Armco, a manufacturer of traffic light systems, found that

Basic Statistics for Business and Economics | 7th Edition | ISBN: 9780077384470 | Authors: Douglas Lind; William Marchal; Samuel Wathen

Chapter 5: Problem 1 Basic Statistics for Business and Economics 7

Some people are in favor of reducing federal taxes to increase consumer spending and others are against it. Two persons are selected and their opinions are recorded. Assuming no one is undecided, list the possible outcomes.

Chapter 5: Problem 83 Basic Statistics for Business and Economics 7

Refer to the Baseball 2008 data, which reports information on the 30 Major League Baseball teams for the 2008 season. Set up a variable that divides the teams into two groups, those that had a winning season and those that did not. That is, create a variable to count the teams that won 81 games or more, and those that won 80 or less. Next create a new variable for attendance, using three categories: attendance less than 2.0 million, attendance of 2,0 million up to 3.0 million, and attendance of 3.0 million or more. a. Create a table that shows the number of teams with a winning season versus those with a losing season by the three categories of attendance. If a team is selected at random, compute the following probabilities: 1. Having a winning season. 2. Having a winning season or attendance of more than 3.0 million. 3. Given attendance of more than 3.0 million, having a winning season. 4. Having a losing season and drawing less than 2.0 million. b. Create a table that shows the number of teams that play on artificial surfaces and natural surfaces by winning and losing records. If a team is selected at random, compute the following probabilities: 1. Selecting a team with a home field that has a natural surface. 2. Is the likelihood of selecting a team with a winning record larger for teams with natural or artificial surfaces? 3. Having a winning record or playing on an artificial surface.

Chapter 5: Problem 2 Basic Statistics for Business and Economics 7

Problem 2E A quality control inspector selects a part to be tested. The part is then declared acceptable, repairable, or scrapped. Then another part is tested. List the possible outcomes of this experiment regarding two parts.

Chapter 5: Problem 3 Basic Statistics for Business and Economics 7

A survey of 34 students at the Wall College of Business showed the following majors: Suppose you select a student and observe his or her major. a. What is the probability he or she is a management major? b. Which concept of probability did you use to make this estimate?

Chapter 5: Problem 4 Basic Statistics for Business and Economics 7

Problem 4E A large company that must hire a new president prepares a final list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery. a. What is the probability one of the minority candidates is hired? ________________ b. Which concept of probability did you use to make this estimate?

Chapter 5: Problem 5 Basic Statistics for Business and Economics 7

Problem 5E In each of the following cases, indicate whether classical, empirical, or subjective probability is used. a. A baseball player gets a hit in 30 out of 100 times at bat. The probability is .3 that he gets a hit in his next at bat. ________________ b. A seven-membcr committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is chosen as the spokesperson? ________________ c. You purchase one of 5 million tickets sold for Lotto Canada. What is the likelihood you win the $1 million jackpot? ________________ d. The probability of an earthquake in northern California in the next 10 years above 5.0 on the Richter Scale is .80.

Chapter 5: Problem 6 Basic Statistics for Business and Economics 7

Problem 6E A firm will promote two employees out of a group of six men and three women. a. List the chances of this experiment if there is particular concern about gender equity. ________________ b. Which concept of probability would you use to estimate these probabilities?

Chapter 5: Problem 7 Basic Statistics for Business and Economics 7

Problem 7E A sample of 40 oil industry executives was selected to test a questionnaire. One question about environmental issues required a yes or no answer. a. What is the experiment? ________________ b. List one possible event. ________________ c. Ten of the 40 executives responded yes. Based on these sample responses, what is the probability that an oil industry executive will respond yes? ________________ d. What concept of probability does this illustrate? ________________ e. Are each of the possible outcomes equally likely and mutually exclusive?

Chapter 5: Problem 8 Basic Statistics for Business and Economics 7

Problem 8E A sample of 2,000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers 0 1,910 1 46 2 18 3 12 4 9 5 or more 5 Total 2,000 a. What is the experiment? ________________ b. List one possible event. ________________ c. What is the probability that a particular driver had exactly two speeding violations? ________________ d. What concept of probability does this illustrate?

