Business Mathematics ISample Midterm Examination 1This test is only presented as a sample of the types of questions that might appear on an examination. The instructor of each section will set his or her own examinations, which may differ from the sample in both length and content.Show all of the steps and all of the work that you use to solve each problem. A list of formulas that you may find useful is provided on the last page of this test1. (16 points) Let I be the event that IBM stock goes up or stays the same tomorrow and let H be theevent that Hewlett-Packard stock goes up or stays the same tomorrow. We believe that P(I) = 0.6, P(H) = 0.3,and P(I or H) = 0.7.(i) What is the probability that IBM and Hewlett-Packard both go up or stay the same tomorrow?(ii) What is the probability that IBM and Hewlett-Packard both go down tomorrow?(iii) What is the real-world interpretation of the statement “P(I) = 0.6?”2. (16 points) X is a random variable that can assume only the values 1, 2, 3, or 10. These have thefollowing probabilities.x 1 2 3 10P(X = x) 0.2 0.5 0.2 0.1(i) Compute P(1 X 3).(ii) Compute E(X).(iii) Compute 3. (16 points) A box contains a one dollar bill and a five dollar bill. You are to draw, at random, one billfrom the box, note its value, and then replace it in the box. Next you draw a second time and note the value ofthe bill that you draw. Let X be the random variable that is the total value of the two bills that you have drawn.(i) Give a sample space S listing the four possible outcomes of the experiment and assign realisticprobabilities to each outcome.(ii) Compute the expected value of X.(iii) What is the real-world interpretation of the number that you found in part (ii)? .21iiXP© 2001 by The Arizona Board of Regentsfor The University of Arizona.All rights reserved.- Business Mathematics I, Sample Test 1: page 2 -4. (16 points) There is a 30% chance of the event E that the economy will go into a recession and a 20%chance of the event J that Johnson Controls, Inc. will go bankrupt. The chance that the economy goes into arecession and that Johnson Controls will go bankrupt is 10%.(i) If we know that Johnson Controls has gone into bankruptcy, what is the probability that the economywill go into a recession?(ii) Are the events that the economy goes into a recession and that Johnson Controls goes bankruptindependent? Why or why not?5. (12 points) Let C be the event that a person likes Coca-Cola better than Pepsicola, and let W be theevent that a person prefers Wendy’s to McDonald’s. Market research has shown that P(C) = 0.6 and that P(W)= 0.7. We assume that soda preference and fast food preference are independent. Find the probability that arandomly selected person prefers Coke, but does not prefer Wendy’s over McDonald’s.6. (12 points) There is a 30% chance that the Federal Reserve raises interest rates and a 70% chance thatthey do not raise rates. If the Federal Reserve raises interest rates, there is an 80% chance that stock priceswill fall. If the Federal Reserve does not raise rates, there is an 40% chance that stock prices will fall. Let Fbe the event that stock prices fall, R be the event that the Federal Reserve raises interest rates, and S be the eventthat the Federal Reserve does not raise rates. Compute P(F).7. (12 points) The following data shows the records of 10 attempted loan work outs at Acadia Bank. Weare going to pick a person at random from current borrowers who are behind in their payments and attempt aloan work out. Consider two events.S: The work out succeeds.H: The borrower selected has High School as his or her highest education level.ResultCustomer NumberFormer BankYears In BusinessEducation LevelState Of EconomyLoan Paid Back?1 BR 3 yes2 Cajun High School yes3 DuPont Normal no4 Cajun High School no5 DuPont Boom yes6 Cajun High School no7 Cajun Graduate Degree yes8 BR 8 no9 DuPont Boom no10 Cajun Bachelor's Degree noBorrowerBank Information- Business Mathematics I, Sample Test 1: page 3 -Use the data to estimate the following.(i) P(S)(ii) P(S|H)Formulas FEPFPEPFEP )()( )(1 EPEPC CCCFEFE CCCFEFE xxXPxXEall)()(
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