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Snow After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter." Explain what he's trying to say, and comment on the validity of his reasoning.

Crash Commercial airplanes have an excellent safety record. Nevertheless, there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers, probably because people are afraid to risk flying. a. A travel agent suggests that since the Law of Averages makes it highly unlikely to have two plane crashes within a few weeks of each other, flying soon after a crash is the safest time. What do you think? b. If the airline industry proudly announces that it has set a new record for the longest period of safe flights, would you be reluctant to fly? Are the airlines due to have a crash?

Auto insurance Insurance companies collect annual payments from drivers in exchange for paying for the cost of accidents. a. Why should you be reluctant to accept a \(\$ 1500\) payment from your neighbor to cover his automobile accidents in the next year? b. Why can the insurance company make that offer?

Electronics Suppose that \(46 \%\) of families living in a certain county own a computer and \(18 \%\) own an HDTV. The Addition Rule might suggest, then, that \(64 \%\) of families own either a computer or an HDTV. What's wrong with that reasoning?

Homes Funding for many schools comes from taxes based on assessed values of local properties. People's homes are assessed higher if they have extra features such as garages and swimming pools. Assessment records in a certain school district indicate that \(37 \%\) of the homes have garages and \(3 \%\) have swimming pools. The Addition Rule might suggest, then, that \(40 \%\) of residences have a garage or a pool. What's wrong with that reasoning?

Speeders Traffic checks on a certain section of highway suggest that \(60 \%\) of drivers are speeding there. Since \(0.6 \times 0.6=0.36\), the Multiplication Rule might suggest that there's a \(36 \%\) chance that two vehicles in a row are both speeding. What's wrong with that reasoning?

Lefties Although it's hard to be definitive in classifying people as right- or left-handed, some studies suggest that about \(14 \%\) of people are left- handed. Since \(0.14 \times 0.14=0.0196,\) the Multiplication Rule might suggest that there's about a \(2 \%\) chance that a brother and a sister are both lefties. What's wrong with that reasoning?

Car repairs A consumer organization estimates that over a 1-year period \(17 \%\) of cars will need to be repaired only once, \(7 \%\) will need repairs exactly twice, and \(4 \%\) will require three or more repairs. What is the probability that a car chosen at random will need a. no repairs? b. no more than one repair? c. some repairs?

Stats projects In a large introductory statistics lecture hall, the professor reports that \(55 \%\) of the students enrolled have never taken a calculus course, \(32 \%\) have taken only one semester of calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that the first groupmate you meet has studied a. two or more semesters of calculus? b. some calculus? c. no more than one semester of calculus?

Polling As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about \(62 \%\) of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from \(43 \%\) in 1997 to \(14 \%\) in 2012 (Source: Pew Research Center for the People and the Press). Each household, of course, is independent of the others. Using the cooperation rate from 2012 , a. what is the probability that the next household on the list will be contacted but will refuse to cooperate? b. what is the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview? c. show another way to calculate the probability in part b.