Chapter 5: Problem 9 Basic Statistics for Business and Economics 7

Problem 9E Bank of America customers select their own three-digit personal identification number (PIN) for use at ATMs. a. Think of this as an experiment and list four possible outcomes. ________________ b. What is the probability Mr. Jones and Mrs. Smith select the same PIN? ________________ c. Which concept of probability did you use to answer (b)?

Chapter 5: Problem 10 Basic Statistics for Business and Economics 7

An investor buys 100 shares of AT&T stock and records its price change daily. a. List several possible events for this experiment. b. Estimate the probability for each event you described in (a). c. Which concept of probability did you use in (b)?

Chapter 5: Problem 11 Basic Statistics for Business and Economics 7

Problem 11E The events A and B are mutually exclusive. Suppose P(A) = .30 and P(B) = .20. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen?

Chapter 5: Problem 12 Basic Statistics for Business and Economics 7

Problem 12E The events X and Y are mutually exclusive. Suppose P(X) = .05 and P(Y) = .02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?

Chapter 5: Problem 13 Basic Statistics for Business and Economics 7

Problem 13E A study of 200 advertising firms revealed their income after taxes: Income after Taxes Number of Firms Under $1 million 102 $1 million to $20 million 61 $20 million or more 37 a. What is the probability an advertising firm selected at random has under $1 million in income after taxes? ________________ b. What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? What rule of probability was applied?

Chapter 5: Problem 14 Basic Statistics for Business and Economics 7

Problem 14E The chair of the board of directors says, “There is a 50 percent chance this company will earn a profit, a 30 percent chance it will break even, and a 20 percent chance it will lose money next quarter.” a. Use an addition rule to find the probability the company will not lose money next quarter. ________________ b. Use the complement rule to find the probability it will not lose money next quarter.

Chapter 5: Problem 15 Basic Statistics for Business and Economics 7

Problem 15E Suppose the probability you will get an A in this class is .25 and the probability you will get a B is .50. What is the probability your grade will be above a C?

Chapter 5: Problem 16 Basic Statistics for Business and Economics 7

Problem 16E Two coins are tossed. If A is the event “two heads” and B is the event “two tails,” are A and Bmutually exclusive? Are they complements?

Chapter 5: Problem 17 Basic Statistics for Business and Economics 7

Problem 17E The probabilities of the events A and B are .20 and .30, respectively. The probability that both Aand B occur is .15. What is the probability of either A or B occurring?

Chapter 5: Problem 18 Basic Statistics for Business and Economics 7

Problem 18E Let P(X) = .55 and P(Y) = .35. Assume the probability that they both occur is .20. What is the probability of either X or Y occurring?

Chapter 5: Problem 19 Basic Statistics for Business and Economics 7

Problem 19E Suppose the two events A and B are mutually exclusive. What is the probability of their joint occurrence?

Chapter 5: Problem 20 Basic Statistics for Business and Economics 7

Problem 20E A student is taking two courses, history and math. The probability the student will pass the history course is .60, and the probability of passing the math course is .70. The probability of passing both is .50. What is the probability of passing at least one?

Chapter 5: Problem 21 Basic Statistics for Business and Economics 7

Problem 21E A survey of grocery stores in the Southeast revealed 40 percent had a pharmacy, 50 percent had a floral shop, and 70 percent had a deli. Suppose 10 percent of the stores have all three departments, 30 percent have both a pharmacy and a deli, 25 percent have both a floral shop and deli, and 20 percent have both a pharmacy and floral shop. a. What is the probability of selecting a store at random and finding it has both a pharmacy and a floral shop? ________________ b. What is the probability of selecting a store at random and finding it has both a pharmacy and a deli? ________________ c. Are the events “select a store with a deli” and “select a store with a pharmacy” mutually exclusive? ________________ d. What is the name given to the event of “selecting a store with a pharmacy, a floral shop, and a deli?” ________________ e. What is the probability of selecting a store that does not have all three departments?

Chapter 5: Problem 22 Basic Statistics for Business and Economics 7

Problem 22E A study by the National Park Service revealed that 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both. a. What is the probability a vacationer will visit at least one of these attractions? ________________ b. What is the probability .35 called? ________________ c. Are the events mutually exclusive? Explain.

Chapter 5: Problem 23 Basic Statistics for Business and Economics 7

Problem 23E Suppose P(A) = .40 and P(B|A) = .30. What is the joint probability of A and B?

