A company is considering upgrading its computer system and a major portion of the upgrade is new operating system. The company has asked an engineer for an evaluation of the operating system. Suppose the probability of a favorable evaluation is 0.65. If the probability the company will up-grade its system given a favorable evaluation is 0.85, what is the probability that the company will upgrade and receive a favorable evaluation?

Solution

Problems: Probability I: Introductory Ideas

Problem-01: Probability I: Introductory Ideas

Give a collectively exhaustive list of the possible outcomes of tossing tow dice.

Problem-02: Probability I: Introductory Ideas

Give the probability for each of the following totals in the rolling of two dice: 1, 2, 5, 6, 7, 10, and 11.

Problem-03: Probability I: Introductory Ideas

Which of the following are pairs of mutually exclusive events in the drawing of one card from a standard deck of 52?. A heart and a queen. A club and...

Problem-04: Probability I: Introductory Ideas

A batter "takes" (does not swing at) each of the pitches he sees. Give the sample space of outcomes for the following experiments in terms of balls and strikes: Two...

Problem-05: Probability I: Introductory Ideas

Consider a stack of nine cards, all spades, numbered 2 through 10, and a die. Give a collectively exhaustive list of the possible outcomes of rolling the die and picking...

Problem-06: Probability I: Introductory Ideas

Consider a stack of nine cards, all spades, numbered 2 through 10, and a die. Give the probability for each of the following totals in the sum of the roll...

Problem-07: Probability I: Introductory Ideas

In a recent meeting of union members supporting Joe Royal for union president, Royal's leading supporting said ''chances are good'' that Royal will defeat the single opponent facing him in...

Problem-08: Probability I: Introductory Ideas

Southern Bell is considering the distriburion of funds for a campaign to increase long-distance calls within North Carolina. The following table lists the markets that the company considers worthy of...

Problem-09: Probability I: Introductory Ideas

Union shop steward B. Lou Khollar has drafted a set of wage and benefit demands to be presented to management. To get an idea of worker support for the package,...

Problem-10: Probability I: Introductory Ideas

Classify the following probability estimates as to their type (Classical, relative frequency, or subjective):. Contact us for the solution

Problem-11: Probability I: Introductory Ideas

Determine the probability of the following events in drawing a card from a standard deck of 52 cards. Contact us for the solution

Problem-12: Probability I: Introductory Ideas

During a recent bridge game, once the lead card had been played and the dummy's hand revealed, the declarer took a moment to count up the number of cards in...

Problem-13: Probability I: Introductory Ideas

Below is a frequency distribution of annual sales commissions from a survey of 300 media salespeople. Contact us for the solution

Problem-14: Probability I: Introductory Ideas

General Buck Turgidson is preparing to make his annual budget presentation to the U.S. Senate and is speculating about his chances of getting all or part of his requested budget...

Problem-15: Probability I: Introductory Ideas

The office manager of an insurance company has the following data on the functioning of the copiers in the office: CopierDays FunctioningDays Out of Service 120951 221743 32582 422931 524713...

Problem-16: Probability I: Introductory Ideas

Classify the following probability estimates as classical, relative frequency, or subjective: The probability the Cubs will win the World Series this year is 0.175. The probability tuition will increase next...

Problem-17: Probability I: Introductory Ideas

Frome the following Venn diagram, which indicates the number of outcomes of an experiment corresponding to each event and number of outcomes that do not correspond to either event, give...

Problem-18: Probability I: Introductory Ideas

An inspector of the Alaska pipeline has the task of comparing the reliability of two pumping stations. Each stations is susceptible to two kinds of failure: pump failure and leakage....

Problem-19: Probability I: Introductory Ideas

From the following Venn diagram, which indicates the number of outcomes of an experiment corresponding to each event give the probabilities indicated: Contact us for the solution

Problem-20: Probability I: Introductory Ideas

Using this Venn diagram, give the probabilities indicated: Contact us for the solution

Problem-21: Probability I: Introductory Ideas

An urn contains 75 marbles: 35 are blue, and 25 of these blue marbles are swirled. The rest of them are red, and 30 of the red ones are swirled....

Problem-22: Probability I: Introductory Ideas

In this section, two expressions were developed for the probability of either of two events, A or B, occurring. Referring to Equations 4-2 and 4-3: Contact us for the solution

Problem-23: Probability I: Introductory Ideas

An employee at Info tech enter product information into the computer. The employee may use a light pen that transmits the information to the PC along with keyboard to issue...

