Statistics Problems 1Sec 1.3………………………………………………………………………………………….docx

Statistics Problems 1
Sec 1.3
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Exposure to microbial products, especially endotoxin, may have
an impact on vulnerability to allergic diseases. The following
are data on concentration (EU/mg) in settled dust for one
sample of urban homes and another of farm homes.
U:

6.0
5.0
11.0
33.0
4.0
5.0
80.0
18.0
35.0
17.0
23.0
F:
3.0
16.0
11.0
9.0
6.0
9.0
2.0
17.0
3.0
7.9
23.0
9.9
4.0
2.0
0.8
(a) Determine the sample mean for each sample. (Round your
answers to two decimal places.)
urban homes
1 EU/mg
farm homes

2 EU/mg
How do they compare?
The average endotoxin concentration is about the same in both
urban and farm homes. The average endotoxin concentration in
farm homes is more than double the average concentration in
urban homes. The average endotoxin concentration in urban
homes is more than double the average concentration in farm
homes.
(b) Determine the sample median for each sample.
urban homes
4 EU/mg
farm homes
5 EU/mg
How do they compare?
The median endotoxin concentration is about the same in both
urban and farm homes. The median endotoxin concentration in
farm homes is roughly double the median concentration in urban
homes. The median endotoxin concentration in urban homes
is roughly double the median concentration in farm homes.
Why is the median for the urban sample so different from the
mean for that sample?
The mean and median for urban homes are so different because
the measure different aspects of the distribution. The mean and
median for urban homes are so different because there are fewer
observations. The mean and median for urban homes are so
different because the few large values raise the mean but not the
median.
(c) Calculate the trimmed mean for each sample by deleting the
smallest and largest observation. (Round your answers to two
decimal places.)
urban homes

8 EU/mg
farm homes
9 EU/mg
What are the corresponding trimming percentages? (Round your
answers to two decimal places.)
urban homes
10 %
farm homes
11 %
How do the values of these trimmed means compare to the
corresponding means and medians?
Urban homes:
The trimmed mean is 12 the mean of the entire sample. The
trimmed mean is 13 the median of the entire sample.
Farm homes:
The trimmed mean is 14 the mean of the entire sample. The
trimmed mean is 15 the median of the entire sample.
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The minimum injection pressure (psi) for injection molding
specimens of high amylose corn was determined for eight
different specimens (higher pressure corresponds to greater
processing difficulty), resulting in the following observations.
14.6
12.5
17.5
14.2
12.0
10.9
9.5
8.0
(a) Determine the values of the sample mean x, sample median ,
and 12.5% trimmed mean xtr. (Round your answers to two
decimal places.)

x
= 1 psi
= 2 psi
xtr
= 3 psi
Compare these values.
The mean is much larger than the median and trimmed mean,
indicating positive skewness. The mean is much larger than the
median and trimmed mean, indicating negative skewness. All
three measures of center are similar, indicating little skewness
to the data set. The median is much larger than the mean and
trimmed mean, indicating negative skewness. The median is
much larger than the mean and trimmed mean, indicating
positive skewness.
(b) By how much could the smallest sample observation,
currently 8.0, be increased without affecting the value of the
sample median?
5 psi
(c) Suppose we want the values of the sample mean and median
when the observations are expressed in kilograms per square
inch (ksi) rather than psi. Is it necessary to reexpress each
observation in ksi, or can the values calculated in part (a) be
used directly? [Hint: 1 kg = 2.2 lb.]
Yes, it is necessary to reexpress each observation. No, the
values obtained in part (a) can be used directly.
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A sample of 26 offshore oil workers took part in a simulated
escape exercise, resulting in the accompanying data on time
(sec) to complete the escape:
380
350

356
360
378
424
323
397
401
374
374
370
364
368
364
327
338
394
392
369
377
359
352
407
332
398
(a) Construct a stem-and-leaf display of the data. (Enter
numbers from smallest to largest separated by spaces. Enter
NONE for stems with no values.)
Stems
Leaves
32
1
33
2
34
3

