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Unformatted text preview: Math 218 Final Examination: Spring 2009 Name (printed) Student ID Signature (handwritten) Instructions This exam consists of 13 pages including this cover page. Before starting the exam, check that you have all 13 pages. Please notice that the separately distributed sheet of tables is printed on both sides. There are ten problems and the point distribution among the problems is shown below. There are 200 points total. Answer all the problems. Please notice that the 4th and 10th problems take up two pages each. You may use a calculator as long as it is not capable of remote communication (eg no cell phones). You may refer to both sides of an 8.5 x 11 inch sheet of handwritten notes. No books or other notes are permitted. Numerical answers alone are not su cient. You must indicate how you derived your answers (show work) to obtain full credit. Points may be deducted if you do not justify your nal answer. Please indicate clearly if you continue your work on the back of the page. When an answer box is provided, put your nal answer in the box. When submitting a numerical answer that is a decimal, use the number of decimal places warranted by the data. When submitting an answer that is a fraction, reduce it to lowest terms. Be sure to include units in your answers where appropriate. If you cannot do part a) of some problem, but you need the answer for b), then you can get partial credit for showing you know what to do. You could write, \let p be the answer to a)," and solve b) in terms of p . Please check your lecture time and professor: 9:00 MWF (Yin) 9:00 MWF (Haskell) 10:00 MWF (Haskell) 10:00 MWF (Lin) 11:00 MWF (Lin) 11:00 MWF (Yin) 12:00 MWF (Voineagu) 12:00 MWF (Lin) 1:00 MWF (Voineagu) 1:00 MWF (Lytvak) 2:00 MW (Dumett) 2:00 MW (Lytvak) Do not write on this page below this line! 1 (20 pts) 6 (16 pts) 2 (20 pts) 7 (20 pts) 3 (20 pts) 8 (20 pts) 4 (22 pts) 9 (20 pts) 5 (20 pts) 10 (22 pts) (100 pts) (100 pts) Total Points 1 2 Problem 1 . A large credit card company nds that 70% of new cardholders pay their rst monthly bill in full. Moreover, 60% of those that pay their rst bill in full also pay their second bill in full. On the other hand, only 10% of those who pay less than the full amount the rst month, pay their second bill in full. a) Suppose 2 new cardholders are chosen at random. What is the probability that they both pay their rst monthly bill in full? (The number of new cardholders is so large that you need not worry about whether the choice is made with replacement or without.) a) b) Find the probability that a randomly chosen customer pays both her rst and second bills in full. b) c) Find the probability that a randomly chosen customer pays exactly one of her rst two bills in full....
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