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SOCY601_HW3_Probability_F02_D1

Course: SOCY 601, Fall 2008
School: Maryland
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Word Count: 644

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601--Neustadtl SOCY/SURV Fall 2002 Homework #3--Elementary Probability Due November 5th, 2002 1. Explain why each of the following situations involves a random trial and list the appropriate number of outcomes of the trial: a) A pilot is about to start three engines of the aircraft. The number of engines that start without trouble is of interest. List all possible outcomes. b) A police squad is about to begin its...

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601--Neustadtl SOCY/SURV Fall 2002 Homework #3--Elementary Probability Due November 5th, 2002 1. Explain why each of the following situations involves a random trial and list the appropriate number of outcomes of the trial: a) A pilot is about to start three engines of the aircraft. The number of engines that start without trouble is of interest. List all possible outcomes. b) A police squad is about to begin its night patrol. The number of incidents the squad investigates that night is of interest. Discuss the possible outcomes. c) A person mails a letter. How many days later the letter reaches its destination is of interest. Assume that after seven days the letter is lost. List all possible outcomes. 2. Two reviewers (1, 2) of academic manuscripts screen all submitted articles. Each reviewer assigns a grade of good (G), fair (F), or poor (P) to a manuscript. a) Describe the sample space for the outcomes of the joint review of a manuscript. b) Is this sample space univariate or bivariate? Explain your answer. c) Let E1 denote the event that at least one reviewer assigns a grade of G. What basic outcomes constitute this outcome? What basic outcomes constitute the compliment of E1? d) Let E2 denote the event that the reviewers give different grades. What basic outcomes constitute the compliment of E2? e) Are E1 and E2 mutually exclusive events? Complimentary events? Explain your answer. f) List the basic outcomes constituting each of the following events: E1 E2 ; E1 E2 ; E1 E2 ; E1 E2 3. On the wheel is an array of numbered compartments referred to as "pockets". The pockets are red, black, or green. The numbers 1 thru 36 are evenly split between red and black, while 0 and 00 are green pockets. Instead of being randomly placed around the wheel, the numbers are ordered to try and achieve balance between both black and red, high and low, and odds evens. and A ball is rolled around the wheel and lands in one of the pockets; we assume that each pocket has equal probability of 1/38. Assume that we are interested in the number, the color, or both of the pocket in which the ball falls: a) b) c) d) e) f) g) Let A={0, 00}. Give the value of P(A). Let B={14, 15, 17, 18}. Give the value of P(B). Let C={odd}. Give the value of P(C). Let D={green}. Give the value of P(D). Let E={red}. Give the value of P(E). Let F={black and 14}. Give the value of P(F). Let G={black or red}. Give the value of P(G). 2 4. The probability of a certain type of smoke detector functioning properly is 0.8. If you have two of these installed in your home, what is the probability that at least one of them functions during a fire? Assume that the smoke detectors operate independently. *** HINT *** If P(E) = at least one functioning, what is P(not E)? How many smoke detectors would you need so that the probability of at least one functioning is 0.99 or greater? 5. Use the 2000 GSS data and SDA (www.webuse.umd.edu) to answer this question. What is the probability distribution associated with th...

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