Chapter 4: Probability Assignment
Project description
Chapter 4: Probability Assignment Instructions: Due Date: 1:30pm on Feb. 18th, 2015 This assignment is to be handed in the Chris Hockey Assignments Drop Box located near Room East 201 no later than above-noted Due Date and Time. Please note that, LATE OR IMPROPERLY DEPOSITED ASSIGNMENTS WILL NOT BE GRADED. Please print clearly! I cannot mark what I cannot read! Please print your name at the top of each page. Staples would be nice. You must show ALL steps and logic in your answers! Instructions on rounding: do NOT use rounded values in calculations; show ALL unrounded answers; and ONLY round final answers when indicated by the question.
1. A first, second and third prize are being drawn from a raffle of 250 tickets. What is the total number of possible outcomes? What is the probability of winning one of the three prizes? 2. The local Family Restaurant has a daily dinner special in which the customer may choose one appetizer, one entree and one dessert from a list of 4 appetizers, 5 entrees and 6 desserts. How many different dinner specials are possible? 3. Six (6) jurors are to be selected for a civil trial from a room of 50 potential jurors. In how many different ways can the jury be formed? 4. Determine the total number of possible five-card hands that can be drawn from a deck of 52 cards. Hint: Consider if the order in which you receive the cards matters. 5. A personalized license plate in Ontario consists of a graphic symbol followed by 3 letters followed by 3 numbers. If there are 36 different graphics symbols available, how many personalized license plates are possible? 6. A board of directors consists of six men and eight women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all four members of the search committee will be men? What is the probability of at least one woman being on the committee? 7. A fair pair of dice is thrown, what is the probability of rolling a 4 or an 11? Hint: If you are not sure, list all possible outcomes for the two dice and count. 8. You have just purchased a box containing 25 light bulbs, three of which are defective. What is the probability that the first two light bulbs removed from the box will be defective?
Page 1 of 2
9. The manufacturers of a new electronic tablet surveyed 250 customers and obtained the following age and gender data in the table shown below. If a customer is randomly selected from this group, use this table to determine the following probabilities:
GENDER
AGE
Less than 30 years
(30 to 45) years
More than 45 years
Total
Male 80 30 21 Female 50 60 9 Total
a) The customer is more than 45 years of age? b) They are male and less than 30 years of age? c) The customer is female or less than 30 years of age? d) The customer is male given that he is (30 to 45) years old? e) If two people are randomly selected from the group, what is the probability that they are both female
Instructions:
Due Date: 1:30pm on Feb. 18th, 2015
• This assignment is to be handed in the “Chris Hockey Assignments Drop Box” located near Room East 201 no later than above-noted Due Date and Time. Please note that,
LATE OR IMPROPERLY DEPOSITED ASSIGNMENTS WILL NOT BE GRADED.
• Please print clearly! I cannot mark what I cannot read!
• Please print your name at the top of each page. Staples would be nice.
• You must show ALL steps and logic in your answers!
• Instructions on rounding: do NOT use rounded values in calculations; show ALL unrounded answers; and ONLY round final answers when indicated by the question.
1. A first, second and third prize are being drawn from a raffle of 250 tickets. What is the total number of possible outcomes? What is the probability of winning one of the three prizes?
2. The local Family Restaurant has a daily dinner special in which the customer may choose one appetizer, one entree and one dessert from a list of 4 appetizers, 5 entrees and 6 desserts. How many different dinner specials are possible?
3. Six (6) jurors are to be selected for a civil trial from a room of 50 potential jurors. In how many different ways can the jury be formed?
4. Determine the total number of possible five-card hands that can be drawn from a deck of 52 cards. Hint: Consider if the order in which you receive the cards matters.
5. A personalized license plate in Ontario consists of a graphic symbol followed by 3 letters followed by 3 numbers. If there are 36 different graphics symbols available, how many personalized license plates are possible?
6. A board of directors consists of six men and eight women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all four members of the search committee will be men? What is the probability of at least one woman being on the committee?
7. A fair pair of dice is thrown, what is the probability of rolling a 4 or an 11? Hint: If you are not sure, list all possible outcomes for the two dice and count.
8. You have just purchased a box containing 25 light bulbs, three of which are defective. What is the probability that the first two light bulbs removed from the box will be defective?
