# EXAM 1-B - STAT 400 Fall 2011 Version B Name BD1 Th 2:30...

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STAT 400 Fall 2011 Name ANSWERS . Version B BD1 BD2 BD3 BD4 Th 2:30 We 4:00 We 4:00 Th 2:30 317 DKH 165 Noyes 143 Altgeld 328 Armory Srijan Sengupta Srijan Sengupta Robert Eisinger Robert Eisinger Exam 1 Please circle your discussion section. Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. The exam is closed book and closed notes. You are allowed to use a calculator and one 8½" x 11" sheet with notes. Page 1 2 3 4 5 6 7 Total Earned / 70

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1. (5) For an anthropology final exam, the instructor will randomly select 3 short essay questions out of 10 possible questions that were announced a week before the exam. The students then can choose any 2 questions out of these 3. Alex did not have enough time to prepare answers for all 10 questions, he prepared answers to only 6. (That is, there are 6 “good” questions and 4 “bad” questions.) What is the probability that Alex has answers prepared for at least 2 out of the 3 questions selected by the instructor for the exam? (That is, what is the probability that there will be at least 2 “good” questions among the 3 questions selected by the instructor?) 10 10 b B or b B 6 4 6 4 “good” “bad” “good” “bad” ± ± ± ± 2 1 3 0 3 10 0 4 3 6 3 10 1 4 2 6 C C C C C C + = 120 1 20 120 4 15 + = 120 80 = 3 2 0.66667 . OR G G B 8 4 9 5 10 6 = 6 1 G B G 8 5 9 4 10 6 = 6 1 B G G 8 5 9 6 10 4 = 6 1 G G G 8 4 9 5 10 6 = 6 1 6 1 × 3 + 6 1 = 3 2 0.66667 .
2. (5) A local meteorologist noticed that if it rains on Saturday, then the probability that it also rains on Sunday is 0.70. However, if it does not rain on Saturday, then the probability that it rains on Sunday is only 0.20. Suppose that the probability that it rains on Saturday is 0.30. Suppose one week it rained on Sunday. What is the probability that it also rained on Saturday?

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EXAM 1-B - STAT 400 Fall 2011 Version B Name BD1 Th 2:30...

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