Probability Assignment

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). PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET AN AMAZING DISCOUNT :)