Chapter 5: Problem 24 Basic Statistics for Business and Economics 7

Problem 24E Suppose P(X1) = .75 and P(Y2|X1) = .40. What is the joint probability of X1 and Y2?

Chapter 5: Problem 25 Basic Statistics for Business and Economics 7

A local bank reports that 80 percent of its customers maintain a checking account, 60 percent have a savings account, and 50 percent have both. If a customer is chosen at random, what is the probability the customer has either a checking or a savings account? What is the probability the customer does not have either a checking or a savings account?

Chapter 5: Problem 26 Basic Statistics for Business and Economics 7

Problem 26E All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .75, the probability the second truck is available is .50, and the probability that both trucks are available is .30, what is the probability neither truck is available?

Chapter 5: Problem 27 Basic Statistics for Business and Economics 7

Problem 27E Refer to the following table. First Event Second Event A1 A2 A3 Total B1 2 1 3 6 B2 1 2 1 4 Total 3 3 4 10 a. Determine P(A1). ________________ b. Determine P(B1|A2). ________________ c. Determine P(B2 and A3).

Chapter 5: Problem 28 Basic Statistics for Business and Economics 7

Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 nondefective ones. a. What is the probability the first two electric toothbrushes sold will be returned to the drugstore because they are defective? b. What is the probability the first two electric toothbrushes sold will not be defective?

Chapter 5: Problem 29 Basic Statistics for Business and Economics 7

Problem 29E Each salesperson at Puchett, Sheets, and Hogan Insurance Agency is rated either below average, average, or above average with respect to sales ability. Each salesperson is also rated with respect to his or her potential for advancement—either fair, good, or excellent. These traits for the 500 salespeople were cross-classified into the following table. Sales Ability Potential for Advancement Fair Good Excellent Below average 16 12 22 Average 45 60 45 Above average 93 72 135 a. What is this table called? ________________ b. What is the probability a salesperson selected at random will have above average sales ability and excellent potential for advancement? ________________ c. Construct a tree diagram showing all the probabilities, conditional probabilities, and joint probabilities.

Chapter 5: Problem 30 Basic Statistics for Business and Economics 7

Problem 30E An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value, (2) decreasing in value, or (3) remaining the same value. List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value.

Chapter 5: Problem 31 Basic Statistics for Business and Economics 7

Problem 31E The board of directors of a small company consists of five people. Three of those are “strong leaders.” If they buy an idea, the entire board will agree. The other “weak” members have no influence. Three salespeople are scheduled, one after the other, to make sales presentations to a board member of the salesperson’s choice. The salespeople are convincing but do not know who the “strong leaders” are. However, they will know who the previous salespeople spoke to. The first salesperson to find a strong leader will win the account. Do the three salespeople have the same chance of winning the account? If not, find their respective probabilities of winning.

Chapter 5: Problem 32 Basic Statistics for Business and Economics 7

Problem 32E If you ask three strangers about their birthdays, what is the probability: (a) All were born on Wednesday? (b) All were born on different days of the week? (c) None were born on Saturday?

Chapter 5: Problem 33 Basic Statistics for Business and Economics 7

Problem 33E Solve the following: a. 40!/35! ________________ b. 7P4 ________________ c. 5C2

Chapter 5: Problem 35 Basic Statistics for Business and Economics 7

Problem 35E A pollster randomly selected 4 of 10 available people. How many different groups of 4 are possible?

Chapter 5: Problem 34 Basic Statistics for Business and Economics 7

Problem 34E Solve the following: a. 20!/17! ________________ b. 9P3 ________________ c. 7C2

Chapter 5: Problem 36 Basic Statistics for Business and Economics 7

Problem 36E A telephone number consists of seven digits, the first three representing the exchange. How many different telephone numbers are possible within the 537 exchange?

Chapter 5: Problem 37 Basic Statistics for Business and Economics 7

Problem 37E An overnight express company must include five cities on its route. How many different routes are possible, assuming that it does not matter in which order the cities are included in the routing?

Chapter 5: Problem 38 Basic Statistics for Business and Economics 7

Problem 38E A representative of the Environmental Protection Agency (EPA) wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?