Problem-24: Probability I: Introductory Ideas

The HAL Corporation wishes to improve the resistance of its personal computer to disk-drive and keyboard failures. At present, the design of the computer is such that disk-drive failures occur...

Problem-25: Probability I: Introductory Ideas

The Herr-McFee Company, which produces nuclear fuel rods,must X-ray and inspect each rod before shipping. Karen Wood, an inspector, has noted that for every 1,000 fuel rods she inspects, 10...

Problem-26: Probability I: Introductory Ideas

What is the probability that in selecting two cards one at a time from a deck with replacement, the second card is Contact us for the solution

Problem-27: Probability I: Introductory Ideas

Sol O'Tarry, a prison administrator, has been reviewing the prison records on attempted escapes by inmates. He has data covering the last 45 years that the prison has been open,...

Problem-28: Probability I: Introductory Ideas

What is the probability that a couple's second child will be (a) A boy, given that their first child was a girl? (b) A girl, given that their first child...

Problem-29: Probability I: Introductory Ideas

In rolling two dice, what is the probability of rolling (a) A total of 7 on the first roll, followed by a total of 11 on the second roll? (b)...

Problem-30: Probability I: Introductory Ideas

A bag contains 32 marbles: 4 are red, 9 are black,12 are blue, 6 are yellow, and 1 is purple. Marbles are drawn one at a time with replacement. What...

Problem-31: Probability I: Introductory Ideas

George, Richard, Paul, and John play the following game. Each man takes one of four balls numbered 1 through 4 from an urn. The man who draws ball 4 loses....

Problem-32: Probability I: Introductory Ideas

The health department routinely conducts independent inspections of each restaurant, with the restaurant passing only if both inspectors pass it. Inspector A is very experienced, and hence, passes only 2...

Problem-33: Probability I: Introductory Ideas

The four floodgates of a small hydroelectric dam fail and are repaired independently of each other. From experience, it's known that each floodgate is out of order 4 percent of...

Problem-34: Probability I: Introductory Ideas

Rob Rales is preparing a report that his employer, the titre Corporation, will eventually deliver to the Federal Aviation Administration. First, the report must be approved by Rob's group leader,...

Problem-35: Probability I: Introductory Ideas

A grocery store is reviewing its restocking policies and has analyzed the number of half-gallon containers of orange juice sold each day for the past month. The data are given...

Problem-36: Probability I: Introductory Ideas

Bill Borde, top advertising executive for Grapevine Concepts, has just launched a publicity campaign for a new restaurant in town, The Black Angus. Bill has just installed four billboards on...

Problem-37: Probability I: Introductory Ideas

According to a survey, the probability that a family owns two cars if its annual income is greater then $35000 is 0.75. Of the households surveyed, 60 percent had incomes...

Problem-38: Probability I: Introductory Ideas)

Friendly's Department Store has been the target of many shoplifters during the past month, but owing to increased security precautions, 250 shoplifters have been caught. Each shoplifter's sex is noted;...

Problem-39: Probability I: Introductory Ideas

Two events, A and B, are statistically dependent. If P(A)=0.39, P(B)=0.21, and P(A or B)=0.47, find the probability that Neither A nor B will occur. Both A and B will...

Problem-40: Probability I: Introductory Ideas

Given that P(A) = 3/14, P(B) = 1/3, P(AC) = 1/7 , and P(B|C) = 5/21, find the following probabilities: P(A|C), P(C|A), P(BC), P(C|B).Contact us for the solution

Problem-41: Probability I: Introductory Ideas

Assume that for two events A and B, P(A) = 0.80, P(A|B) = P(A), and P(C|A) = 0.85. Is this a consistent assignment of probabilities?Contact us for the solution

Problem-42: Probability I: Introductory Ideas

At a soup kitchen, a social worker gathers the following data. Of those visiting the kitchen, 59 percent are men, 32 percent are alcoholics, and 21 percent are male alcoholics....

Problem-43: Probability I: Introductory Ideas

During a study of auto accidents, the Highway Safety Council found that 60 percent of all accidents occur at night, 52 percent are alcohol-related, and 37 percent occur at night...

Problem-44: Probability I: Introductory Ideas

If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida. From data...

Problem-45: Probability I: Introductory Ideas

Al Cascade, president of the Litre Corporation, is studying his company's chances of being awarded an impotent water purification system contract for the Tennessee Valley Authority. Accordingly, two events are...

