz 3, Form B Answer Key
1. 111 0.3075
361 =
2. 108 0.2992
361 =
3. 67 0.2680
250 =
4. 70 0.2767
253 =
Chapter 5, Quiz 3, Form B Answer Key Page 1 of 1
Chapter 5: Probability
Section 5.7
Name ___________________________
1. At the State Fair the rifle range offers 4 different hats as prizes for perfect scores, one
hat for each of the State University campuses. The hats are in boxes. When someone
gets a perfect score, a box is chosen at random and given to that person. No
substitutions are allowed. A local football fan (an ace shot who never misses) wishes
to collect all 4 hat designs. There are a very large number of hats on hand and there
are equal numbers of each hat design, so each design has a probability of 0.25 of
being the prize at any given time. You are to design a simulation that could be used
to estimate the average number of perfect scores needed to get a complete the set of
hats.
a) To simulate this strategy, assign digits to the hat designs that will result in the
probability of selection of each design being 0.25.
Hat 1 Digits: Hat 2 Digits:
Hat 3 Digits: Hat 4 Digits:
b) Describe how you would use a random digit table to conduct one run of your
simulation. Hint: one run continues until a complete set of the 4 hats is acquired.
Chapter 5, Quiz 4, Form A
Page 1 of 3
c) Using the following lines from a random number table, demonstrate how your
assignment of digits in part (a) would be used to carry out one run of the
simulation. (You may mark above the digits to help explain your procedure.)
61790 55300 05756 72765 96409 12531 35013 82853 73676 57890 99400
37754 42648 82425 36290 45467 71709 77558 00095 32863 29485 82226
Chapter 5, Quiz 4, Form A
Page 2 of 3
d) Suppose that the rifle range manager decides to order different numbers of hats,
consistent with the popularity of each campus’s football team. Hat 1 will be put
in 50% of the boxes, Hats 2 and 3 will each be put in 20% of the boxes, and Hat 4
will be put in 10% of the boxes. Assign digits to the hats in a way that will be
consistent with these probabilities.
Hat 1 Digits: Hat 2 Digits:
Hat 3 Digits: Hat 4 Digits:
e) Perform three runs, and use your results to estimate the probability that it would
take more than 10 boxes to complete the set of 4 hats. (You may mark above the
digits to help explain your procedure.)
19223 95734 05756 28713 96409 12531 42544 82853 73676 47150 99400
37754 42648 82425 36290 45467 71709 77558 00095 32863 29485 82226
68417 35013 15529 72765 85089 57067 50211 47487 82739 57890 20807
81676 55300 94383 14893 60940 72024 17868 24943 61790 90656 87964
Chapter 5, Quiz 4, Form A
Page 3 of 3
Chapter 5, Quiz 4, Form A Answer Key
1. Answers will vary!
a) The student could conceivably assign single digits to represent hats and ignore the
other digits, such as:
1 = hat 1, 2 = hat 2, etc.
A more efficient use of the table might use two digits for hats, such as:
1 or 2 = hat 1, 3 or 4 = hat 2; etc.
b) The student should mention the following:
1. Where to start on the table and what direction to proceed
2. Numbers not assigned to hats in part (a) should be ignored
3. A stopping rule, e.g. stop when 4 different hats are acquired.
c) Student output should match the procedure in part (b)
d) Assign digits to represent hats, such as:
0 – 4 = hat 1; 5 – 6 = hat 2; 7 – 8 = hat 3; 9 = hat 4
e) The 5 runs should be consistent with the assignments in part (d); in addition, the
estimated proportion should be consistent with the 5 runs.
Chapter 5, Quiz 4, Form A Answer Key Page 1 of 1
Chapter 5: Probability
Section 5.7
Name ___________________________
1. A man has five ties and each day chooses a tie at random to wear to work. He is
colorblind and is wife frequently complains that he wears the same tie two days in a
row. Your task is to design and conduct a simulation that could be used to estimate
the probability that he wears the same tie two or more days in a row in a 5-day work
week.
a) To simulate the strategy of selecting a tie at random, assign digits to the ties that
will result in the probability of selection of each tie being equal.
Tie 1 Digits: Tie 2 Digits:
Tie 3 Digits: Tie 4 Digits:
Tie 5 Digits:
b) Describe how you would use a random digit table to conduct one run of your
simulation. Hint: one run consists of selecting ties on the 5 days in the work week.