Chapter 5: Problem 39 Basic Statistics for Business and Economics 7

Problem 39E A national pollster has developed 15 questions designed to rate the performance of the president of the United States. The pollster will select 10 of these questions. How many different arrangements are there for the order of the 10 selected questions?

Chapter 5: Problem 40 Basic Statistics for Business and Economics 7

Problem 40E A company is creating three new divisions and seven managers are eligible to be appointed head of a division. How many different ways could the three new heads be appointed? Hint: Assume the division assignment makes a difference.

Chapter 5: Problem 41 Basic Statistics for Business and Economics 7

Problem 41E The marketing research department at Vernors plans to survey teenagers about a newly developed soft drink. Each will be asked to compare it with his or her favorite soft drink. a. What is the experiment? ________________ b. What is one possible event?

Chapter 5: Problem 42 Basic Statistics for Business and Economics 7

Problem 42E The number of times a particular event occurred in the past is divided by the number of occurrences. What is this approach to probability called?

Chapter 5: Problem 43 Basic Statistics for Business and Economics 7

Problem 43E The probability that the cause and the cure for all cancers will be discovered before the year 2020 is .20. What viewpoint of probability does this statement illustrate?

Chapter 5: Problem 44 Basic Statistics for Business and Economics 7

Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following amounts in tips per 8-hour shift. a. What is the probability of a tip of $200 or more? b. Are the categories " $0 up to $20”, “$20 up to $50," and so on considered mutually exclusive? c. If the probabilities associated with each outcome were totaled, what would that total be? d. What is the probability of a tip of up to $50 ? e. What is the probability of a tip of less than $200 ?

Chapter 5: Problem 45 Basic Statistics for Business and Economics 7

Problem 45E Winning all three “Triple Crown” races is considered the greatest feat of a pedigree racehorse. After a successful Kentucky Derby, Big Brown is a 1 to 2 favorite to win the Preakness Stakes. a. If he is a 1 to 2 favorite to win the Belmont Stakes as well, what is his probability of winning the Triple Crown? ________________ b. What do his chances for the Preakness Stakes have to be in order for him to be “even money” to earn the Triple Crown?

Chapter 5: Problem 46 Basic Statistics for Business and Economics 7

Problem 46E The first card selected from a standard 52-card deck is a king. a. If it is returned to the deck, what is the probability that a king will be drawn on the second selection? ________________ b. If the king is not replaced, what is the probability that a king will be drawn on the second selection? ________________ c. What is the probability that a king will be selected on the first draw from the deck and another king on the second draw (assuming that the first king was not replaced)?

Chapter 5: Problem 47 Basic Statistics for Business and Economics 7

Problem 47E Armco, a manufacturer of traffic light systems, found that under accelerated-life tests, 95 percent of the newly developed systems lasted 3 years before failing to change signals properly. a. If a city purchased four of these systems, what is the probability all four systems would operate properly for at least 3 years? ________________ b. Which rule of probability does this illustrate? ________________ c. Using letters to represent the four systems, write an equation to show how you arrived at the answer to part (a).

Chapter 5: Problem 48 Basic Statistics for Business and Economics 7

Problem 48E Refer to the following picture. a. What is the picture called? ________________ b. What rule of probability is illustrated? ________________ c. B represents the event of choosing a family that receives welfare payments. What does P(B) + P(~B) equal?

Chapter 5: Problem 49 Basic Statistics for Business and Economics 7

Problem 49E In a management trainee program at Claremont Enterprises, 80 percent of the trainees are female and 20 percent male. Ninety percent of the females attended college, and 78 percent of the males attended college. a. A management trainee is selected at random. What is the probability that the person selected is a female who did not attend college? ________________ b. Are gender and attending college independent? Why? ________________ c. Construct a tree diagram showing all the probabilities, conditional probabilities, and joint probabilities. ________________ d. Do the joint probabilities total 1.00? Why?

Chapter 5: Problem 50 Basic Statistics for Business and Economics 7

Problem 50E Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of the scheduled time is .90. We select four flights from yesterday for study. a. What is the likelihood all four of the selected flights arrived within 15 minutes of the scheduled time? ________________ b. What is the likelihood that none of the selected flights arrived within 15 minutes of the scheduled time? ________________ c. What is the likelihood at least one of the selected flights did not arrive within 15 minutes of the scheduled time?