35
4
36
5
37
6
38
7
39
8
40
9
41
10
42
11
How does it suggest that the sample mean and median will
compare?
The display is reasonably symmetric, so the mean and median
will be close. The display is positively skewed, so the median
will be greater than the mean. The display is positively
skewed, so the mean will be greater than the median. The
display is negatively skewed, so the median will be greater than
the mean. The display is negatively skewed, so the mean will be
greater than the median.
(b) Calculate the values of the sample mean x and median .
[Hint: Σxi = 9628.] (Round your answers to two decimal
places.)
x =
13 sec
=
14 sec
(c) By how much could the largest time, currently 424, be

increased without affecting the value of the sample median?
(Enter ∞ if there is no limit to the amount.)
By how much could this value be decreased without affecting
the value of the sample median? (Enter ∞ if there is no limit to
the amount.)
(d) What are the values of x and when the observations are
reexpressed in minutes? (Round your answers to two decimal
places.)
x
= 17 min
= 18 min
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The article "Snow Cover and Temperature Relationships in
North America and Eurasia"† used statistical techniques to
relate the amount of snow cover on each continent to average
continental temperature. Data presented there included the
following ten observations on October snow cover for Eurasia
during the years 1970-1979 (in million km2):
6.5 12.0 14.9 10.0 10.7 7.9 21.9 12.5 14.5 9.2
What would you report as a representative, or typical, value of
October snow cover for this period, and what prompted your
choice?
The mean of this sample because the mean is always the best
central measure. The mean of this sample because a potential
outlier may produce a misleading median. The median of this
sample because the median is always the best central measure.
The median of this sample because a potential outlier may
produce a misleading mean.
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Blood pressure values are often reported to the nearest 5 mmHg
(100, 105, 110, etc.). The actual blood pressure values for nine
randomly selected individuals are given below.
108.6
117.4
128.4
120.0
103.7
112.0
98.3
121.5
123.2
(a) What is the median of the reported blood pressure values?
1 mmHg
(b) Suppose the blood pressure of the second individual is 117.7
rather than 117.4 (a small change in a single value). What is the
new median of the reported values?
2 mmHg
What does this say about the sensitivity of the median to
rounding or grouping in the data?

When there is rounding or grouping, the median is only
sensitive to large changes. When there is rounding or grouping,
the median is not sensitive to small changes. When there is
rounding or grouping, the median can be highly sensitive to
small change.
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The propagation of fatigue cracks in various aircraft parts has
been the subject of extensive study in recent years. The

accompanying data consists of propagation lives (flight
hours/104) to reach a given crack size in fastener holes intended
for use in military aircraft.
0.725
0.842
0.865
0.911
0.924
0.943
0.961
1.010
1.038
1.049
1.082
1.126
1.137
1.158
1.242
1.366
(a) Compute and compare the values of the sample mean x and
median . (Round your answers to four decimal places.)
x
= 1 flight hours/104
= 2 flight hours/104
(b) By how much could the largest sample observation be
decreased without affecting the value of the median? (Enter
your answer to three decimal places.)
3 flight hours/104
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A sample of n = 10 automobiles was selected, and each was
subjected to a 5-mph crash test. Denoting a car with no visible
damage by S (for success) and a car with such damage by F,
results were as follows:
S F F S S S F F S F
(a) What is the value of the sample proportion of successes x/n?
1
(b) Replace each S with a 1 and each F with a 0. Then calculate
x for this numerically coded sample.
x = 2

How does x compare with x/n?
The proportion in part (a) is exactly equal to the mean in part
(b). The proportion in part (a) is greater than the mean in part
(b). The proportion in part (a) is less than the mean in part
(b).
(c) Suppose it is decided to include 15 more cars in the
experiment. How many of these would have to be S's to give x/n
= 0.72 for the entire sample of 25 cars?
4 cars
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An article reported the following data on oxygen consumption
(mL/kg/min) for a sample of ten firefighters performing a fire-
suppression simulation:
28.9
49.1
30.1
28.5
28.4
25.5
33.7
29.3
23.3
31.1
Compute the following. (Round your answers to four decimal

places.)
(a) The sample range
1 mL/kg/min
(b) The sample variance s2 from the definition (i.e., by first
computing deviations, then squaring them, etc.)
2 mL2/kg2/min2
(c) The sample standard deviation
3 mL/kg/min
(d) s2 using the shortcut method
4 mL2/kg2/min2
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Suppose the value of Young's modulus (GPa) was determined
for cast plates consisting of certain intermetallic substrates,
resulting in the following sample observations:
116.6
115.9
114.6
115.4

