An academic department with five faculty members—Anderson, Box, Cox, Cramer, and Fisher—must select two of its members to serve on a personnel review committee. Because the work will be time-consuming, no one is anxious to serve, so it is decided that the representative will be selected by putting the names on identical pieces of paper and then randomly selecting two. a. ?What is the probability that both Anderson and Box will be selected? [?Hint: List the equally likely outcomes.] b. ?What is the probability that at least one of the two members whose name begins with ? ?is selected? c. ?If the five faculty members have taught for 3, 6, 7, 10, and 14 years, respectively, at the university, what is the probability that the two chosen representatives have a total of at least 15 years’ teaching experience there?

Problem 27E Answer: Step1: We have An academic department with five faculty members—Anderson, Box, Cox, Cramer, and Fisher—must select two of its members to serve on a personnel review committee. Because the work will be time-consuming, no one is anxious to serve, so it is decided that the representative will be selected by putting the names on identical pieces of paper and then randomly selecting two. Our goal is to find, a. What is the probability that both Anderson and Box will be selected b. What is the probability that at least one of the two members whose name begins with C is selected c. If the five faculty members have taught for 3, 6, 7, 10, and 14 years, respectively, at the university, what is the probability that the two chosen representatives have a total of at least 15 years’ teaching experience there Step2: Let us assume that, Anderson - A, Box - B, Cox - Co, Cramer - Cr, Fisher - F. The possible outcomes are {(A, B), (A, Co), (A, Cr), (A, F), (B, Co), (B, Cr), (B, F), (Co, Cr), (Co, F), (Cr, F)} a). The probability that both Anderson and Box will be selected is given by no. of favourable event P( both Anderson and Box will be selected) = total no. of events = 1 10 = 0.1 Therefore, P( both Anderson and Box will be selected) = 0.1. b). The probability that at least one of the two members whose name begins with C is selected is given by P(at least one C) = {(A, Co), (A, Cr), (B, Co), (B, Cr), (Co, Cr), (Co, F), (Cr, F)} total no. of events = 7 10 = 0.7 Therefore, P(at least one C) = 0.7. Step3: c). P(at least 15 years) = {(3, 14), (6, 10), (6, 14), (7, 10), (7, 14), (10, 14)} total no. of events = 6 10 = 0.6 Therefore, P(at least 15 years) = 0.6.