Chapter 5: Problem 51 Basic Statistics for Business and Economics 7

Problem 51E There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are production workers, 40 are supervisors, 2 are secretaries, and the remaining employee is the president. Suppose an employee is selected: a. What is the probability the selected employee is a production worker? ________________ b. What is the probability the selected employee is either a production worker or a supervisor? ________________ c. Refer to part (b). Are these events mutually exclusive? ________________ d. What is the probability the selected employee is neither a production worker nor a supervisor?

Chapter 5: Problem 53 Basic Statistics for Business and Economics 7

Problem 53E Four sports teams remain in a single-elimination playoff competition. If one team is favored in its semi-final match by odds of 2 to 1 and another squad is favored in its contest by odds of 3 to 1, what is the probability that: a. Both favored teams win their games? ________________ b. Neither favored team wins its game? ________________ c. At least one of the favored teams wins its game?

Chapter 5: Problem 54 Basic Statistics for Business and Economics 7

Problem 54E There are three clues labeled “daily double” on the game show Jeopardy. If three equally matched contenders play, what is the probability that: a. A single contenders finds all three “daily doubles”? ________________ b.The returning champion gets all three of the “daily doubles”? ________________ c. Each of the players selects precisely one of the “daily doubles”?

Chapter 5: Problem 52 Basic Statistics for Business and Economics 7

Problem 52E Chipper Jones of the Atlanta Braves had the highest batting average in the 2008 Major League Baseball season. His average was .364. So assume the probability of getting a hit was .364 for each time he batted. In a particular game assume he batted three times. a. This is an example of what type of probability? ________________ b. What was the probability of getting three hits in a particular game? ________________ c. What was the probability of not getting any hits in a game? ________________ d. What was the probability of getting at least one hit?

Chapter 5: Problem 55 Basic Statistics for Business and Economics 7

Problem 55E Brooks Insurance, Inc., wishes to offer life insurance to men age 60 via the internet. Mortality tables indicate the likelihood of a 60-year-old man surviving another year is .98. If the policy is offered to five men age 60: a. What is the probability all five men survive the year? ________________ b. What is the probability at least one does not survive?

Chapter 5: Problem 56 Basic Statistics for Business and Economics 7

Problem 56E Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: a. What is the probability all three of the selected homes have a security system? ________________ b. What is the probability none of the three selected homes have a security system? ________________ c. What is the probability at least one of the selected homes has a security system? ________________ d. Did you assume the events to be dependent or independent?

Chapter 5: Problem 57 Basic Statistics for Business and Economics 7

Problem 57E Refer to Exercise 62, but assume there are 10 homes in the Quail Creek area and four of them have a security system. Three homes are selected at random: a. What is the probability all three of the selected homes have a security system? ________________ b. What is the probability none of the three selected homes have a security system? ________________ c. What is the probability at least one of the selected homes has a security system? ________________ d. Did you assume the events to be dependent or independent?

Chapter 5: Problem 58 Basic Statistics for Business and Economics 7

Problem 58E There are 20 families living in the Willbrook Farms Development. Of these families 10 prepared their own federal income taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 3 by H&R Block. a. What is the probability of selecting a family that prepared their own taxes? ________________ b. What is the probability of selecting two families both of which prepared their own taxes? ________________ c. What is the probability of selecting three families, all of which prepared their own taxes? ________________ d. What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block?

Chapter 5: Problem 59 Basic Statistics for Business and Economics 7

Problem 59E The board of directors of Saner Automatic Door Company consists of 12 members, 3 of whom are women. A new policy and procedures manual is to be written for the company. A committee of 3 is randomly selected from the board to do the writing. a. What is the probability that all members of the committee are men? ________________ b. What is the probability that at least 1 member of the committee is a woman?

Chapter 5: Problem 61 Basic Statistics for Business and Economics 7

Problem 61E Althoff and Roll, an investment firm in Augusta, Georgia, advertises extensively in the Augusta Morning Gazette, the newspaper serving the region. The Gazette marketing staff estimates that 60 percent of Althoff and Roll’s potential market read the newspaper. It is further estimated that 85 percent of those who read the Gazette remember the Althoff and Roll advertisement. a. What percent of the investment firm’s potential market sees and remembers the advertisement? ________________ b. What percent of the investment firm’s potential market sees, but does not remember the advertisement?