Page 1 of 2
9. The manufacturers of a new electronic tablet surveyed 250 customers and obtained the following age and gender data in the table shown below. If a customer is randomly selected from this group, use this table to determine the following probabilities:
GENDER
AGE
Less than 30 years
(30 to 45) years
More than 45 years
Total
Male
80
30
21
Female
50
60
9
Total
a) The customer is more than 45 years of age?
b) They are male and less than 30 years of age?
c) The customer is female or less than 30 years of age?
d) The customer is male given that he is (30 to 45) years old?
e) If two people are randomly selected from the group, what is the probability that they are both female?
Page 2 of 2
36.
experimental plan for lab
Project description
write an experimental plan for lab experiment. USE 3rd person only. I will attach the paper for this experiment
In the Laboratory
www.JCE.DivCHED.org • Vol. 84 No. 4 April 2007 • Journal of Chemical Education 689
Attention from the media and general public has recently
soared with regard to forensic chemistry. This rising awareness
can be attributed to television shows such as CSI and
Forensic Files that have made chemical analysis exciting. By
utilizing a forensic-based experiment in an instrumental methods
course, student interest in the laboratory can be stimulated.
In addition, students will gain valuable experience with
an analytical technique(s) that is used in real situations by forensic
laboratories.
The oldest method of personal identification for forensic
purposes is latent fingerprint analysis. The ability to identify
suspects from fingerprints left at a crime scene is a result
of the arrangement of ridges on the finger pads being unique
and permanent to each person (1). Recently, with advances
in modern technology, scientists have begun to examine
whether information in addition to ridge patterns can be
gained from fingerprints. For example, researchers have discovered
that they can obtain a suspect’s DNA profile by applying
the polymerase chain reaction to skin debris present
in fingerprints left on forensic evidence (2, 3). In parallel to
this advancement, progress has been made in determining the
chemical composition of a latent fingerprint using infrared
(IR) microspectroscopy and gas chromatography–mass spectrometry
(GC–MS) (4–8).
Fingerprints primarily consist of material secreted by the
eccrine glands located in the palms and fingertips and the sebaceous
glands that are located most abundantly on the scalp
and face (6). These chemical components include inorganic
salts such as iron and sodium, amino acids, and lipids such as
fatty acids, wax esters, squalene, and cholesterol (9). IR (7, 8)
and GC–MS (4–6) studies have examined whether differences
in the chemical composition of fingerprints can be used to
establish age, gender, and so forth. This information could
allow a suspect pool to be reduced even if the fingerprints
obtained from a crime scene were smudged or patterns were
not matched after being processed in the Integrated Automated
Fingerprint Identification System (10).
We have adapted a procedure described by Asano et al.
(5) and Archer et al. (4) for fingerprint extraction and analysis
by GC–MS for use in an undergraduate instrumental analysis
course. In the experiment, students collect fingerprint
residue samples on glass beads or glass slides, extract the chemical
constituents from the residue using chloroform, convert
the fatty acids and other components into trimethylsilyl derivatives,
and finally, analyze the products using GC–MS. By
converting the constituents into less polar, thermally stable
materials through silylation, students gain experience in a technique
that is frequently required to make samples amenable
to GC analysis (11). Furthermore, students can perform a
MS library search to identify the components present in their
fingerprint residue and then compare their results to demonstrate
that more information than just ridge pattern might
be obtained from fingerprints found at crime scenes.
Experimental Procedure
Equipment
A Hewlett Packard G1800C GCD system (Palo Alto, CA)
with a quadrupole mass spectrometer and a ZB-5 column
(Phenomenex, Torrance, CA; 30 m × 0.25 mm) was employed
for this experiment. The injection port and detector were set
at 280 C. Helium was used as the carrier gas at a flow rate of
1 mLmin. Injections (1 mL) were made in splitless mode and
the column was initially set at 50 C and held for 1 min. The
temperature was then ramped at 10 Cmin to a final temperature
of 310 C and held for 20 min.