Chapter 5, Quiz 4, Form B
Page 1 of 4
c) Using the following lines from a random number table, conduct 2 runs and estimate
the probability that he wears the same tie two or more days in a row in a 5 day work
week. (You may mark above the digits to help explain your procedure.)
37754 42648 82425 36290 45467 71709 77558 00095 32863 29485 82226
68417 35013 15529 72765 85089 57067 50211 47487 82739 57890 20807
Chapter 5, Quiz 4, Form B
Page 2 of 4
2. Forty-five percent of donors have type O blood. The blood bank needs 4 donors with
type O blood to restock their reserves. The director has the option of waiting to get 4
type O donors during the day, or ordering type O blood from a neighboring blood
bank. Your task is to design and conduct a simulation to estimate the probability it
takes 12 or more donors to get 4 with type O blood.
a) To simulate the arrival of blood donors from this population, assign digits to the
blood types that will result in a probability of success (Type O donor) of 0.45.
Type O Digits: Other than Type O Digits:
b) Describe how you would use a random digit table to conduct one run of your
simulation, where one run consists of observing the blood type of donors until 4
type O donors have visited the blood bank.
Chapter 5, Quiz 4, Form B
Page 3 of 4
c) Using the following lines from a random digit table, perform three runs of your
simulation. Based on your results, what is your estimate of the probability of getting
4 Type O donors before 12 donors arrive at the blood bank? (You may mark above
the digits to help explain your procedure.)
68417 35013 15529 72765 85089 57067 50211 47487 82739 57890 20807
81676 55300 94383 14893 60940 72024 17868 24943 61790 90656 87964
73311 12190 06628 71683 12285 39814 29103 81733 73035 57446 99209
Chapter 5, Quiz 4, Form B
Page 4 of 4
Chapter 5, Quiz 4, Form B Answer Key
1. Answers will vary!
a) The student could conceivably assign single digits to represent ties and ignore the
other digits, such as:
1 = tie 1, 2 = tie 2, etc.
A more efficient use of the table might use two digits for ties, such as:
1 or 2 = tie 1; 3 or 4 = tie 2; etc.
b) The student should mention the following:
1. Where to start on the table and what direction to proceed
2. Numbers (if any)_not assigned to ties in part (a) should be ignored
3. A stopping rule, e.g. stop after 5 tie selections.
c) Student output should match the procedure in part (b)
2.
a) Assign double digits to represent Type O blood, such as:
01 to 45 = Type O; 00 and 46 – 99 = Other
b) The student should mention the following:
1. Where to start on the table and what direction to proceed
2. A stopping rule, e.g. stop after 4 Type O donors are acquired
3. A stopping rule, e.g. stop after 4 Type O donors are acquired.
c) Student output should match the procedure in part (b)
Chapter 5, Quiz 4, Form B Answer Key Page 1 of 1
Chapter 5: Probability
Name _______________________________
1. A small ferryboat transports vehicles from one island to another. Consider the chance
experiment where the type of vehicle — passenger (P) or recreational (R) vehicle — is
recorded for each of the next two vehicles that arrive at the dock.
a) List all the outcomes in the sample space.
b) Using the sample space in part (a), list the outcomes in each of the following events.
A = the event that both vehicles are passenger cars
B = the event that both vehicles are of the same type
C = the event that there is at least one passenger car
A:
B:
C:
Chapter 5 Test, Form A
Page 1 of 7
2. In a survey of airline travelers, passengers traveling alone in the coach section were
asked if they are bothered by a seatmate of the opposite gender using a shared
armrest.
The table below contains the data gathered in this study.
Bothered Not bothered
Females 19 26
Males 38 18
Suppose one of these passengers is to be randomly selected for a follow-up interview.
Use the information in the table to answer the questions below. In showing your
work, define and use appropriate notation.
a) What is the probability that the selected passenger is female?
b) What is the probability that the selected passenger is female or is bothered?
c) What is the probability that the selected passenger is male and is not bothered?
Chapter 5 Test, Form A
Page 2 of 7
3. In the survey of travelers described in problem 2, passengers were also classified by
age:
Suppose one of these passengers is to be randomly selected. Calculate the probability
that:
a) The selected passenger is under 40, given that the passenger is female.
b) The selected passenger is bothered, given that the passenger is over 40.
c) The selected passenger is male and over 40.
