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Advertising Use the following information for Problems 36 and 37. A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially, the probabilities that a customer patronizes A, B, or C are 0.2,0.6, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect. If A runs the advertising campaign for 3 weeks, find the probability of a customer patronizing each business in the third week.

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Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340

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Chapter
Section
BuyFindarrow_forward

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340
Chapter 7.7, Problem 36E
Textbook Problem
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Advertising Use the following information for Problems 36 and 37. A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially, the probabilities that a customer patronizes A, B, or C are 0.2,0.6, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect.

Chapter 7.7, Problem 36E, Advertising Use the following information for Problems 36 and 37. A local business A has two

If A runs the advertising campaign for 3 weeks, find the probability of a customer patronizing each business in the third week.

To determine

To calculate: The third probability vector if the transition matrix is P=(0.70.20.10.40.40.20.40.40.2) and initial probability vector is A0=[0.20.60.2].

Explanation of Solution

Given Information:

The transition matrix is;

P=(0.70.20.10.40.40.20.40.40.2)

And initial probability vector is;

A0=[0.20.60.2]

Formula used:

The probability vectors depend on the initial probability vector and transition matrix. They are given as;

An=A0Pn

Calculation:

The transition matrix is;

P=(0.70.20.10.40.40.20.40.40.2)

And initial probability vector is;

A0=[0.20.60.2]

Use the formula to calculate the first stage probability vector as;