Materials
The following chemicals are needed for the experiment:
chloroform, ethyl acetate, and bis(trimethylsilyl)trifluoroacetamide
(BSTFA, Sigma-Aldrich, St. Louis, MO). Small
glass beads (from a craft store), microscope glass slides, cotton
swabs, and 4-mL vials with Teflon-lined caps are utilized
for sample collection and extraction.
Procedure
Two fingerprint-collection procedures were designed and
tested. In the first method, glass beads were washed with chloroform
prior to sample collection. Viton (DuPont Dow Elastomers)
or other appropriate gloves should be worn. Five clean
beads were placed in a 4-mL vial. To obtain a fingerprint
sample, volunteers rubbed their fingertips across their forehead,
removed the glass beads from the sampling vial, and
then rubbed the beads between their fingertips for approximately
15 s. The beads were then immediately placed back
into the vial and 400 mL of chloroform was added to extract
the fingerprint residue. In the second collection procedure, a
latent print was taken from a flat surface, a glass microscope
slide. Slides were cleaned using chloroform and the fingerprint
sample was obtained in the same way, except that instead
of rubbing beads between their fingertips, the volunteers
pressed their thumbs on the slides for approximately 15 s. A
cotton swab soaked in chloroform was then used to remove
the print from the slide. The cotton swab end was cut with
scissors, placed in a 4-mL vial, and 2 mL of chloroform was
added to extract the fingerprint residue.
Chemical Composition of Latent Fingerprints W
by Gas Chromatography–Mass Spectrometry
An Experiment for an Instrumental Analysis Course
Brittany Hartzell-Baguley, Rachael E. Hipp, Neal R. Morgan, and Stephen L. Morgan*
Department of Chemistry and Biochemistry, The University of South Carolina, Columbia, SC 29208;
*morgan@mail.chem.sc.edu
In the Laboratory
690 Journal of Chemical Education • Vol. 84 No. 4 April 2007 • www.JCE.DivCHED.org
The following steps of the procedure were used for both
collection methods. The vial was capped, shaken to mix, and
left to stand at ambient temperature. After 30 min, the extract
was removed from the beads or the cotton swab using a
disposable glass pipet, transferred to a new 4-mL vial, and
evaporated to dryness under a stream of nitrogen at ambient
temperature. For analysis, the extract was reconstituted with
25 µL of ethyl acetate and derivatized with 25 µL of N,Nbis(
trimethylsilyl)trifluoroacetamide (BSTFA). After adding
the derivatization agent, nitrogen was blown over the solution,
the vial was capped, and the solution mixed. The sample
was then heated at 90 C for 30 min and analyzed by GC–
MS as described above. Glass beads or glass slides without
deposited fingerprints were also taken through the extraction–
derivatization procedure to serve as a control.
Hazards
Caution must be used when working with chloroform,
ethyl acetate, and BSTFA. Chloroform is a cancer suspect
agent, ethyl acetate is flammable, and BSTFA is flammable,
corrosive, and a respiratory tract, skin, and eye irritant. These
chemicals should be used in a hood while wearing appropriate
gloves, eye protection, and a lab coat.
Results and Discussion
More fingerprint residue was typically obtained using the
glass bead method (as evaluated by abundance levels in total
ion chromatograms). However, we suggest use of a glass slide
substrate to provide the students with a more real-world
sample. Figures 1 and 2 show chromatograms of representative
fingerprint samples, obtained from glass beads and a glass
slide, respectively. Peaks were identified through library matching
with a NIST library of mass spectra (12). Squalene, the
biosynthetic precursor to steroids, was the largest peak observed
in most fingerprint samples. Other major constituents
identified included long chain fatty acids (saturated and unsaturated),
short chain fatty acids, and cholesterol. Certain
long chain fatty acids were present in all samples tested: myristic
acid (saturated C14), palmitoleic acid (unsaturated C16),
palmitic acid (saturated C16), oleic acid (unsaturated C18),
and stearic acid (saturated C18). However, the relative intensity
of these peaks varied widely among the different volunteers
tested. Short chain fatty acids that were identified in
some of the samples included octanoic and nonanoic acids.
In addition to differences in the relative quantities of
fatty acid compounds, chromatograms from female volunteers
were often found to contain signature cosmetic ingredients.
