OldExams1-1 - IE 111 Fall 2006 Exam 1.1.1 NAME Instructions...

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IE 111 Fall 2006 Exam 1.1.1 NAME _________________________ Instructions The test is open notes and open book You must show all relevant work to receive full credit. Answers involving factorials, combinations and permutations need not be calculated out. Question 1. Consider the Venn diagram at right with events A, B, C, and D as shown when you answer questions a) through e). a) Give a set representation of the shaded region, _______________________ Circle the most appropriate answer for each of the following questions (where NMI means “need more information”). b) T F NMI (A B ) D and (A D) C are mutually exclusive. c) T F NMI B and C are independent d) T F NMI P(A|B) ≥ P(B|A) e) T F NMI P(B) ≤ P(D) Question 2. The Tigers and Phillies have split the first 4 games of the World Series (each team has won two games). Thus we now have a best 2 out of 3 series. The probability that either team wins game 5, 6, and 7 (if game 7 is necessary) varies because of the different pitchers and home field advantage. The probability that the Tigers win game five is 0.7. The probability that the Tigers win game 6 is 0.4. The probability that the Tigers win game 7 is 0.5. The outcome of each game is independent of other games. a) Find the probability that the Tigers win the World Series. b) Given that the Phillies win game five, find the probability that the Tigers win the World Series Question 3. I have two urns. Urn A has 1 red ball and 3 black balls. Urn B has 2 red balls and 2 black balls. Suppose I first pick an urn at random, then pick a ball from that urn. a) What is P(I get a red ball)? C A B S D
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b) After picking the first ball, find P(I chose urn A | the ball is red) c) If I continue the process, that is pick an urn at random, pick a ball, do not replace the ball; pick an urn at random, pick a second ball without replacement; etc. Find P(the first 3 balls chosen are all red) Question 4. A company plans to build 6 new warehouses. 13 sites are available for this purpose. Sites 1 thru 6 are in Pennsylvania, sites 7 thru 10 are in New Jersey, and sites 11 thru 13 are in Maryland a) How many ways are available to build 6 warehouses on 13 sites? b) Suppose one warehouse must be located on site #7. Now how many ways are there? c) Suppose at least 4 warehouses must be built in PA. Now how many ways are there? d) Suppose each of the six warehouses store different goods. How does this change your answer to part a)? e) If each configuration is equally likely, what is the probability that there will be a warehouse on site #3?
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IE 111 Fall 2006 Exam 1.2.2 NAME _________________________ Instructions The test is open notes and open book You must show all relevant work to receive full credit. Answers involving factorials, combinations and permutations need not be calculated out. Question 1. A, B, and C are events. P(A)=0.51. P(B)=0.38 and P(C)=0.53. Events A and B are mutually exclusive. B and C are independent. Find the following: a) P(C ) b) P(A B) c) P(A B) d) P(C|B) e) P(B C) f) P(B |A) Question 2.
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