Bothered Not bothered Totals
Females under 40 14 10 24
Males under 40 23 2 25
Females over 40 5 16 21
Males over 40 15 16 31
Totals 57 44 101
Chapter 5 Test, Form A
Page 3 of 7
4. Students in two classes of upper-level mathematics were classified according to class
standing and gender, resulting in the following table.
Distribution of students: Advanced math
One of these students will be selected at random. Define events A,
B, and C as follows:
A = the event that the selected student is a female
B = the event that the selected student is a male
C = the event that the selected student is a senior.
For each pair of events in the following table, indicate whether the two events are
disjoint and/or independent by putting a Y or N in each of the cells.
Y = Yes, N = No
Disjoint Independent
A, B
B, C
A, C
Jr Sr
Males 45 30
Females 30 20
Chapter 5 Test, Form A
Page 4 of 7
5. Suppose 70% of orders on a particular website are shipped to the person who is
making the order and the remaining 30% are shipped to people other than the person
placing the order. Gift wrapping is requested for 60% of the orders being shipped to
other people, but for only 10% of orders shipped to the person making the order.
a) What is the probability that a randomly selected order will be gift wrapped and
sent to a person other than the person making the order?
b) What is the probability that a randomly selected order will be gift wrapped?
c) Is gift-wrapping independent of the destination of the gift? Provide a statistical
justification for your response.
Chapter 5 Test, Form A
Page 5 of 7
6. Black bears (Ursus americanus) have a tendency to wander looking for food, and
they have a high level of curiosity. These characteristics will sometimes get them
into trouble when they travel through national parks. When they become “nuisances,”
the Park Service transplants them to other areas if possible. Data on the gender of
transplanted bears and the outcome of the transplant for bears transplanted in Glacier
National Park over a 10-year period are given in the table below.
a) If a bear is randomly selected from the 153 bears in the sample, what is the
probability it is male and became a nuisance in another area after relocation?
b) If a bear is randomly selected from the 153 bears in the sample, what is the
probability that it is female or was successfully transplanted?
c) If a bear is randomly selected from the bears in the sample, what is the probability
that it returned to the capture area, given that it is a female?
Male Female Totals
Successful 32 17 49
Returned to capture area 34 45 79
Nuisance in another area 14 4 18
Killed outside of park 3 4 7
Totals 83 70 153
Chapter 5 Test, Form A
Page 6 of 7
d) After combining the above data with other National Parks, officials estimated that
only about 22% of black bears in all parks become enough of a nuisance to be
transplanted. They further estimate that 84% of nuisance bears are male, and fifty
percent of non-nuisance bears are females. If a randomly selected bear were
observed to be a male, what is the probability it would be enough of a nuisance to
be transplanted?
7. At Thomas Jefferson High School, students are heavily involved in extra-curricular
activities. Suppose that a student is to be selected at random from the students at this
school. Let the events A, M, and S be defined as follows, with the probabilities
listed:
A = a randomly selected student is active in the performing arts: P(A) = 0.20
M = a randomly selected student is active music: P(M) = 0.32
S = a randomly selected student is active in sports: P(S) = 0.35
Also
( ) 0.18; ( ) 0.07; ( | ) 0.30P A M P A S P M S    
Calculate each of the following (show your work):
a) ( | )P A M
b) ( )P A M
c) ( )P M S
Chapter 5 Test, Form A
Page 7 of 7
Chapter 5, Test Form A Answer Key
1. { }, , ,PP RR PR RP
2. A: { }PP B: { },PP RR C: { }, ,PR RP PP
a) 45 0.4455
101 =
b) 83 0.8218
101 =
c) 18 0.1782
101 =
3.
a) 24 0.5333
45 =
b) 20 0.3846
52 =
c) 31 0.3069
101 =
4.
Disjoint Independent
A, B Y N
B, C N Y
A, C N Y
Chapter 5, Test Form A Answer Key Page 1 of 2
5.
a) ( )( )0.3 0.6 0.18=
b) ( )( ) ( )( )0.7 0.1 0.3 0.6 0.25+ =
c) No – The probability of gift wrapping is different when shipping to the person
making the order and when shipping to a person other than the one making the
order.