Problem-46: Probability I: Introductory Ideas

A company is considering upgrading its computer system and a major portion of the upgrade is new operating system. The company has asked an engineer for an evaluation of the...

Problem-47: Probability I: Introductory Ideas

The university's library has been randomly surveying patrons over the last month to see who is using the library and what services they have been using. Patrons are classified as...

Problem-48: Probability I: Introductory Ideas

The southeast regional manager of General Express, a parcel-delivery firm, is worried about the likelihood of strikes by his pilots is 0.75 and the probability of a strike by his...

Problem-49: Probability I: Introductory Ideas

Given: The probabilities of three events, A, B, and C, occurring are P(A)= 0.35, P(B)= 0.45, and P(C)=0.2. Assuming that A,B,or C has occurred, the probabilities of another event, X,...

Problem-50: Probability I: Introductory Ideas

A doctor has decided to prescribe two new drugs to 200 heart patients as follows: 50 get drug B, and 100 get both. The 200 patients were chosen so that...

Problem-51: Probability I: Introductory Ideas

Two related experiments are performed. The first has three possible mutually exclusive outcomes: A,B, and C. The second has two possible, mutually exclusive outcomes: X We know P(A) = 0.2...

Problem-52: Probability I: Introductory Ideas

Martin Coleman, credit manager for Back's knows that the company uses three methods to encourage collection of delinquent accounts. From past collection records, he learns that 70 percent of the...

Problem-53: Probability I: Introductory Ideas

A public interest group was planning to make a court challenge to auto insurance rates in one of three cities: Atlanta, Baltimore, or Cleveland. The probability that it would choose...

Problem-54: Probability I: Introductory Ideas

EconOcon is planning its company picnic. The only thing that will cancel the picnic is a thunderstorm. The Weather Service has predicted dry conditions with probability 0.2, moist conditions with...

Problem-55: Probability I: Introductory Ideas

An independent research group has been studying the chances that an accident at a nucler power plant will result in radiation leakage. The group considers thatthe only possible types of...

Problem-56: Probability I: Introductory Ideas

A physical therapist at Enormous State University knows that the football team will play 40 percent of its games on artificial turf this season. He also knows that a football...

Problem-57: Probability I: Introductory Ideas

The physical therapist from Exercise 4-48 is interested in studying the relationship between foot injuries and position played. His data, gathered over a 3-year period, are summarized in the following...

Problem-58: Probability I: Introductory Ideas

A state Democratic official has decided that changes in the state unemployment rate will have a major effect on her party's chance of gaining or losing seats in the state...

Problem-59: Probability I: Introductory Ideas

T.C Fox, marketing director for Metro-Goldmine Motion pictures, believes that the studio's upcoming release has a 60 percent chance of being a hit, a 25 percent chance of being a...

Problem-60: Probability I: Introductory Ideas

"The chance of rain today is 80 percent." Which of the following best explains this statement?Contact us for the solution

Problem-61: Probability I: Introductory Ideas

Studies have shown that the chance of a new car being a "lemon"(One with multiple warranty problems) is greater for cars manufactured on Mondays and Fridays. Most consumers don't know...

Problem-62: Probability I: Introductory Ideas

Isaac T.Olduso, an engineer for Atlantic Aircraft, disagrees, with his supervisor about the likelihood of landing-gear failure on the company's new airliner.Contact us for the solution

Problem-63: Probability I: Introductory Ideas

Congressman Bob Forehead has been thinking about the upcoming midterm elections and has prepared the following list of possible developments in his career during the midterm elections:He wins his party’s...

Problem-64: Probability I: Introductory Ideas

Which of the following pairs of events are mutually exclusive? (a) A defense department contractor loses a major contract, and the same contractor increases its work force by 50 percent....

Problem-65: Probability I: Introductory Ideas

The scheduling offi cer for a local police department is trying to decide whether to schedule additional patrol units in each of two neighborhoods. She knows that on any given...

Problem-66: Probability I: Introductory Ideas

The Environmental Protection Agency is trying to assess the pollution effect of a paper mill that is to be built near Spokane, Washington. In studies of six similar plants built...

Problem-67: Probability I: Introductory Ideas

The American Cancer Society is planning to mail out questionnaires concerning breast cancer. From past experience with questionnaires, the Cancer Society knows that only 15 percent of the people receiving...

Problem-68: Probability I: Introductory Ideas

McCormick and Tryon, Inc., is a “shark watcher,” hired by fi rms fearing takeover by larger companies. This fi rm has found that one of its clients, Pare and Oyd...