115.6
(a) Calculate x.
1 GPa
Calculate the deviations from the mean. (Enter your answers to
two decimal places.)
x
116.6
115.9
114.6
115.4
115.6
deviation
2
3
4
5
6
(b) Use the deviations calculated in part (a) to obtain the sample
variance and the sample standard deviation. (Round your
answers to three decimal places.)
s2
=
7 GPa2
s
=
8 GPa
(c) Calculate s2 by using the computational formula for the
numerator Sxx. (Round your answer to three decimal places.)
9 GPa2
(d) Subtract 100 from each observation to obtain a sample of
transformed values. Now calculate the sample variance of these
transformed values. (Round your answer to three decimal

places.)
10 GPa2
Compare it to s2 for the original data.
The variance in part (d) is greater than the variance in part (b).
The variance in part (d) is equal to the variance in part (b).
The variance in part (d) is smaller than the variance in part (b).
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The accompanying observations are on stabilized viscosity (cP)
for specimens of a certain grade of asphalt with 18% rubber
added:
2751
2909
3023
2800
2856
(a) What are the values of the sample mean x and sample
median ?
x =
1 cP
=
2 cP
(b) Calculate the sample variance using the computational
formula. [Hint: First subtract a convenient number from each
observation.] (Round your answer to the nearest whole number.)
3 cP2
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A study of the relationship between age and various visual
functions (such as acuity and depth perception) reported the
following observations on the area of scleral lamina (mm2)
from human optic nerve heads:
2.80
2.61
2.70
3.92
2.27
2.65
3.86
4.16
3.80
4.27
3.37
4.60
2.48
3.61
2.80
3.51
2.92

(a) Calculate Σxi and Σxi2. (Round Σxi2 to two decimal places.)
Σxi
= 1 mm2
Σxi2
= 2 mm4
(b) Use the values calculated in part (a) to compute the sample
variance s2 and then the sample standard deviation s. (Round
your answers to three decimal places.)
s2
= 3 mm4
s
= 4 mm2
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A woman sued a computer keyboard manufacturer, charging that

her repetitive stress injuries were caused by the keyboard. The
injury awarded about $3.5 million for pain and suffering, but
the court then set aside that award as being unreasonable
compensation. In making this determination, the court identified
a "normative" group of 27 similar cases and specified a
reasonable award as one within two standard deviations of the
mean of the awards in the 27 cases. The 27 awards were (in
$1000s) 38, 61, 72, 112, 136, 143, 146, 151, 238, 290, 340, 410,
600, 750, 750, 750, 1050, 1100, 1136, 1150, 1200, 1200, 1250,
1578, 1700, 1825, and 2000, from which
Σxi = 20,176, Σxi2 = 24,656,604.
What is the maximum possible amount that could be awarded
under the two-standard-deviation rule? (Round your answer to
the nearest whole number.)
1 thousand dollars
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An article reported the following data on oxidation-induction
time (min) for various commercial oils:
85
104
130
160
180
195
131
145
213
105
145
152
151
136
87
99
91
119
129
(a) Calculate the sample variance and standard deviation.
(Round your answers to three decimal places.)

s2
= 1 min2
s
= 2 min
(b) If the observations were reexpressed in hours, what would
be the resulting values of the sample variance and sample
standard deviation? Answer without actually performing the
reexpression. (Round your answer to three decimal places.)
s2
= 3 hr2
s
= 4 hr
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–/2
The first four deviations from the mean in a sample of n = 5
reaction times were 0.4, 0.9, 1.2, and 1.5. What is the fifth
deviation from the mean?
1
Give a sample for which these are the five deviations from the
mean.
−3.6, −3.1, −2.8, −2.5, −4
4.4, 4.9, 5.2, 5.5, 0
−0.6, −0.1, 0.2, 0.5, 0
1.4, −0.1, 2.2, 2.5, −5.0
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A company utilizes two different machines to manufacture parts
of a certain type. During a single shift, a sample of n = 20 parts
produced by each machine is obtained, and the value of a
particular critical dimension for each part is determined. The
comparative boxplot below is constructed from the resulting
data.
Compare and contrast the two samples. (Select all that apply.)
A typical value is much larger for machine 1 than for machine
2.Machine 2's sample values have considerably more variation
than machine 1's sample values.Machine 1's sample values have
considerably more variation than does machine 2's sample
values.A typical value seems to be about the same for the two
machines.Machine 1 and machine 2's sample values have about
the same amount of variation.The only outlier that exists is from
machine 1.A typical value is much larger for machine 2 than for
machine 1.The only outlier that exists is from machine 2.There
are no outliers present.
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Observations on burst strength (lb/in2) were obtained both for
test nozzle closure welds and for production canister nozzle
welds.†
Test
7200
6100
7300
7300
8000
7400
7300
7300
8000
6700
8300
Cannister
5250
5625
5900
5900
5700
6050
5800
6000
5875

