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Exam1.2a_Soln - IE 111 9:00 Section Exam 1.2a Fall 2011...

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IE 111 NAME _______Solutions___________ 9:00 Section Exam 1.2a Fall 2011 Instructions Open book, open notes Clearly indicate your answer You must show all relevant work and justify your answers appropriately Partial credit will be given, but not without sufficient support Factorials, permutations, combinations and other complex formulas do not need to be evaluated. You can leave as 4 C 2 for example. Cases where you should compute a final number are noted. Each question is worth 25 points My guess is that this is a long test. 100s 000000 Ave 78.54 90s 00022257 Med 83 80s 2235888 SD 19.39 70s 244488 60s 3789 50s 24 40s 3 30s 268
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Question 1 Consider the events shown in the Venn diagram above: Suppose P(A)=0.2 P(B)=0.1 P(C)=0.4 P(D)=0.3 P(A|B)=0.1. Suppose also that A and C are independent. (Please compute a final probability for each part). a) Find P(C ′∩ D) = 0 since (C ′∩ D)= b) Find P(C ′∩ D ) = P(C ) = 1-P(C) = 0.6 c) Find P(A ′∩ B ′∩ D) = P(D) = 0.3 d) Find P(A C D) = P(A C) = P(A)+P(C)- P(A C) = 0.2+0.4-(0.2)(0.4) = 0.52 e) Find P(A B) = P(A)+P(B)- P(A B)
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