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 of all checks are returned for insuffi cient funds, and of those, in 50 percent of cases, there was cash given back to the customer. Overall, 10 percent of customers ask for cash back at the end of their transaction with the store. For 1,000 customer visits, how many transactions will involve: (a) Insuffi cient funds? (b) Cash back to the customer? (c) Both insuffi cient funds and cash back? (d) Either insuffi cient funds or cash back?
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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 5.
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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) The life-spans of the current U.S. and Russian presidents. (c) The amounts of settlements in asbestos poisoning cases in Maryland and New York. (d) The takeover of a company and a rise in the price of its stock. (e) The frequency of organ donation in a community and the predominant religious orientation of that community
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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 York City. In the last year, 7, 8, and 5 percent of the passengers on the Atlanta, Kansas City, and Detroit fl ights, respectively, have been bumped. Further, 55, 20, and 25 percent of the late-night GLF passengers at LaGuardia take the Atlanta, Kansas City, and Detroit fl ights, respectively. What is the probability that a bumped passenger was scheduled to be on the (a) Atlanta fl ight? (b) Kansas City fl ight? (c) Detroit fl ight?
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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 increase. Specifi cally, the plant will be expanded if either (1) consumer sales increase 50 percent over the present sales level or (2) a major government contract is obtained. The company also believes that both these events will not happen in the same year. The planning director has obtained the following estimates: The probability of consumer sales increasing by 50 percent within 1, 2, 3, and 4 years is 0.05, 0.08, 0.12, and 0.16, respectively. The probability of obtaining a major government contract within 1, 2, 3, and 4 years is 0.08, 0.15, 0.25, and 0.32, respectively What is the probability that the plant will expand (a) Within the next year (in year 1)? (b) Between 1 and 2 years from now (in year 2)? (c) Between 2 and 3 years from now (in year 3)? (d) Between 3 and 4 years from now (in year 4)?
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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 sample space. (a) Each pair of events (A and B, A and C, and B and C) may occur together, but all three may not occur together. (b) A and B are mutually exclusive, but not A and C nor B and C. (c) A, B, and C are all mutually exclusive of one another. (d) A and B are mutually exclusive, B and C are mutually exclusive, but A and C are not mutually exclusive.
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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 of operation, only 2 percent of the packages carried by rail and only 3.5 percent of the packages carried by truck have been lost. Mr. Bludeau calls the claims manager to inform him that a package containing a week of comics has been lost. If UPD sends 60 percent of the packages in that area by rail, which mode of transportation was more likely used to carry the lost comics? How does the solution change if UPD loses only 2 percent of its packages, regardless of the mode of transportation?
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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 when it is the only engine working. (b) An automobile is recalled for brake failure and has steering problems, given that 15 percent of that model were recalled for brake failure and 2 percent had steering problems. (c) A citizen fi les his or her tax return and cheats on it, given that 70 percent of all citizens fi le returns and 25 percent of those who fi le cheat.
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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 0.053 for out-of-town and local clients, respectively. If a salesperson walks into Show Me’s offi ce and announces “It’s a deal!” was the agent more likely to have conducted a showing for an out-of-town or local client?
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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 his state. An aide jotted down the opinions of 15 attendees at each meeting
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