Matthew Petroccio Section 003 910734059 mjp5641 Fall 2015 - EBF 304W Homework 3 Due: Thursday, 19 November 2015, in class 50 points Instructions: Each of the following questions is worth 10 points. Please answer all questions clearly and completely. If you use graphs or tables in your answers, they must be clear enough that I can understand them (this means labeling axes, variables, and so forth). If a question requires you to make calculations, you must show your work. If you make calculations using Excel, please include your spreadsheet output as an appendix. Your homework must be typed up and pages must be stapled togetherI will not accept homework that is handwritten or unstapled. See the syllabus for other formatting details. Question 1 (10 points): Write a few sentences arguing that the inhalation of second-hand smoke is a voluntary risk. Answer: Second hand smoke may seem out of someone's control but it is a voluntary risk. If a person is smoking near you, you have the option of moving out of their radius of smoke. Nothing is forcing you to inhale the smoke, which makes the situation very avoidable. This is a risk that is deliberately at an individual level. Question 2 (10 points): Write a few sentences arguing that the inhalation of second-hand smoke is an involuntary risk. Answer: Second hand smoke is an involuntary risk. This because you are not the one smoking the cigarette, therefore, you have no control over the smoke being created. If you were to smoke the cigarette yourself, you would be able to stop and the situation would not happen. In the case of second hand exposure, you have no control over the cigarette being smoked in the first place. Question 3 (10 points): Producing gas from the shale formations requires drilling through the water table to access the shale formations at greater depths. The wells are typically \"cased\" with concrete and steel sleeves to prevent natural gas or fracturing fluids from entering the water table. A single well may have multiple layers of casing. Suppose that the failure rate for a single layer of casing in a single well was 1 in 1,000. A typical Marcellus shale well might have three casing layers. What is the probability of methane contamination from three faulty casings in a Marcellus shale well? Assume that the failure rate for casings are all independent. Page 1 of 2 Matthew Petroccio Section 003 910734059 mjp5641 Answer: 1/1000 = .001 and with 3 casing layers per well, you take .001^3 finding that the probability of contamination is .000000001% Question 4 (10 points): Many Pennsylvania households have had methane-tainted water even without natural gas drilling. Suppose that 10% of households have high background levels of methane in their drinking water prior to the onset of natural gas drilling. Suppose also that the probability of a casing failure leading to an elevated level of methane in drinking water is 95%. Suppose that a household living near a natural gas drilling site observes a high level of methane in their water. What is the likelihood that the high methane level was caused by a failed well casing? Assume a single-cased well for this example. Answer: P(High Methane) = .1 P(High Methane/Faulty Well Casing) = .95 (P(High Methane/Faulty Well Casing) x (P(Faulty Well Casing)) P(High Methane) (.95 x .001) (.1) = .0095 = .95% Question 5 (10 points): Failure Rate = .001 In a well-known incident in Susquehanna County, fifteen families had their well water contaminated with methane. Assume that there were 50 wells drilled in the area of the contamination, and each was single-cased. Further assume that each well could contaminate at most one drinking water source. Using the Poisson model, calculate the likelihood of fifteen casing failures. K = 1/1000 x 50 = .05 X = 15 (e^-.05 x .05^15) / (15)! = 2.219e^-32 Likelihood of fifteen casing failures = 2.219e^-32 % Page 2 of 2