A1=[0.20.60.2](0.70.20.10.40.40.20.40.40.2)=[0.14+0.24+0

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Chapter 7 Solutions

Mathematical Applications for the Management, Life, and Social Sciences
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Ch. 7.1 - 8. An urn contains three red balls numbered 1, 2,...Ch. 7.1 - 9. From a deck of 52 ordinary playing cards, one...Ch. 7.1 - 10. From a deck of 52 ordinary playing cards, one...Ch. 7.1 - 11. Suppose a fair coin is tossed two times....Ch. 7.1 - 12. Suppose a fair coin is tossed four times....Ch. 7.1 - 13. Use Table 7.1 to determine the following...Ch. 7.1 - 14. (a) When a pair of distinguishable dice is...Ch. 7.1 - 15. If a pair of dice, one green and one red, is...Ch. 7.1 - 16. If a green die and a red die are rolled,...Ch. 7.1 - 17. Suppose a die is tossed 1200 times and a 6...Ch. 7.1 - 18. Suppose that a coin is tossed 3000 times and...Ch. 7.1 - 19. If the probability that an event will occur is...Ch. 7.1 - 20. If the probability that an event E will not...Ch. 7.1 - 21. If the odds that a particular horse will win a...Ch. 7.1 - 22. If the odds that an event E will not occur are...Ch. 7.1 - 23. Drug use Forty-six percent of marijuana use...Ch. 7.1 - 24. 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Volvo XC90 The new Volvo XC90 Twin-Engine...Ch. 7.5 - 26. Menu selections A restaurant has an early...Ch. 7.5 - 27. License plates A state wants each of its...Ch. 7.5 - 28. Racing Eight horses are entered in a race. In...Ch. 7.5 - 29. Management Four candidates for manager of a...Ch. 7.5 - 30. Testing An examination consists of 12...Ch. 7.5 - 31. Molecules Biologists have identified 4 kinds...Ch. 7.5 - 32. Families A member of a family of four is asked...Ch. 7.5 - 33. Management A department store manager wants to...Ch. 7.5 - 34. Call letters The call letters for radio...Ch. 7.5 - 35. Testing How many ways can a 10-question...Ch. 7.5 - 36. Testing How many ways can a 10-question...Ch. 7.5 - 37. Poker A flush (5 cards from the same suit) is...Ch. 7.5 - 38. Committees In how many ways can a committee of...Ch. 7.5 - 39. License plates South Carolina previously had...Ch. 7.5 - 40. Astronauts If 8 people are qualified for the...Ch. 7.5 - 41. 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License plates Suppose that all license plates...Ch. 7.6 - 6. Spelling (a) In how many different orders can...Ch. 7.6 - 7. ATMs (a) An automatic teller machine requires...Ch. 7.6 - 8. Keys Keys for antique General Motors cars had...Ch. 7.6 - 9. Phone numbers If the first digit of a...Ch. 7.6 - 10. License plates If a license plate has seven...Ch. 7.6 - 11. Rewards As a reward for a record year, the Ace...Ch. 7.6 - 12. Mutual funds The retirement plan for a company...Ch. 7.6 - 13. Testing In a 10-question matching test with 10...Ch. 7.6 - 14. Testing In a 10-question matching test with 15...Ch. 7.6 - 15. Quality control A box of 12 batteries has 3...Ch. 7.6 - 16. Quality control Suppose that 6 batteries are...Ch. 7.6 - 17. Quality control A retailer purchases 100 of a...Ch. 7.6 - 18. Quality control A box containing 500 smart...Ch. 7.6 - 19. Banking To see whether a bank has enough...Ch. 7.6 - 20. Diversity A high school principal must select...Ch. 7.6 - 21. Diversity Suppose that an employer plans to...Ch. 7.6 - 22. Lottery Four men and three women are...Ch. 7.6 - 23. Management Suppose that a children’s...Ch. 7.6 - 24. Sales A car dealer has 12 different cars that...Ch. 7.6 - 25. Diversity Suppose that two openings on an...Ch. 7.6 - 26. Politics Suppose that four of the eight...Ch. 7.6 - 27. Management Suppose that an indecisive company...Ch. 7.6 - 28. Quality control Suppose that 10 computer chips...Ch. 7.6 - 29. Lotteries In New York State, there is a state...Ch. 7.6 - 30. Diversity A task force studying age...Ch. 7.6 - 31. Insurance An insurance company receives 25...Ch. 7.6 - 32. Evaluation Employees of a firm receive annual...Ch. 7.6 - 33. Poker What is the probability of being dealt a...Ch. 7.6 - 34. Bridge A standard deck of cards contains 13...Ch. 7.6 - 35. Poker A flush (5 cards from the same suit) is...Ch. 7.6 - 36. Bridge Find the probability of being dealt a...Ch. 7.6 - 37. Lottery scandal On April 24, 1980, the winning...Ch. 7.7 - CHECKPOINT 1. Use the transition matrix and the...Ch. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Can the matrices in Problems 5-8 be transition...Ch. 7.7 - Can the matrices in Problems 5-8 be transition...Ch. 7.7 - Can the matrices in Problems 5-8 be transition...Ch. 7.7 - Can the matrices in Problems 5-8 be transition...Ch. 7.7 - In Problems 9-12, use the given transition matrix...Ch. 7.7 - In Problems 9-12, use the given transition matrix...Ch. 7.7 - In Problems 9-12, use the given transition matrix...Ch. 7.7 - In Problems 9-12, use the given transition matrix...Ch. 7.7 - 13. Use the matrix and initial probability vector...Ch. 7.7 - 14. Use the matrix and initial probability vector...Ch. 7.7 - 15. Use the matrix and initial probability vector...Ch. 7.7 - 16. Use the matrix and initial probability vector...Ch. 7.7 - In Problems 17-20, find the steady-state vector...Ch. 7.7 - In Problems 17-20, find the steady-state vector...Ch. 7.7 - In Problems 17-20, find the steady-state vector...Ch. 7.7 - In Problems 17-20, find the steady-state vector...Ch. 7.7 - Politics Use the following information for...Ch. 7.7 - Politics Use the following information for...