Exam1.1a_Soln - IE 111 8:00 Section Exam 1.1a Fall 2011...

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IE 111 NAME _______Solutions___________ 8:00 Section Exam 1.1a 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.
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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. Suppose also that A and C are independent. (Please compute a final probability for each part). a) Find P(A ′∩ B) = 0 since (A ′∩ B) = b) Find P(A ′∩ B ) = P(A ) = 1-P(A) = 0.8 c) Find P(A ′∩ B ′∩ D) = P(D) = 0.3 d) Find P(A B D) = P(A D) = P(A)+P(D) = 0.5 (A and D are M.E.) e) Find P(A C) = P(A)+P(C)-P(A C) = P(A)+P(C)-P(A)P(C) = 0.2 + 0.4 - (0.2)(0.4) = 0.52 Question 2
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