The substances observed included a wide variety of
high molecular weight hydrocarbons (tetracosane, octacosane,
etc.) likely from cosmetics containing petroleum jelly, and
octyl methyoxycinnamate, a common UVB sunscreen ingredient
or penetration enhancer in makeup. Figure 1 shows the
peak resulting from this latter compound at 21.5 min (peak
9). The volunteer that provided this fingerprint residue was
able to locate the likely source; the chemical was a major constituent
of her foundation makeup. Trace quantities of nicotine
could also be identified in chromatograms obtained from
smokers and initial experiments suggest that the quantity of
urea present in fingerprint residues is gender dependent.
Summary
This experiment enables students to gain a fundamental
knowledge of derivatization, gas chromatography, and
mass spectrometry. Furthermore, the forensic science aspect
of the laboratory can be used to stimulate student interest
while teaching how to use a common analytical instrument
to obtain a real-world measurement.
Acknowledgments
Rachael E. Hipp was supported by the Arnold and Mabel
Beckman Foundation Scholars Program. This work was also
partially supported by the University of South Carolina.
WSupplemental Material
Instructions for the students and notes for the instructor
are available in this issue of JCE Online.
Figure 2. Total ion chromatogram obtained from a male volunteer
after extracting his fingerprint residue from a glass slide. Peak identification:
(1) urea, (2) nonanoic acid, (3) dodecanoic acid, (4) myristic
acid, (5) palmitoleic acid, (6) palmitic acid, (7) oleic acid, (8)
stearic acid, and (9) squalene.
Figure 1. Total ion chromatogram obtained from a female volunteer
after extracting her fingerprint residue from glass beads. Peak identification:
(1) urea, (2) nonanoic acid, (3) dodecanoic acid, (4) myristic
acid, (5) palmitoleic acid, (6) palmitic acid, (7) oleic acid, (8)
stearic acid, (9) octyl methoxycinnamate, (10) squalene, and (11)
cholesterol.
In the Laboratory
www.JCE.DivCHED.org • Vol. 84 No. 4 April 2007 • Journal of Chemical Education 691
Literature Cited
1. Advances in Fingerprint Technology; Lee, H. C., Gaensslen, R.
E., Eds.; Elsevier Science Publishing Co.: New York, 1991.
2. Van Oorschot, R. A. H.; Jones, M. K. Nature 1997, 387, 767.
3. Van Hoofstat, D. E. O.; Deforce, D. L. D.; De Pauw, I. P. H.;
Van den Eeckhout, E. G. Electrophoresis 1999, 20, 2870–2876.
4. Archer, N. E.; Charles, Y.; Elliot, J. A.; Jickells, S. Forensic Sci.
Int. 2005, 154, 224–239.
5. Asano, K. G.; Bayne, C. K.; Horsman, K. M.; Buchanan, M.
V. J. Forensic Sci. 2002, 47, 1–3.
6. Mong, G. M.; Petersen, C. E.; Clauss, T. R. W. Advanced Fingerprint
Analysis Project: Fingerprint Constituents, Pacific Northwest National
Laboratory: Richland, WA; Sept. 1999. http://www.osti.gov/energycitations/
servlets/purl/14172-SQLzxz/webviewable/14172.pdf (accessed Jan 2007).
7. Williams, D. K.; Schwartz, R. L.; Bartick, E. G. Appl. Spectrosc.
2004, 58, 313–316.
8. Bartick, E.; Schwartz, R.; Bhargava, R.; Schaeberle, M.;
Fernandez, D.; Levin, I. Spectrochemical Analysis and
Hyperspectral Imaging of Latent Fingerprints. In Proceedings,
16th Meeting of the International Association of Forensic Sciences,
Montpellier, France, Sept 2–7, 2002.
9. Latent Fingerprint Composition, Victoria Forensic Science
Centre. http://www.nifs.com.au/F_S_A/Latent%20fingerprint%
20composition.pdf (accessed Jan 2006).
10. Integrated Automated Fingerprint Identification System. http://
www.fbi.gov/hq/cjisd/iafis.htm (accessed Jan 2006).
11. Mabbott, G. A. J. Chem. Educ. 1990, 67, 441–445.
12. NIST/EPA/NIH Mass Spectral Library with Search Program.
http://www.nist.gov/srd/nist1a.htm (accessed Jan 2007).
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