Explanation Given: 23% chance that a humanities major will change to a science major from one year to the next. 40% chance that a humanities major will change to undecided. Science major will change to humanities with probability .12 and to undecided with probability 0.38 .An undecided student will switch to humanities or science with probabilities of .45 and .28, respectively. Formula used: V P = V Here, V is the equilibrium vector and P is the transition matrix. Calculations: Use the property that total probability of an event is unity. From the given information, the following transition matrix: Changed to Humanity Changed to Science Changed to Uncecided Humanity Science Undecided [ 0.37 0.12 0.45 0.23 0.50 0.28 0.4 0.38 0.27 ] Let’s take this transition matrix to be, P = [ 0.37 0.23 040 0.12 0.50 0.38 0.45 0.28 0.27 ] For long-run probability, we need to find the equilibrium vector. Let’s assume equilibrium vector to be V = [ v 1 v 2 v 3 ] From the property of equilibrium vector. V P = V Now put the corresponding matrices as, [ v 1 v 2 v 3 ] [ 0.37 0.23 0.40 0.12 0.50 0.38 0.45 0.28 0.27 ] = [ v 1 v 2 v 3 ] Simplified to get; [ 0.37 v 1 + 0.12 v 2 + .045 v 3 0.23 v 1 + 0.50 v 2 + 0.28 v 3 0.40 v 1 + 0.38 v 2 + 0.27 v 3 ] = [ v 1 v 2 v 3 ] Now equate both sides as, 0.37 v 1 + 0.12 v 2 + .045 v 3 = v 1 ; 0.23 v 1 + 0.50 v 2 + 0.28 v 3 = v 2 and 0.40 v 1 + 0.38 v 2 + 0.27 v 3 = v 3 Simplify to get; 0.63 v 1 − 0.12 v 2 − .045 v 3 = 0 ; 0.23 v 1 − 0.50 v 2 + 0.28 v 3 = 0 and 0.40 v 1 + 0.38 v 2 − 0.73 v 3 = 0 Here, observe that adding the 2 nd and 3 rd equations obtained above reproduces the 1 st equation itself. Therefore, overall only two equations here. 0.23 v 1 − 0.50 v 2 + 0.28 v 3 = 0 …...…... (1) 0.40 v 1 + 0.38 v 2 − 0.73 v 3 = 0 …...…... (2) Also, from the property of equilibrium vector that the sum of all its entries must be equal to unity. Thus, v 1 + v 2 + v 3 = 1 …...…... (3) Now write equations (1), (2) and (3) in matrix form as, [ 0.23 − 0.50 0.28 0.40 0

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

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Chapter 9.5, Problem 42E

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To calculate: The long-range prediction for the fraction of students in humanities majors, science majors, or undecided.

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Chapter 9.5, Problem 43E

Chapter 9.5, Problem 44E

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Chapter 9 Solutions

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

Ch. 9.1 - Checkpoint 1 (a) Give the probability distribution...Ch. 9.1 - Checkpoint 2 Find the expected value of the number...Ch. 9.1 - Prob. 3CP Ch. 9.1 - Prob. 4CP Ch. 9.1 - Prob. 5CP Ch. 9.1 - Prob. 6CP Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E

Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - 44. Physical Science One of the few methods that...Ch. 9.1 - Prob. 43E Ch. 9.1 - Find the expected number of returns per...Ch. 9.2 - Prob. 1CP Ch. 9.2 - Prob. 2CP Ch. 9.2 - Prob. 3CP Ch. 9.2 - Prob. 4CP Ch. 9.2 - Prob. 5CP Ch. 9.2 - Prob. 6CP Ch. 9.2 - Prob. 7CP Ch. 9.2 - Prob. 8CP Ch. 9.2 - Prob. 9CP Ch. 9.2 - Prob. 10CP Ch. 9.2 - Checkpoint 10 Solve the problems in Example 14. Ch. 9.2 - Prob. 12CP Ch. 9.2 - Prob. 13CP Ch. 9.2 - Prob. 14CP Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Evaluate the given factorials, permutations, and...Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Use a calculator to find values for Exercises...Ch. 9.2 - Use a calculator to find values for Exercises...Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Use a calculator to find values for Exercises...Ch. 9.2 - Use a calculator to find values for Exercises...Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Use the multiplication principle to solve the...Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - 37. Define permutation in your own words. Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Prob. 44E Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Prob. 47E Ch. 9.2 - Prob. 48E Ch. 9.2 - Prob. 49E Ch. 9.2 - Prob. 50E Ch. 9.2 - Prob. 51E Ch. 9.2 - Prob. 52E Ch. 9.2 - Prob. 53E Ch. 9.2 - Prob. 54E Ch. 9.2 - Prob. 55E Ch. 9.2 - Prob. 56E Ch. 9.2 - Prob. 57E Ch. 9.2 - Prob. 58E Ch. 9.2 - Prob. 59E Ch. 9.2 - Prob. 60E Ch. 9.2 - Prob. 61E Ch. 9.2 - Prob. 62E Ch. 9.2 - Prob. 63E Ch. 9.2 - Prob. 64E Ch. 9.2 - Prob. 65E Ch. 9.2 - Prob. 66E Ch. 9.2 - Prob. 67E Ch. 9.2 - Prob. 68E Ch. 9.2 - Prob. 69E Ch. 9.2 - Prob. 70E Ch. 9.2 - Prob. 71E Ch. 9.2 - Prob. 72E Ch. 9.3 - Checkpoint 1 The ski club has 8 women and 7 men....Ch. 9.3 - Checkpoint 2 A batch of 15 granite slabs is mined,...Ch. 9.3 - Checkpoint 3 Find the probability of being dealt a...Ch. 9.3 - Checkpoint 4 Martha, Leonard, Calvin, and Sheila...Ch. 9.3 - Checkpoint 5 Evaluate (a) n = 3; (b) n = 6. Ch. 9.3 - Prob. 6CP Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Find the probability that the 2-card hand in...Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Natural Science A shipment contains 8 igneous, 7...Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - 27. Example 16 in Section 9.2 shows that the...Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - For Exercises 32–34, refer to Example 6 in this...Ch. 9.3 - For Exercises 32–34, refer to Example 6 in this...Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Prob. 37E Ch. 9.3 - Prob. 38E Ch. 9.4 - Checkpoint 1 Find the probability of obtaining ...Ch. 9.4 - Checkpoint 2 According to the study in Example 1,...Ch. 9.4 - Prob. 3CP Ch. 9.4 - Prob. 4CP Ch. 9.4 - Prob. 5CP Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - Prob. 18E Ch. 9.4 - Prob. 19E Ch. 9.4 - Prob. 20E Ch. 9.4 - Prob. 21E Ch. 9.4 - Labor Force According to data from the US. Bureau...Ch. 9.4 - Prob. 23E Ch. 9.4 - Prob. 24E Ch. 9.4 - Prob. 25E Ch. 9.4 - Prob. 26E Ch. 9.4 - Prob. 27E Ch. 9.4 - Prob. 28E Ch. 9.4 - Prob. 29E Ch. 9.4 - Prob. 30E Ch. 9.4 - Prob. 31E Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 33E Ch. 9.4 - Prob. 34E Ch. 9.4 - Prob. 35E Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 37E Ch. 9.4 - Prob. 38E Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - Prob. 41E Ch. 9.4 - Prob. 42E Ch. 9.4 - Prob. 43E Ch. 9.4 - Prob. 44E Ch. 9.5 - Prob. 1CP Ch. 9.5 - Prob. 2CP Ch. 9.5 - Prob. 3CP Ch. 9.5 - Prob. 4CP Ch. 9.5 - Prob. 5CP Ch. 9.5 - Prob. 6CP Ch. 9.5 - Prob. 1E Ch. 9.5 - Prob. 2E Ch. 9.5 - Prob. 3E Ch. 9.5 - Prob. 4E Ch. 9.5 - Prob. 5E Ch. 9.5 - Prob. 6E Ch. 9.5 - Prob. 7E Ch. 9.5 - Prob. 8E Ch. 9.5 - Prob. 9E Ch. 9.5 - Prob. 10E Ch. 9.5 - Prob. 11E Ch. 9.5 - Prob. 12E Ch. 9.5 - Prob. 13E Ch. 9.5 - Prob. 14E Ch. 9.5 - Prob. 15E Ch. 9.5 - Prob. 16E Ch. 9.5 - Prob. 17E Ch. 9.5 - Prob. 18E Ch. 9.5 - Prob. 19E Ch. 9.5 - Prob. 20E Ch. 9.5 - Prob. 21E Ch. 9.5 - Prob. 22E Ch. 9.5 - Prob. 23E Ch. 9.5 - Prob. 24E Ch. 9.5 - Prob. 25E Ch. 9.5 - Prob. 26E Ch. 9.5 - Prob. 27E Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 30E Ch. 9.5 - Prob. 29E Ch. 9.5 - Prob. 31E Ch. 9.5 - Prob. 32E Ch. 9.5 - Prob. 33E Ch. 9.5 - Prob. 34E Ch. 9.5 - Prob. 35E Ch. 9.5 - Prob. 36E Ch. 9.5 - Prob. 38E Ch. 9.5 - Prob. 37E Ch. 9.5 - 40. Business An insurance company classifies its...Ch. 9.5 - Prob. 40E Ch. 9.5 - Prob. 41E Ch. 9.5 - Prob. 43E Ch. 9.5 - Prob. 42E Ch. 9.5 - Prob. 44E Ch. 9.5 - Prob. 45E Ch. 9.5 - Prob. 46E Ch. 9.6 - Prob. 1CP Ch. 9.6 - Prob. 2CP Ch. 9.6 - Prob. 3CP Ch. 9.6 - Prob. 1E Ch. 9.6 - Prob. 2E Ch. 9.6 - Prob. 3E Ch. 9.6 - Prob. 4E Ch. 9.6 - Prob. 5E Ch. 9.6 - Prob. 6E Ch. 9.6 - Prob. 7E Ch. 9.6 - Prob. 8E Ch. 9.6 - Prob. 9E Ch. 9.6 - Prob. 10E Ch. 9 - Prob. 1RE Ch. 9 - In Exercises 1–4, (a) sketch the histogram of the...Ch. 9 - In Exercises 1–4, (a) sketch the histogram of the...Ch. 9 - In Exercises 1–4, (a) sketch the histogram of the...Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Games of Chance Solve the given problems. Business...Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Solve the given problems. 14. How many variations...Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 1CE Ch. 9 - Prob. 2CE Ch. 9 - Prob. 3CE Ch. 9 - Prob. 4CE Ch. 9 - Prob. 5CE Ch. 9 - Prob. 1EP Ch. 9 - 2. Investigate whether your own state or a state...

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