Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). a. What are the 16 outcomes in ? b. Which outcomes are in the event that exactly three of the selected mortgages are fixed rate? c. Which outcomes are in the event that all four mortgages are of the same type? d. Which outcomes are in the event that at most one of the four is a variable-rate mortgage? e. What is the union of the events in parts (c) and (d), and what is the intersection of these two events? f. What are the union and intersection of the two events in parts (b) and (c)?
Problem 4E Answer: Step1: We have Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). Our goal is to find, a. What are the 16 outcomes in S b. Which outcomes are in the event that exactly three of the selected mortgages are fixed rate c. Which outcomes are in the event that all four mortgages are of the same type d. Which outcomes are in the event that at most one of the four is a variable-rate mortgage e. What is the union of the events in parts (c) and (d), and what is the intersection of these two events f. What are the union and intersection of the two events in parts (b) and (c) Step2: a). The 16 outcomes in S is given below table Home Mortgage Number Outcome 1 2 3 4 1 F F F F 2 F F F V 3 F F V F 4 F F V V 5 F V F F 6 F V F V 7 F V V F 8 F V V V 9 V F F F 10 V F F V 11 V F V F 12 V F V V 13 V V F F 14 V V F V 15 V V V F 16 V V V V Step3: b). The outcomes are in the event that exactly three of the selected mortgages are fixed rate is given below Outcome numbers = {4, 6, 7, 10, 11, 13.} (select rows which contains 2 V's and 2 F's) c). The outcomes are in the event that all four mortgages are of the same type is given below Outcome numbers = {1, 16.(select rows which contains 4 V's and 4 F's ) Step4: d). The outcomes are in the event that at most one of the four is a variable-rate mortgage is given by Outcome numbers = {1, 2, 3, 5(select rows which contains 3 F's or more than 3 F's) e). The Union: outcomes = {1, 2, 3, 5, 9, 16.} (The union is D with FFFF, that is VVVV, FFFF, VFFF, FVFF, FFVF, FFFV) The Intersection: outcome =(The intersection is D with FFFF, that is the only common element is FFFF) f). The Union: outcomes = {1, 4, 6, 7, 10, 11, 13, 16.} (B and C are disjoint sets, that is VFFF, FVFF, FFVF, FFFV, VVVV, FFFF BandC = Empty).