6100
5850
6600
A comparative boxplot is given below.
Comment on interesting features (the cited article did not
include such a picture, but the authors commented that they had
looked at one). (Select all that apply.)
The test nozzle welds have much more variable burst
strengths.The production canister welds have much higher burst
strengths.The test nozzle welds data contain 2 outliers.The
production canister welds data contain 2 outliers.The production
canister welds have consistently lower burst strengths than the
test nozzle welds.The production canister welds have much
more variable burst strengths.
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Consider randomly selecting a student at a certain university,
and let A denote the event that the selected individual has a
Visa credit card and B be the analogous event for a MasterCard.
Suppose that P(A) = 0.3, P(B) = 0.5, and P(A ∩ B) = 0.25.
(a) Compute the probability that the selected individual has at
least one of the two types of cards (i.e., the probability of the
event A ∪ B).
1
(b) What is the probability that the selected individual has

neither type of card?
2
(c) Describe, in terms of A and B, the event that the selected
student has a Visa card but not a MasterCard.
A ∪ B'
A ∩ B'
A' ∩ B'
A' ∩ B
A' ∪ B'
Calculate the probability of this event.
4
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Suppose that 45% of all adults regularly consume coffee, 65%
regularly consume carbonated soda, and 75% regularly consume
at least one of these two products.
(a) What is the probability that a randomly selected adult
regularly consumes both coffee and soda?
1
(b) What is the probability that a randomly selected adult
doesn't regularly consume at least one of these two products?
2
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An individual is presented with three different glasses of cola,
labeled C, D, and P. He is asked to taste all three and then list
them in order of preference. Suppose the same cola has actually
been put into all three glasses.
(a) What are the simple events in this ranking experiment?
(Enter your answer in set notation.)
What probability would you assign to each one? 1 0ver 3 is 1/3
All of the simple events have the same probability,
1
3
.
All of the simple events have the same probability,
1
6
.
It is impossible to determine the probability of the simple
events with the given information. The probability of an
individual event where D is ranked first is
1

5
.
The probability of another individual event is
1
15
.
The probability of an individual event where D is ranked first is
1
12
.
The probability of another individual event is
1
4
.
(b) What is the probability that C is ranked first? (Round your
answer to three decimal places.)
3
(c) What is the probability that C is ranked first and D is ranked
last? (Round your answer to three decimal places.)
4
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A box contains six 40-W bulbs, four 60-W bulbs, and eight 75-
W bulbs. If bulbs are selected one by one in random order, what
is the probability that at least two bulbs must be selected to
obtain one that is rated 75 W? (Round your answer to three
decimal places.)
1
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–/2
Human visual inspection of solder joints on printed circuit
boards can be very subjective. Part of the problem stems from
the numerous types of solder defects (e.g., pad non-wetting,
knee visibility, voids) and even the degree to which a joint
possesses one or more of these defects. Consequently, even
highly trained inspectors can disagree on the disposition of a
particular joint. In one batch of 10,000 joints, inspector A found
720 that were judged defective, inspector B found 756 such
joints, and 1328 of the joints were judged defective by at least
one of the inspectors. Suppose that one of the 10,000 joints is
randomly selected.
(a) What is the probability that the selected joint was judged to
be defective by neither of the two inspectors? (Enter your
answer to four decimal places.)
1
(b) What is the probability that the selected joint was judged to
be defective by inspector B but not by inspector A? (Enter your
2
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A certain factory operates three different shifts. Over the last
year, 200 accidents have occurred at the factory. Some of these
can be attributed at least in part to unsafe working conditions,
whereas the others are unrelated to working conditions. The
accompanying table gives the percentage of accidents falling in
each type of accident-shift category.
Unsafe
Conditions
Unrelated
to Conditions
Day
13%
32%
Shift
Swing
9%
13%
Night

