Appm 3750 Exam 1 Sp13

APPM 3570 — Exam #1 — February 20, 2013 On the front of your bluebook, write (1) your name, (2) 3570/EXAM 1, (3) instructor’s name (Bhat or Kleiber), (4) SPRING 2013 and draw a grading table with space for 4 problems. Do only 4 of 5 problems. On the front of your blue book, write down which 4 problems you are attempting, if you do more than 4 problems, only the first 4 problems done will be graded. Correct answers with no supporting work may receive little or no credit. Start each problem on a new page in your bluebook. At the end of the exam, please sign the honor code pledge printed on your bluebook. No books, notes or electronic devices of any kind are allowed. Show all work, justify your answers. 1. (25 pts) Suppose events A, B and C, all defined on the same sample space, have the following probabilities: P(A) = 0.22, P(B) = 0.25, P(C) = 0.28, P(A ∩ B) = 0.11, P(A ∩ C) = 0.05, P(B ∩ C) = 0.07 and P(A ∩ B ∩ C) = 0.01. For each of the following parts, your answer should be in the form of a complete mathematical statement. (a) Let D be the event that at least one of A, B, C occurs. Describe D using set notation and a Venn diagram. Find P(D). (b) Let E be the event that exactly one of A, B, and C occurs. Describe E using set notation and a Venn diagram. Find P(E). (c) What is the probability that A will occur and B will not occur? (d) Given that A has occurred, compute the probability that B will occur. (e) Given that at least one of the three events has occurred, compute the probability that all three events will occur. 2. (25 pts) A mechanic at a local car dealership is parking cars in a lot. The mechanic plans to park 4 Hondas, 4 Toyotas and 2 Subarus in a row, with all orderings equally likely. (a) Carefully define the sample space. (b) How many ways are there to park the cars in a row if each car is distinct? What about if we only identify each car by its manufacturer? (c) Suppose the cars are randomly parked in a row, find the probability that two Subarus are