6.
a) 14 0.0915
153 =
b) 102 0.6667
153 =
c) 45 0.6429
70 =
d) ( )( )
( )( ) ( )( )
0.22 0.84 0.3215
0.22 0.84 0.78 0.50 =
+
7.
a) ( ) ( )
( )
0.18
| 0.5625
0.32
P A M
P A M P M
∩
= = =
b) ( ) ( ) ( ) ( ) 0.20 0.32 0.18 0.34P A M P A P M P A M∪ = + − ∩ = + − =
c) ( ) ( ) ( ) ( )( )| 0.35 0.30 0.105P M S P S P M S∩ = = =
Chapter 5, Test Form A Answer Key Page 2 of 2
Chapter 5: Probability
Name _______________________________
1. At Beth & Mary’s Ice Cream Emporium customers always choose one topping to
sprinkle on their ice cream. The toppings are classified as either candy (C) or fruit
(F) toppings. Consider the chance experiment where the choice of toppings — (C) or
(F) — is recorded for each of the next two customers who order ice cream.
a) List all the outcomes in the sample space.
b) Using your sample space in part (a), list the outcomes in each of the following
events.
A = the event that both customers pick a candy topping
B = the event that both customers pick the same type of topping
C = the event that at least one customer picks a candy topping
A:
B:
C:
Chapter 5 Test, Form B
Page 1 of 8
2. First graders at an elementary school were classified according to whether they were
the first born child in the family or not, and also whether both parents worked outside
the home. This resulted in the accompanying table.
First Born Older Siblings
Both work outside home
17 40
At least one parent does not
work outside home 8 25
Suppose that one of these students is selected at random. Define events A, B, and C as
follows:
A = the event that the selected student is a first born
B = the event that the selected student’s parents both work outside the home
C = the event that the selected student has older siblings
For each pair of events in the following table, indicate whether the two events are disjoint
and/or independent by putting a Y or N in the appropriate cells.
Y = Yes, N = No
Disjoint Independent
A, B
B, C
A, C
Chapter 5 Test, Form B
Page 2 of 8
3. The adult diamond python (Morelia spilota), an Australian snake, is about 3 feet long.
In a multi-year study of the habitats of these creatures, 997 were captured. The
following table displays the capture locations of these snakes by season of the year
and habitat. The “other” category includes trees, logs, rocks, open ground, and under
filtering cover such as shrubs.
Diamond Python Habitat
Suppose one of these diamond pythons is selected at random.
Calculate the probability that:
a) The selected diamond python was captured in a building, given that it was
captured in the spring.
b) The selected diamond python was captured somewhere other than in a building
given that it was captured in the spring or summer.
c) The selected diamond python was captured in a building in the summer.
Buildings Other Total
Spring 10 343 353
Summer 36 273 309
Autumn 17 157 174
Winter 0 161 161
Total 63 934 997
Chapter 5 Test, Form B
Page 3 of 8
4. In November 2002, Janet Napolitano, a Democrat, was elected Governor of Arizona,
defeating Republican Matt Salmon and Independent Richard Mahoney. This was a
somewhat surprising outcome, since there are more registered Republicans than
Democrats in the state. The table below presents data from a survey of a sample of
voters in the election. The candidate supported by the voter is represented by the
rows, and the party affiliation of the voter is represented by the columns. Suppose
that one of these voters is selected at random. Use the information in the table to
answer the questions below.
Voters who are registered as…
Voted for… Democrat Republican Independent Totals
Napolitano (D) 184 42 56 282
Salmon (R) 26 205 45 276
Mahoney (I) 6 5 31 42
Totals 216 252 132 600
a) What is the probability that the selected voter voted for Napolitano?
b) What is the probability that the selected voter is a registered Democrat?
c) What is the probability that the selected voter voted for Napolitano, given that the
selected voter is a Democrat?
Chapter 5 Test, Form B
Page 4 of 8
d) A local reporter, commenting on this election, said, “Napolitano won because she
attracted a larger share of crossover voters.” (A crossover voter is one who votes
differently than his or her registration category. For example, a Democrat party
member voting Republican, or an Independent voting for a Democrat candidate
would be crossover voters). What is the probability that the selected voter voted
for Napolitano, given that he or she is a crossover voter?