2%
31%
Suppose one of the 200 accident reports is randomly selected
from a file of reports, and the shift and type of accident are
determined.
(a) What are the simple events? (Let S1, S2, and S3 represent
the day, swing, and night shifts, respectively. Let C1 and C2
represent the unsafe conditions and unrelated to conditions,
respectively. Enter your answer in set notation.)
(b) What is the probability that the selected accident was
attributed to unsafe conditions?
2
(c) What is the probability that the selected accident did not
occur on the day shift?
3
0
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An insurance company offers four different deductible levels—
none, low, medium, and high—for its homeowner's
policyholders and three different levels—low, medium, and
high—for its automobile policyholders. The accompanying table
gives proportions for the various categories of policyholders
who have both types of insurance. For example, the proportion
of individuals with both low homeowner's deductible and low
auto deductible is 0.07 (7% of all such individuals).
Homeowner's
Auto
N

L
M
H
L
0.04
0.07
0.05
0.04
M
0.07
0.10
0.20
0.08
H
0.02
0.03
0.15
0.15
Suppose an individual having both types of policies is randomly
selected.
(a) What is the probability that the individual has a medium
auto deductible and a high homeowner's deductible?
1
(b) What is the probability that the individual has a low auto
deductible? A low homeowner's deductible?
auto deductible
2
homeowner's deductible
3
(c) What is the probability that the individual is in the same
category for both auto and homeowner's deductibles?

4
(d) Based on your answer in part (c), what is the probability
that the two categories are different?
5
(e) What is the probability that the individual has at least one
low deductible level?
6
(f) Using the answer in part (e), what is the probability that
neither deductible level is low?
7
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–/3
The route used by a certain motorist in commuting to work
contains two intersections with traffic signals. The probability
that he must stop at the first signal is 0.4, the analogous
probability for the second signal is 0.45, and the probability
that he must stop at at least one of the two signals is 0.5.
(a) What is the probability that he must stop at both signals?
1
(b) What is the probability that he must stop at the first signal
but not at the second one?
2
(c) What is the probability that he must stop at exactly one
signal?
3
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–/4
A certain system can experience three different types of defects.
Let Ai (i = 1,2,3) denote the event that the system has a defect
of type i. Suppose that the following probabilities are true.
P(A1) = 0.14 P(A2) = 0.10 P(A3) = 0.06
P(A1 ∪ A2) = 0.16 P(A1 ∪ A3) = 0.16
P(A2 ∪ A3) = 0.13 P(A1 ∩ A2 ∩ A3) = 0.02
(a) What is the probability that the system does not have a type
1 defect?
1
(b) What is the probability that the system has both type 1 and
type 2 defects?
2
(c) What is the probability that the system has both type 1 and
type 2 defects but not a type 3 defect?
3
(d) What is the probability that the system has at most two of
these defects?
4

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–/3
An academic department with five faculty members—Anderson,
Box, Cox, Cramer, and Fisher—must select two of its members
to serve on a personnel review committee. Because the work
will be time-consuming, no one is anxious to serve, so it is
decided that the representative will be selected by putting the
names on identical pieces of paper and then randomly selecting
two.
(a) What is the probability that both Anderson and Box will be

selected? [Hint: List the equally likely outcomes.]
1
(b) What is the probability that at least one of the two members
whose name begins with C is selected?
2
(c) If the five faculty members have taught for 3, 6, 7, 10, and
14 years, respectively, at the university, what is the probability
that the two chosen representatives have a total of at least 12
years teaching experience there?
3
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–/3
A family consisting of three persons—A, B, and C—goes to a
medical clinic that always has a doctor at each of stations 1, 2,
and 3. During a certain week, each member of the family visits
the clinic once and is assigned at random to a station. The
experiment consists of recording the station number for each
member. Suppose that any incoming individual is equally likely
to be assigned to any of the three stations irrespective of where
other individuals have been assigned. What is the probability
that
(a) All three family members are assigned to the same station?
(Round your answer to three decimal places.)
1
(b) At most two family members are assigned to the same
station? (Round your answer to three decimal places.)
2
(c) Every family member is assigned to a different station?
3
0
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Sec 2.3
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A friend of mine is giving a dinner party. His current wine
supply includes 10 bottles of zinfandel, 12 of merlot, and 8 of
cabernet (he only drinks red wine), all from different wineries.
(a) If he wants to serve 3 bottles of zinfandel and serving order
is important, how many ways are there to do this?
1 ways
(b) If 6 bottles of wine are to be randomly selected from the 30
for serving, how many ways are there to do this?
2 ways
(c) If 6 bottles are randomly selected, how many ways are there
to obtain two bottles of each variety?
3 ways
(d) If 6 bottles are randomly selected, what is the probability
that this results in two bottles of each variety being chosen?
4
(e) If 6 bottles are randomly selected, what is the probability
that all of them are the same variety? (Round your answer to
three decimal places.)
5
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–/6
A stereo store is offering a special price on a complete set of
components (receiver, compact disc player, speakers, turntable).
A purchaser is offered a choice of manufacturer for each
component:
Receiver: Kenwood, Onkyo, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity
Turntable: Onkyo, Sony, Teac, Technics
A switchboard display in the store allows a customer to hook
together any selection of components (consisting of one of each
type). Use the product rules to answer the following questions:

