Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Textbook Question

Chapter 7.1, Problem 13E

Use Table 7.1 to determine the following probabilities if a distinguishable pair of dice is rolled.

(a) Pr(sum is 4)

(b) Pr(sum is 10)

To find the probability of obtaining a given sum when a pair of dice is rolled, we need to determine the outcomes. However, the sums {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} are not equally likely; there is only one way to obtain a sum of 2, but there are several ways to obtain a sum of 6. If we distinguish between the two dice we are rolling and we record all the possible outcomes for each die, we see that there are 36 possibilities, each of which is equally likely. Table 7.1 shows these possibilities, with the event “sum = 9" encircled.

TABLE 7.1

Chapter 7.1, Problem 13E, 13. Use Table 7.1 to determine the following probabilities if a distinguishable pair of dice is

This list of possible outcomes for finding the sum of two dice is an equiprobable sample space for the experiment. Because the 36 elements in the sample space are equally likely, we can find the probability that a given sum results by determining the number of ways this sum can occur and dividing that number by 36.

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Chapter 7 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 7.1 - CHECKPOINT 1. If a coin is drawn from a box...Ch. 7.1 - CHECKPOINT 2. A ball will be drawn from a bag...Ch. 7.1 - CHECKPOINT 3. A coin is tossed, and a die is...Ch. 7.1 - 1. One ball is drawn at random from a bag...Ch. 7.1 - 2. One ball is drawn at random from a bag...Ch. 7.1 - 3. If you draw one card at random from a deck of...Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - 6. A die is rolled. What is the probability...Ch. 7.1 - 7. An urn contains three red balls numbered 1, 2,...