Chapter 5: Problem 62 Basic Statistics for Business and Economics 7

Problem 62E An Internet company located in Southern California has season tickets to the Los Angeles Lakers basketball games. The company president always invites one of the four vice presidents to attend games with him, and claims he selects the person to attend at random. One of the four vice presidents has not been invited to attend any of the last five Lakers home games. What is the likelihood this could be due to chance?

Chapter 5: Problem 63 Basic Statistics for Business and Economics 7

Problem 63E A computer-supply retailer purchased a batch of 1,000 CD-R disks and attempted to format them for a particular application. There were 857 perfect CDs, 112 CDs were usable but had bad sectors, and the remainder could not be used at all. a. What is the probability a randomly chosen CD is not perfect? ________________ b. If the disk is not perfect, what is the probability it cannot be used at all?

Chapter 5: Problem 60 Basic Statistics for Business and Economics 7

Problem 60E A recent survey reported in BusinessWeek dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money. CEO Paid More CEO Paid Less Than $1 Million Than $1 Million Total Shareholders made money 2 11 13 Shareholders lost money 4 3 7 Total 6 14 20 If a company is randomly selected from the list of 20 studied, what is the probability: a. the CEO made more than $1 million? ________________ b. the CEO made more than $1 million or the shareholders lost money? ________________ c. the CEO made more than $1 million given the shareholders lost money? ________________ d. of selecting 2 CEOs and finding they both made more than $1 million?

Chapter 5: Problem 64 Basic Statistics for Business and Economics 7

Problem 64E An investor purchased 100 shares of Fifth Third Bank stock and 100 shares of Santee Electric Cooperative stock. The probability the bank stock will appreciate over a year is .70. The probability the electric utility will increase over the same period is .60. a. What is the probability both stocks appreciate during the period? ________________ b. What is the probability the bank stock appreciates but the utility does not? ________________ c. What is the probability at least one of the stocks appreciates?

Chapter 5: Problem 65 Basic Statistics for Business and Economics 7

Problem 65E With each purchase of a large pizza at Tony’s Pizza, the customer receives a coupon that can be scratched to see if a prize will be awarded. The odds of winning a free soft drink are 1 in 10, and the odds of winning a free large pizza are 1 in 50. You plan to eat lunch tomorrow at Tony’s. What is the probability: a. That you will win either a large pizza or a soft drink? ________________ b. That you will not win a prize? ________________ c. That you will not win a prize on three consecutive visits to Tony's? ________________ d. That you will win at least one prize on one of your next three visits to Tony’s?

Chapter 5: Problem 66 Basic Statistics for Business and Economics 7

Problem 66E For the daily lottery game in Illinois, participants select three numbers between 0 and 9. A number cannot be selected more than once, so a winning ticket could be, say, 307 but not 337. Purchasing one ticket allows you to select one set of numbers. The winning numbers are announced on TV each night. a. How many different outcomes (three-digit numbers) are possible? ________________ b. If you purchase a ticket for the game tonight, what is the likelihood you will win? ________________ c. Suppose you purchase three tickets for tonight’s drawing and select a different number for each ticket. What is the probability that you will not win with any of the tickets?

Chapter 5: Problem 68 Basic Statistics for Business and Economics 7

Problem 68E It was found that 60 percent of the tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing. Forty percent visited Xi’an with its magnificent terracotta soldiers, horses, and chariots, which lay buried for over 2,000 years. Thirty percent of the tourists went to both Beijing and Xi’an. What is the probability that a tourist visited at least one of these places?

Chapter 5: Problem 67 Basic Statistics for Business and Economics 7

Problem 67E Several years ago Wendy’s Hamburgers advertised that there are 256 different ways to order your hamburger. You may choose to have, or omit, any combination of the following on your hamburger: mustard, ketchup, onion, pickle, tomato, relish, mayonnaise, and lettuce. Is the advertisement correct? Show how you arrive at your answer.

Chapter 5: Problem 69 Basic Statistics for Business and Economics 7

Problem 69E A new chewing gum has been developed that is helpful to those who want to stop smoking. If 60 percent of those people chewing the gum are successful in stopping smoking, what is the probability that in a group of four smokers using the gum at least one quits smoking?