5. All statistics teachers love Girl Scout Cookies. The number of boxes of Girl Scout
cookies a statistics teacher orders is (of course) determined by the roll of a 4-sided
fair die. If a one appears, 6 boxes are ordered; if any other number appears, 2 boxes
are ordered.
a) What is the probability that a statistics teacher places an order for 2 boxes of Girl
Scout cookies?
b) What is the probability that two statistics teachers (each rolling a die to determine
the number of boxes ordered) will each order 6 boxes each?
c) What is the probability that for two statistics teachers (each rolling a die to
determine the number of boxes ordered), the first will order 6 boxes and the
second will order 2 boxes?
d) What is the probability that for two statistics teachers (each rolling a die to
determine the number of boxes ordered), exactly one will order 6 boxes?
Chapter 5 Test, Form B
Page 5 of 8
6. Like many professionals, the clergy in mainline Protestant churches have pension
plans. Due to the nature of the ministry, investment strategies may involve what are
known as “screens.” Screens are rules that prevent a pension fund administrator from
investing in corporations that are involved with, for example, alcohol, gambling,
tobacco and weapons of mass destruction. Ministers may elect to invest in two broad
categories: “regular” and “social purpose” funds, which would typically use screens
in their investment strategy. The use of screens may reduce their monthly benefit at
retirement.
The data below are from a survey of ministers about their support in principle for the
use of such screens. Each minister asked if the screens should be applied to the
regular funds, the social purpose funds, both, or neither. The ministers were also
classified by the current percentage of their investments in the social purpose funds:
0%, 10 – 59%, 60% or greater.
a) What is the probability that a minister selected at random from those who
participated in the survey was uncertain about the use of screens?
Use screens for: 0%
group
10-59%
group
60+%
group
Total
Social purpose
funds only
70 94 58 222
Both social
purpose
and regular funds
83 235 266 584
Neither 47 11 3 61
Uncertain 23 15 6 44
Total 223 355 333 911
Chapter 5 Test, Form B
Page 6 of 8
b) What is the probability that a minister selected at random from those who
participated in the survey was in the 60+% group and supported the use of screens
for social purpose funds only?
c) What is the probability that a minister selected at random from those who
participated in the survey felt the screens should be used for social purpose funds
only or for both social purpose and regular funds, given that they were in the 10-
59% group?
d) What is the probability that a randomly selected “uncertain” minister would be in
the 0% group?
Chapter 5 Test, Form B
Page 7 of 8
7. Three of the most common pets are cats, dogs, and fish. Many families have more
than one type of pet, and some have all three! Define the following events, with the
probabilities given. (The fish-and-cats combination doesn’t seem too popular!)
F = a randomly selected family has at least one pet fish: P(F) = 0.20
D = a randomly selected family has at least one pet dog: P(D) = 0.32
C = a randomly selected family has at least one pet cat: P(C) = 0.35
Also
( ) 0.18; ( ) 0.07; ( | ) 0.30P F D P F C P D C    
Suppose that a family is selected at random. Calculate each of the following (show
your work):
a) ( | )P F D
b) ( )P F D
c) ( )P C D
Chapter 5 Test, Form B
Page 8 of 8
Chapter 5, Test Form B Answer Key
1.
a) { }CC, CF, FC, FF
b) A: { }CC B: { },CC FF C: { }, , FCCC CF
2.
3.
a) 10 0.0283
353 =
b) 616 0.9305
662 =
c) 36 0.0361
997 =
4.
a) 282 0.4700
600 =
b) 216 0.3600
600 =
c) 184 0.8519
216 =
d) 98 0.5444
180 =
Disjoint Independent
A, B N N
B, C N N
A, C Y N
Chapter 5, Test Form B Answer Key Page 1 of 2
5.
a) 3 0.75
4 =
b) 1 0.0625
16 =
c) ( )( )0.25 0.75 0.1875=
d) ( )( ) ( )( )0.25 0.75 0.75 0.25 0.3750+ =
6.
a) 44 0.0483
911 =
b) 58 0.0637
911 =
c) 329 0.9268
355 =
d) 23 0.5227
44 =
7.
a) ( ) ( )
( )
0.18
F | D 0.5625
0.32
P F D
P P D
∩
= = =
b) ( ) ( ) ( ) ( ) 0.20 0.32 0.18 0.34P F D P F P D P F D∪ = + − ∩ = + − =
c) ( ) ( ) ( ) ( )( )D | C 0.35 0.30 0.105P D C P C P∩ = = =
Chapter 5, Test Form B Answer Key Page 2 of 2