Question 2: A survey in the U.S. asked companies about the procedures they use in hiring. Only 54% of the responding companies review the applicant's university results as part of the hiring process, and only 44% consider faculty references. Assume that these percentages are also true for the population of companies in Canada and that 35% of all companies use both the applicant's university results and faculty references. 1. What is the probability that a randomly selected company uses either faculty references or university results as part of the hiring process? 2. What is the probability that a randomly selected company uses either faculty references or university results but not both as part of the hiring process? 3. What is the probability that a randomly selected company uses neither faculty references nor university results as part of the hiring process? 4. Construct a probability matrix for this problem and indicate the locations of your answers for parts (a), (b), and (c) on the matrix.

Question 3: Suppose that in Guelph, 30% of the families have a MasterCard, 20% have an American Express card, and 25% have a Visa card. Eight percent of the families have both a MasterCard and an American Express card. Twelve percent have both a Visa card and a MasterCard. Six percent have both an American Express card and a Visa card. No families have all three cards. 1. What is the probability of selecting a family that has either a Visa card or an American Express card? 2. If a family has a MasterCard, what is the probability that it has a Visa card? 3. If a family has a Visa card, what is the probability that it has a Master- Card? 4. Is possession of a Visa card independent of possession of a MasterCard? Why or why not? 5. Is possession of an American Express card mutually exclusive of possession of a Visa card?

Question 4: Given X = {1, 3, 5, 7, 8, 9}, Y = {2, 4, 7, 9}, and Z = {1, 2, 3, 4, 7}, solve the following. 1. A = (X Y ) Z 2. B = (Y Z) (X Y