Exam 3 A. Miller Spring 2008 Math 240 0No notes, no books, no calculators, no cell phones, no pagers, no electronicdevices of any kind.NameCircle your Discussion Section:DIS 301 9:55 T B305 VAN VLECKDIS 302 9:55 R 115 INGRAHAMDIS 305 1:20p T B105 VAN VLECKDIS 306 1:20p R B333 VAN VLECKProblem Points Score1 202 203 204 205 20Total 100Solutions will be posted shortly after the exam:www.math.wisc.edu/∼miller/m240Exam 3 A. Miller Spring 2008 Math 240 11. (20 pts) Define f inductively as follows:f(x, 0) = x2f(x, n + 1) = (f (x, n) + x)2(a) Give a recursive algorithm for computing f.(b) Give an iterative algorithm for computing f.Exam 3 A. Miller Spring 2008 Math 240 22. (20 pts) Seventeen people on a basketball team show up to play.(a) How many ways are there to choose a team of five players? (i.e., withno assigned positions).(b) Three who showed up are Seniors and five are Freshman. How manyways are there to choose a team of five (as in part (a)) if at least one playermust be a Senior but no player is a Freshman?Exam 3 A. Miller Spring 2008 Math 240 33. (20 pts)(a) What is the coefficient of x3in the expansion of (2x − 1)8?(b) A fair die is rolled 8 times. What is the probability that it comes up6 exactly 3 times?Exam 3 A. Miller Spring 2008 Math 240 44. (20 pts) A snack food company is planning to introduce a new product,crunchyballsofsaltfatandsugar. The company commissions a marketing re-port for each new product which predicts its success. Of all new productsproduced by the company 30% have been a success. Furthermore 70% oftheir successful products were predicted be forehand to be a success whileonly 40% of the failed new products were predicted to be successful. Whatis the probability that their new snack food will be a success given that themarketing report has predicted it will be successful?Exam 3 A. Miller Spring 2008 Math 240 55. (20 pts) The final exam in M240 consists of 20 True-False problems and10 Multiple-Choice problems. Suppose that Max has a probability of 75%of getting a True-False question right and 60% of getting multiple choiceproblem correct. If T-F questions are 3 points each and M-C are 4 pointseach, what is the expected value of Max’s score on the final?Exam 3 A. Miller Spring 2008 Math 240 6Answers1.(a)function f(x, n)if n = 0, output x2else ouput f(x, n − 1)(b)input (x, n)z = x2For i = 1 to n:z = (z + x)2next ioutput z2. (a) C(17, 5) (b) C(12, 5) − C(9, 5)3. (a) (−8)C(8, 3) (b) C(8,3)(16)3(56)54.375.