Problem-69: Probability I: Introductory Ideas

As the administrator of a hospital, Cindy Turner wants to know what the probability is that a person checking into the hospital will require X-ray treatment and will also have...

Problem-70: Probability I: Introductory Ideas

An air traffi c controller at Dulles Airport must obey regulations that require her to divert one of two airplanes if the probability of the aircraft’s colliding exceeds 0.025. The...

Problem-71: Probability I: Introductory Ideas

In a staff meeting called to address the problem of returned checks at the supermarket where you are interning as a fi nancial analyst, the bank reports that 12 percent...

Problem-72: Probability I: Introductory Ideas

Working Mother magazine got the following results when it polled some of its readers concerning the day-care arrangements they had chosen for their children between the ages of 2 and...

Problem-73: Probability I: Introductory Ideas

Which of the following pairs of events are statistically independent? (a) The times until failure of a calculator and of a second calculator marketed by a different fi rm. (b)...

Problem-74: Probability I: Introductory Ideas

F. Liam Laytor, supervisor of customer relations for GLF Airlines, is studying his company’s overbooking problem. He is concentrating on three late-night fl ights out of LaGuardia Airport in New...

Problem-75: Probability I: Introductory Ideas

An electronics manufacturer is considering expansion of its plant in the next 4 years. The decision depends on the increased production that will occur if either government or consumer sales...

Problem-76: Probability I: Introductory Ideas

Draw Venn diagrams to represent the following situations involving three events, A, B, and C, which are part of a sample space of events but do not include the whole...

Problem-77: Probability I: Introductory Ideas

Cartoonist Barry Bludeau sends his comics to his publisher via Union Postal Delivery. UPD uses rail and truck transportation in Mr. Bludeau’s part of the country. In UPD’s 20 years...

Problem-78: Probability I: Introductory Ideas

Determine the probability that (a) Both engines on a small airplane fail, given that each engine fails with probability 0.05 and that an engine is twice as likely to fail...

Problem-79: Probability I: Introductory Ideas

Two-fi fths of clients at Show Me Realty come from an out-of-town referral network, the rest are local. The chances of selling a home on each showing are 0.075 and...

Problem-80: Probability I: Introductory Ideas

A senior North Carolina senator knows he will soon vote on a controversial bill. To learn his constituents’ attitudes about the bill, he met with groups in three cities in...

Problem-81: Probability I: Introductory Ideas

The breakdown by political party of the 435 members of the U.S. House of Representatives before and after the 1992 Congressional elections wasContact us for the solution

Problem-82: Probability I: Introductory Ideas

A produce shipper has 10,000 boxes of bananas from Ecuador and Honduras. An inspection has determined the following information:Contact us for the solution

Problem-83: Probability I: Introductory Ideas

Marcia Lerner will graduate in 3 months with a master’s degree in business administration. Her school’s placement offi ce indicates that the probability of receiving a job offer as the...

Problem-84: Probability I: Introductory Ideas

A standard set of pool balls contains 15 balls numbered from 1 to 15. Pegleg Woodhull, the famous blind poolplayer, is playing a game of 8-ball, in which the 8-ball...

Problem-85: Probability I: Introductory Ideas

BMT, Inc., is trying to decide which of two oil pumps to use in its new race car engine. One pump produces 75 pounds of pressure and the other 100....

Problem-86: Probability I: Introductory Ideas

Sandy Irick is the public relations director for a large pharmaceutical fi rm that has been attacked in the popular press for distributing an allegedly unsafe vaccine. The vaccine protects...

Problem-87: Probability I: Introductory Ideas

The pressroom supervisor for a daily newspaper is being pressured to find ways to print the paper closer to distribution time, thus giving the editorial staff more leeway for last-minute...

Problem-88: Probability I: Introductory Ideas

Refer to Exercise 4-83. The supervisor has noted that the web tore during each of the last four runs and that the speed of the press was not changed during...

Problem-89: Probability I: Introductory Ideas

Airlines serve as ''flagship carriers'' in Europe, and for symbolic and strategic reasons, many have been state owned. But governments have had to pay heavy subsidies and some airlines have...

Problem-90: Probability I: Introductory Ideas

In the summer of 1995, Boeing successfully introduced into commercial airline service the 777, a large plane capable of carrying more than 300 passengers. They immediately sought approval from the...

Probability I: Introductory Ideas

Problem-46: Probability I: Introductory Ideas

Solution

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