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - 33. Population demographics Suppose a government...Ch. 7.7 - 34. Psychology A psychologist found that a...Ch. 7.7 - 35. Charitable contributions The local community...Ch. 7.7 - Advertising Use the following information for...Ch. 7.7 - Advertising Use the following information for...Ch. 7.7 - Genetics Use the following information for...Ch. 7.7 - Genetics Use the following information for...Ch. 7.7 - Genetics Use the following information for...Ch. 7 - 1. If one ball is drawn from a bag containing 9...Ch. 7 - 2. Suppose a ball is drawn from a bag containing 9...Ch. 7 - 3. If the probability that an event E occurs is...Ch. 7 - 4. Suppose that a fair coin is tossed two times....Ch. 7 - 5. Suppose that a fair coin is tossed three times....Ch. 7 - 6. A card is drawn at random from an ordinary deck...Ch. 7 - 7. A deck of 52 cards is shuffled. A card is...Ch. 7 - 8. If the probability of winning a game is 1/4 and...Ch. 7 - 9. A card is drawn from a deck of 52 playing...Ch. 7 - 10. A card is drawn at random from a deck of...Ch. 7 - 11. A bag contains 4 red balls numbered 1, 2, 3, 4...Ch. 7 - 12. A bag contains 4 red balls and 3 black balls....Ch. 7 - 13. A box contains 2 red balls and 3 black balls....Ch. 7 - 14. A bag contains 8 white balls, 5 red balls, and...Ch. 7 - 15. A bag contains 8 white balls, 5 red balls, and...Ch. 7 - 16. A bag contains 3 red, 5 black, and 8 white...Ch. 7 - 17. An urn contains 4 red and 6 white balls. One...Ch. 7 - 18. Urn I contains 3 red and 4 white balls, and...Ch. 7 - 19. Bag A contains 3 red, 6 black, and 5 white...Ch. 7 - 20. Compute . Ch. 7 - 21. Compute . Ch. 7 - 22. How many 3-letter sets of initials are...Ch. 7 - 23. How many combinations of 8 things taken 5 at a...Ch. 7 - 24. Explain why each given matrix is not a...Ch. 7 - 25. For the initial probability vector and the...Ch. 7 - 26. Find the steady-state vector associated with...Ch. 7 - 27. Senior citizens In a certain city, 30,000...Ch. 7 - 28. Newspapers According to funny2.com, the odds...Ch. 7 - 29. United Nations Of 100 job applicants to the...Ch. 7 - Productivity Suppose that in a study of leadership...Ch. 7 - Productivity Suppose that in a study of leadership...Ch. 7 - Productivity Suppose that in a study of leadership...Ch. 7 - 33. Quality control A product must pass an initial...Ch. 7 - 34. Auto styles A certain make of car comes with...Ch. 7 - 35. Color blindness Sixty men out of 1000 and 3...Ch. 7 - 36. Purchasing A regional survey found that of...Ch. 7 - 37. Quality control In a manufacturing process...Ch. 7 - 38. Management A personnel director ranks 4...Ch. 7 - 39. Management An organization wants to select a...Ch. 7 - 40. Utilities A utility company sends teams of 4...Ch. 7 - 41. Committees An organization wants to select a...Ch. 7 - 42. Juries A jury will be deadlocked if one or...Ch. 7 - 43. License plates The RBC Heritage Classic...Ch. 7 - 44. Blood types In a book describing the mass...Ch. 7 - 45. Scheduling A college registrar adds 4 new...Ch. 7 - 46. Lottery Pennsylvania’s Daily Number pays 500...Ch. 7 - 47. Lottery If a person “boxes” (see Problem 46) a...Ch. 7 - 48. Quality control A supplier has 200 compact...Ch. 7 - 49. Stocks Mr. Way must sell stocks from 3 of the...Ch. 7 - 50. Quality control A sample of 6 fuses is drawn...Ch. 7 - Income levels Use the following information for...Ch. 7 - Income levels Use the following information for...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - 10. A cat hits the letters on a computer keyboard...Ch. 7 - 11. In a certain region of the country with a...Ch. 7 - 12. In a group of 20 people, 15 are right-handed,...Ch. 7 - 13. In a group of 20 people, 15 are right-handed,...Ch. 7 - 14. The state of Arizona has a “6 of 42” game in...Ch. 7 - 15. The multistate “5 of 50” game draws 5 balls...Ch. 7 - 16. Computer chips come from two suppliers, with ...Ch. 7 - 17. A placement test is given by a university to...Ch. 7 - 18. Lactose intolerance affects about of...Ch. 7 - 19. A car rental firm has 350 cars. Seventy of the...Ch. 7 - 20. NACO Body Shops has found that 14% of the cars...Ch. 7 - 21. Garage door openers have 10 on-off switches on...Ch. 7 - 22. A publishing company has determined that a new...

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