Chapter 5: Problem 70 Basic Statistics for Business and Economics 7

Problem 70E Reynolds Construction Company has agreed not to erect all “look-alike” homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways can the exterior and interior plans be offered to potential home buyers?

Chapter 5: Problem 71 Basic Statistics for Business and Economics 7

Problem 71E A new sports car model has defective brakes 15 percent of the time and a defective steering mechanism 5 percent of the time. Let’s assume (and hope) that these problems occur independently. If one or the other of these problems is present, the car is called a “lemon.” If both of these problems are present, the car is a “hazard.” Your instructor purchased one of these cars yesterday. What is the probability it is: a. A lemon? ________________ b. A hazard?

Chapter 5: Problem 72 Basic Statistics for Business and Economics 7

Problem 72E The state of Maryland has license plates with three numbers followed by three letters. How many different license plates are possible?

Chapter 5: Problem 74 Basic Statistics for Business and Economics 7

Problem 74E Tim Bleckie is the owner of Bleckie Investment and Real Estate Company. The company recently purchased four tracts of land in Holly Farms Estates and six tracts in Newburg Woods. The tracts are all equally desirable and sell for about the same amount. a. What is the probability that the next two tracts sold will be in Newburg Woods? ________________ b. What is the probability that of the next four sold at least one will be in Holly Farms? ________________ c. Are these events independent or dependent?

Chapter 5: Problem 75 Basic Statistics for Business and Economics 7

Problem 75E A computer password consists of four characters. The characters can be one of the 26 letters of the alphabet. Each character may be used more than once. How many different passwords are possible?

Chapter 5: Problem 73 Basic Statistics for Business and Economics 7

Problem 73E There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are female, of which only one is over 60. a. What is the probability that a candidate is over 60 and female? ________________ b. Given that the candidate is male, what is the probability he is less than 60? ________________ c. Given that the person is over 60, what is the probability the person is female?

Chapter 5: Problem 76 Basic Statistics for Business and Economics 7

Problem 76E A case of 24 cans contains 1 can that is contaminated. Three cans are to be chosen randomly for testing. a. How many different combinations of 3 cans could be selected? ________________ b. What is the probability that the contaminated can is selected for testing?

Chapter 5: Problem 78 Basic Statistics for Business and Economics 7

Problem 78E Two components, A and B, operate in series. Being in series means that for the system to operate, both components A and B must work. Assume the two components are independent. What is the probability the system works under these conditions? The probability A works is .90 and the probability B functions is also .90.

Chapter 5: Problem 77 Basic Statistics for Business and Economics 7

Problem 77E A puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column. The puzzle asks the reader to match each president with his vice president. If you make the matches randomly, how many matches are possible? What is the probability all 10 of your matches are correct?

Chapter 5: Problem 79 Basic Statistics for Business and Economics 7

Problem 79E You take a trip by air that involves three independent flights. If there is an 80 percent chance each specific leg of the trip is done on time, what is the probability all three flights arrive on time?

Chapter 5: Problem 81 Basic Statistics for Business and Economics 7

Problem 81E Twenty-two percent of all liquid crystal displays (LCDs) are manufactured by Samsung. What is the probability that in a collection of three independent LCD purchases, at least one is a Samsung?

Chapter 5: Problem 82 Basic Statistics for Business and Economics 7

Problem 82E Refer to the Real Estate data, which reports information on homes sold in the Phoenix, Arizona, area during the last year. a. Sort the data into a table that shows the number of homes that have a pool versus the number that don’t have a pool in each of the five townships. If a home is selected at random, compute the following probabilities. 1. The home is in Township 1 or has a pool. 2. Given that it is in Township 3, that it has a pool. 3. Has a pool and is in Township 3. b. Sort the data into a table that shows the number of homes that have a garage attached versus those that don’t in each of the five townships. If a home is selected at random, compute the following probabilities: 1. The home has a garage attached. 2. Given that it is in Township 5, that it does not have a garage attached. 3. The home has a garage attached and is in Township 3. 4. Does not have a garage attached or is in Township 2.

Chapter 5: Problem 80 Basic Statistics for Business and Economics 7

Problem 80E The probability a HP network server is down is .05. If you have three independent servers, what is the probability that at least one of them is operational?

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Textbook Solutions for Basic Statistics for Business and Economics

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Armco, a manufacturer of traffic light systems, found that

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