(a) In how many ways can one component of each type be
selected?
1 ways
(b) In how many ways can components be selected if both the
receiver and the compact disc player are to be Sony?
2 ways
(c) In how many ways can components be selected if none is to
be Sony?
3 ways
(d) In how many ways can a selection be made if at least one
Sony component is to be included?
4 ways
(e) If someone flips switches on the selection in a completely
random fashion, what is the probability that the system selected
contains at least one Sony component? Exactly one Sony
component? (Round your answer to three decimal places.)
at least one Sony component
5
exactly one Sony component
6
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A production facility employs 10 workers on the day shift, 8
workers on the swing shift, and 6 workers on the graveyard
shift. A quality control consultant is to select 6 of these workers
for in-depth interviews. Suppose the selection is made in such a
way that any particular group of 6 workers has the same chance
of being selected as does any other group (drawing 6 slips
without replacement from among 24).
(a) How many selections result in all 6 workers coming from the
day shift?
1 selections
What is the probability that all 6 selected workers will be from

the day shift? (Round your answer to four decimal places.)
2
(b) What is the probability that all 6 selected workers will be
from the same shift? (Round your answer to four decimal
places.)
3
(c) What is the probability that at least two different shifts will
be represented among the selected workers? (Round your
4
(d) What is the probability that at least one of the shifts will be
unrepresented in the sample of workers? (Round your answer to
four decimal places.)
5
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–/1
An academic department with five faculty members narrowed its
choice for department head to either candidate A or candidate
B. Each member then voted on a slip of paper for one of the
candidates. Suppose there are actually three votes for A and two
for B. If the slips are selected for tallying in random order, what
is the probability that A remains ahead of B throughout the vote
count (e.g., this event occurs if the selected ordering is
AABAB, but not for ABBAA)?
1
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–/4
A box in a certain supply room contains seven 40-W lightbulbs,
four 60-W bulbs, and five 75-W bulbs. Suppose that three bulbs
are randomly selected. (Round your answers to four decimal
places.)
(a) What is the probability that exactly two of the selected bulbs
are rated 75-W?
1
(b) What is the probability that all three of the selected bulbs
have the same rating?
2
(c) What is the probability that one bulb of each type is
selected?
3
(d) Suppose now that bulbs are to be selected one by one until a
75-W bulb is found. What is the probability that it is necessary
to examine at least six bulbs?
4
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–/3
Twenty-one telephones have just been received at an authorized
service center. Seven of these telephones are cellular, seven are
cordless, and the other seven are corded phones. Suppose that
these components are randomly allocated the numbers 1, 2, . . . ,
21 to establish the order in which they will be serviced. (Round
your answers to four decimal places.)
(a) What is the probability that all the cordless phones are
among the first fourteen to be serviced?
1
(b) What is the probability that after servicing fourteen of these
phones, phones of only two of the three types remain to be
serviced?
2
(c) What is the probability that two phones of each type are
among the first six serviced?
3

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–/2
A starting lineup in basketball consists of two guards, two
forwards, and a center.
(a) A certain college team has on its roster four centers, five
guards, five forwards, and one individual (X) who can play
either guard or forward. How many different starting lineups
can be created? [Hint: Consider lineups without X, then lineups
with X as guard, then lineups with X as forward.]
1 lineups
(b) Now suppose the roster has 5 guards, 4 forwards, 4 centers,
and 2 "swing players" (X and Y) who can play either guard or

forward. If 5 of the 15 players are randomly selected, what is
the probability that they constitute a legitimate starting lineup?
2
0
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