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 - Prob. 12E 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 - Prob. 15E Ch. 7.1 - Prob. 16E 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 - Prob. 19E Ch. 7.1 - Prob. 20E 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 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - 25. Car maintenance A car rental firm has 425...Ch. 7.1 - Prob. 26E Ch. 7.1 - 27. Voting The table gives the average number of...Ch. 7.1 - Prob. 28E Ch. 7.1 - 29. Sales promotion In a sales promotion, a...Ch. 7.1 - 30. Management A dry cleaning firm has 12...Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - 33. Blood types Human blood is classified by blood...Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - 39. Fraud A company selling substandard drugs to...Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - 44. Quality control A supply of 500 plasma...Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - 48. Quality control A computer store offers used...Ch. 7.1 - 49. Genetics A newly married couple plan to have...Ch. 7.1 - 50. Management A frustrated store manager is asked...Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - Prob. 61E Ch. 7.1 - Prob. 62E Ch. 7.1 - Prob. 63E Ch. 7.1 - 64. Ice cream The odds of an American home having...Ch. 7.1 - Prob. 65E Ch. 7.1 - 66. Rain If the probability of rain today is ,...Ch. 7.1 - Prob. 68E Ch. 7.2 - CHECKPOINT 1. If a ball is drawn from a bag...Ch. 7.2 - Prob. 2CP Ch. 7.2 - Prob. 1E Ch. 7.2 - Prob. 2E Ch. 7.2 - In Problems 1-4, one card is drawn from a deck of...Ch. 7.2 - Prob. 4E Ch. 7.2 - 5. An ordinary die is tossed. What is the...Ch. 7.2 - 6. A card is drawn at random from a deck of 52...Ch. 7.2 - 7. If the probability that event E will occur is...Ch. 7.2 - Prob. 8E Ch. 7.2 - In Problems 9-12, one ball is drawn from a bag...Ch. 7.2 - In Problems 9-12, one ball is drawn from a bag...Ch. 7.2 - Prob. 11E Ch. 7.2 - In Problems 9-12, one ball is drawn from a bag...Ch. 7.2 - 13. Suppose a die is biased (unfair) so that each...Ch. 7.2 - Prob. 14E Ch. 7.2 - 15. A bag contains 4 white, 7 black, and 6 green...Ch. 7.2 - 16. In a game where only one player can win, the...Ch. 7.2 - 17. A cube has 2 faces painted red, 2 painted...Ch. 7.2 - Prob. 18E Ch. 7.2 - 19. A ball is drawn from a bag containing 13 red...Ch. 7.2 - 20. A ball is drawn from a bag containing 13 red...Ch. 7.2 - 21. Drug use Forty-six percent of marijuana use...Ch. 7.2 - 22. Breast cancer According to the American Cancer...Ch. 7.2 - 23. Car maintenance A car rental firm has 425...Ch. 7.2 - 25. Linguistics Of 100 students, 24 can speak...Ch. 7.2 - 25. Linguistics Of 100 students, 24 can speak...Ch. 7.2 - 26. Management A company employs 65 people. Eight...Ch. 7.2 - Prob. 27E Ch. 7.2 - 28. Mountain biking Rob Lee knows that he can...Ch. 7.2 - 29. Salaries The table gives the percent of...Ch. 7.2 - Prob. 30E Ch. 7.2 - 31. Workers The table gives the projected number...Ch. 7.2 - 32. Causes of death In the United States in 2014,...Ch. 7.2 - 33. HIV cases The table gives the numbers of new...Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - 37. Education A mathematics class consists of 16...Ch. 7.2 - 38. Parts delivery Repairing a copy machine...Ch. 7.2 - Oil drilling The table summarizes the opinions of...Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - 43. Drinking age A survey questioned 1000 people...Ch. 7.2 - 44. Job bids Three construction companies have bid...Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.2 - Prob. 48E Ch. 7.3 - CHECKPOINT 1. Suppose that one ball is drawn from...Ch. 7.3 - Prob. 2CP Ch. 7.3 - CHECKPOINT 3. Two balls are drawn with replacement...Ch. 7.3 - 1. A card is drawn from a deck of 52 playing...Ch. 7.3 - Prob. 2E Ch. 7.3 - 3. A die has been “loaded so that the probability...Ch. 7.3 - 4. A die has been “loaded” so that the probability...Ch. 7.3 - 5. A bag contains 9 red balls numbered 1, 2, 3, 4,...Ch. 7.3 - Prob. 6E Ch. 7.3 - 7. A bag contains 4 red balls and 6 white balls....Ch. 7.3 - 8. A fair die is rolled. Find the probability that...Ch. 7.3 - 9. A fair coin is tossed 3 times. Find the...Ch. 7.3 - 10. A fair coin is tossed 14 times. What is the...Ch. 7.3 - 11. A die is thrown twice. What is the probability...Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - 15. (a) A box contains 3 red balls, 2 white balls,...Ch. 7.3 - Prob. 16E Ch. 7.3 - 17. Two balls are drawn from a bag containing 3...Ch. 7.3 - Prob. 18E Ch. 7.3 - 19. A bag contains 9 nickels, 4 dimes, and 5...Ch. 7.3 - Prob. 20E Ch. 7.3 - 21. A red ball and 4 white balls are in a box. If...Ch. 7.3 - 22. From a deck of 52 playing cards, two cards are...Ch. 7.3 - 23. One card is drawn at random from a deck of 52...Ch. 7.3 - Prob. 24E Ch. 7.3 - 25. Two balls are drawn without replacement from a...Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Carbon emissions The table gives the results of a...Ch. 7.3 - Prob. 30E Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - Prob. 42E Ch. 7.3 - 43. Quality control Each computer component that...Ch. 7.3 - Prob. 44E Ch. 7.3 - 45. Lactose intolerance Lactose intolerance...Ch. 7.3 - 46. Quality control If 3% of all light bulbs a...Ch. 7.3 - 47. Quality control To test its shotgun shells, a...Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - Prob. 50E Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.3 - 53. Maintenance Twenty-three percent of the cars...Ch. 7.3 - Prob. 54E Ch. 7.3 - 55. Testing An unprepared student must take a...Ch. 7.3 - Prob. 56E Ch. 7.3 - Prob. 57E Ch. 7.3 - 58. Racing Suppose that the odds that Blackjack...Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Prob. 61E Ch. 7.3 - 62. Crime In an actual case.’ probability was used...Ch. 7.4 - CHECKPOINT 1. Urn I contains 3 gold coins, urn II...Ch. 7.4 - Prob. 2CP Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 2E Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 4E Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 6E Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - Prob. 14E Ch. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - 17. Lactose intolerance Lactose intolerance...Ch. 7.4 - 18. Genetics What is the probability that a couple...Ch. 7.4 - 19. Marksmanship Suppose that a marksman hits the...Ch. 7.4 - 20. Majors In a random survey of students...Ch. 7.4 - 21. Quality control Suppose a box contains 3...Ch. 7.4 - 22. Education The probability that an individual...Ch. 7.4 - 23. Alcoholism A small town has 8000 adult males...Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - 26. Insurance rates Ideally, auto insurance rates...Ch. 7.4 - 27. Pregnancy test A self-administered pregnancy...Ch. 7.4 - Prob. 28E Ch. 7.4 - 29. Survey In a Student Activity Participation...Ch. 7.4 - Prob. 30E Ch. 7.5 - CHECKPOINT 1. If a state permits either a letter...Ch. 7.5 - Prob. 2CP Ch. 7.5 - Prob. 3CP Ch. 7.5 - Prob. 4CP Ch. 7.5 - Prob. 5CP Ch. 7.5 - 1. Compute . Ch. 7.5 - Prob. 2E Ch. 7.5 - 3. Compute . Ch. 7.5 - 4. Compute . Ch. 7.5 - 5. Compute . Ch. 7.5 - Prob. 6E Ch. 7.5 - 7. How many four-digit numbers can be formed from...Ch. 7.5 - Prob. 8E Ch. 7.5 - 9. Compute . Ch. 7.5 - Prob. 10E Ch. 7.5 - Prob. 11E Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - 15. Compute . Ch. 7.5 - 16. Compute . Ch. 7.5 - 17. Compute . Ch. 7.5 - Prob. 18E Ch. 7.5 - 19. Compute . Ch. 7.5 - Prob. 20E Ch. 7.5 - Prob. 21E Ch. 7.5 - Prob. 22E Ch. 7.5 - 23. Binz, not Benz Mercedes Benz E-Class sedans...Ch. 7.5 - 24. Ice cream cones Baskin-Robbins’logo includes...Ch. 7.5 - Prob. 25E Ch. 7.5 - 26. Menu selections A restaurant has an early...Ch. 7.5 - Prob. 27E Ch. 7.5 - 28. Racing Eight horses are entered in a race. In...Ch. 7.5 - Prob. 29E Ch. 7.5 - 30. Testing An examination consists of 12...Ch. 7.5 - Prob. 31E Ch. 7.5 - Prob. 32E 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 - Prob. 35E Ch. 7.5 - 36. Testing How many ways can a 10-question...Ch. 7.5 - Prob. 37E Ch. 7.5 - Prob. 38E Ch. 7.5 - Prob. 39E Ch. 7.5 - 40. Astronauts If 8 people are qualified for the...Ch. 7.5 - 41. Sales A traveling salesperson has 30 products...Ch. 7.5 - Prob. 42E Ch. 7.5 - Prob. 43E Ch. 7.5 - Prob. 44E Ch. 7.5 - Prob. 45E Ch. 7.5 - Prob. 46E Ch. 7.5 - 47. Committees In how many ways can a committee...Ch. 7.5 - Prob. 48E Ch. 7.5 - Prob. 49E Ch. 7.5 - 50. Auto dealerships An auto dealer has 4 cars, 2...Ch. 7.6 - CHECKPOINT 1. If three wires (red, black, and...Ch. 7.6 - Prob. 2CP Ch. 7.6 - 1. Education If a child is given cards with A, C,...Ch. 7.6 - Prob. 2E Ch. 7.6 - Politics A poll asks voters to rank Social...Ch. 7.6 - 4. Photography Two men and a woman are lined up to...Ch. 7.6 - 5. License plates Suppose that all license plates...Ch. 7.6 - Prob. 6E 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 - Prob. 10E 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 - Prob. 14E 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 - Prob. 18E 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 - Prob. 23E 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 - Prob. 26E Ch. 7.6 - 27. Management Suppose that an indecisive company...Ch. 7.6 - 28. Quality control Suppose that 10 computer chips...Ch. 7.6 - Prob. 29E Ch. 7.6 - Prob. 30E Ch. 7.6 - Prob. 31E Ch. 7.6 - 32. Evaluation Employees of a firm receive annual...Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 7.6 - 35. Poker A flush (5 cards from the same suit) is...Ch. 7.6 - Prob. 36E Ch. 7.6 - Prob. 37E Ch. 7.7 - Prob. 1CP Ch. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Prob. 2E 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 - Prob. 5E Ch. 7.7 - Prob. 6E Ch. 7.7 - Prob. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - In Problems 9-12, use the given transition matrix...Ch. 7.7 - Prob. 10E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - 15. Use the matrix and initial probability vector...Ch. 7.7 - Prob. 16E Ch. 7.7 - In Problems 17-20, find the steady-state vector...Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Politics Use the following information for...Ch. 7.7 - Prob. 22E 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 - Prob. 26E Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Car selection Use the following information for...Ch. 7.7 - 33. Population demographics Suppose a government...Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Prob. 36E Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E 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 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE 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 - Prob. 14RE Ch. 7 - 15. A bag contains 8 white balls, 5 red balls, and...Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - 19. Bag A contains 3 red, 6 black, and 5 white...Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - 23. How many combinations of 8 things taken 5 at a...Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - 26. Find the steady-state vector associated with...Ch. 7 - 27. Senior citizens In a certain city, 30,000...Ch. 7 - Prob. 28RE Ch. 7 - 29. United Nations Of 100 job applicants to the...Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE 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 - Prob. 35RE 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 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - 42. Juries A jury will be deadlocked if one or...Ch. 7 - 43. License plates The RBC Heritage Classic...Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Prob. 46RE 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 - Prob. 52RE Ch. 7 - Prob. 1T Ch. 7 - Prob. 2T 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 - Prob. 6T Ch. 7 - Prob. 7T Ch. 7 - Prob. 8T Ch. 7 - Prob. 9T Ch. 7 - 10. A cat hits the letters on a computer keyboard...Ch. 7 - Prob. 11T Ch. 7 - Prob. 12T Ch. 7 - Prob. 13T Ch. 7 - Prob. 14T Ch. 7 - Prob. 15T 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 - Prob. 19T Ch. 7 - Prob. 20T Ch. 7 - Prob. 21T Ch. 7 - 22. A publishing company has determined that a new...

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Solution Summary: The author calculates the probability of the sum of numbers equal to 4 if a pair of distinguishable dice is rolled.

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Chapter 7 Solutions