42. No-shows. An airline offers discounted

1. Homes. Real estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features. What is the probability that a home for sale has a) a pool or a garage? b) neither a pool nor a garage? c) a pool but no garage?

2. Travel. Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. Whats the probability that an American chosen at random has a) traveled to Canada but not Mexico? b) traveled to either Canada or Mexico? c) not traveled to either country?

3. Amenities. A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TVs, and 21% had both a TV and a refrigerator. Whats the probability that a randomly selected dorm room has a) a TV but no refrigerator? b) a TV or a refrigerator, but not both? c) neither a TV nor a refrigerator?

4. Workers. Employment data at a large company reveal that 72% of the workers are married, that 44% are college graduates, and that half of the college grads are married. Whats the probability that a randomly chosen worker a) is neither married nor a college graduate? b) is married but not a college graduate? c) is married or a college graduate?

5. Global survey. The marketing research organization GfK Custom Research North America conducts a yearly survey on consumer attitudes worldwide. They collect demographic information on the roughly 1500 respondents from each country that they survey. Here is a table showing the number of people with various levels of education in five countries: If we select someone at random from this survey, a) what is the probability that the person is from the United States? b) what is the probability that the person completed his or her education before college? c) what is the probability that the person is from France or did some post-graduate study? d) what is the probability that the person is from France and finished only primary school or less?

6. Birth order. A survey of students in a large Introductory Statistics class asked about their birth order (1 = oldest or only child) and which college of the university they were enrolled in. Here are the results: Suppose we select a student at random from this class. What is the probability that the person is a) a Human Ecology student? b) a firstborn student? c) firstborn and a Human Ecology student? d) firstborn or a Human Ecology student?

7. Cards. You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities: a) The card is a heart, given that it is red. b) The card is red, given that it is a heart. c) The card is an ace, given that it is red. d) The card is a queen, given that it is a face card.

8. Pets. In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random: a) The pet is male, given that it is a cat. b) The pet is a cat, given that it is female. c) The pet is female, given that it is a dog

9. Health. The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table. Whats the probability that a) a man has both conditions? b) a man has high blood pressure? c) a man with high blood pressure has high cholesterol? d) a man has high blood pressure if its known that he has high cholesterol?

10. Death penalty. The table shows the political affiliations of American voters and their positions on the death penalty. a) Whats the probability that i) a randomly chosen voter favors the death penalty? ii) a Republican favors the death penalty? iii) a voter who favors the death penalty is a Democrat? b) A candidate thinks she has a good chance of gaining the votes of anyone who is a Republican or in favor of the death penalty. What portion of the voters is that?

11. Global survey, take 2. Look again at the table summarizing the Roper survey in Exercise 5. a) If we select a respondent at random, whats the probability we choose a person from the United States who has done post-graduate study? b) Among the respondents who have done postgraduate study, whats the probability the person is from the United States? c) Whats the probability that a respondent from the United States has done post-graduate study? d) Whats the probability that a respondent from China has only a primary-level education? e) Whats the probability that a respondent with only a primary-level education is from China?

12. Birth order, take 2. Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 6. a) If we select a student at random, whats the probability the person is an Arts and Sciences student who is a second child (or more)? b) Among the Arts and Sciences students, whats the probability a student was a second child (or more)? c) Among second children (or more), whats the probability the student is enrolled in Arts and Sciences? d) Whats the probability that a first or only child is enrolled in the Agriculture College? e) What is the probability that an Agriculture student is a first or only child?

13. Sick kids. Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat?

14. Sick cars. Twenty percent of cars that are inspected have faulty pollution control systems. The cost of repairing a pollution control system exceeds $100 about 40% of the time. When a driver takes her car in for inspection, what's the probability that she will end up paying more than $100 to repair the pollution control system?

15. Cards. You are dealt a hand of three cards, one at a time. Find the probability of each of the following. a) The first heart you get is the third card dealt. b) Your cards are all red (that is, all diamonds or hearts). c) You get no spades. d) You have at least one ace.

16. Another hand. You pick three cards at random from a deck. Find the probability of each event described below. a) You get no aces. b) You get all hearts. c) The third card is your first red card. d) You have at least one diamond.

17. Batteries. A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome. a) The first two you choose are both good. b) At least one of the first three works. c) The first four you pick all work. d) You have to pick 5 batteries to find one that works.

18. Shirts. The soccer teams shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described. a) The first two you grab are the wrong sizes. b) The first medium shirt you find is the third one you check. c) The first four shirts you pick are all extra-large. d) At least one of the first four shirts you check is a medium.

19. Eligibility. A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer course, and 7% have done both. a) What percent of the junior Biology majors are ineligible for BioResearch? b) Whats the probability that a junior Biology major who has taken Statistics has also taken a computer course? c) Are taking these two courses disjoint events? Explain. d) Are taking these two courses independent events? Explain.

20. Benefits. Fifty-six percent of all American workers have a workplace retirement plan, 68% have health insurance, and 49% have both benefits. We select a worker at random. a) Whats the probability he has neither employersponsored health insurance nor a retirement plan? b) Whats the probability he has health insurance if he has a retirement plan? c) Are having health insurance and a retirement plan independent events? Explain. d) Are having these two benefits mutually exclusive? Explain.

21. For sale. In the real-estate ads described in Exercise 1, 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features. a) If a home for sale has a garage, whats the probability that it has a pool too? b) Are having a garage and a pool independent events? Explain. c) Are having a garage and a pool mutually exclusive? Explain.

22. On the road again. According to Exercise 2, the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. a) Whats the probability that someone who has traveled to Mexico has visited Canada too? b) Are traveling to Mexico and to Canada disjoint events? Explain. c) Are traveling to Mexico and to Canada independent events? Explain.

23. Cards. If you draw a card at random from a wellshuffled deck, is getting an ace independent of the suit? Explain.

24. Pets again. The local animal shelter in Exercise 8 reported that it currently has 24 dogs and 18 cats available for adoption; 8 of the dogs and 6 of the cats are male. Are the species and sex of the animals independent? Explain.

25. Unsafe food. Early in 2007 Consumer Reports published the results of an extensive investigation of broiler chickens purchased from food stores in 23 states. Tests for bacteria in the meat showed that 81% of the chickens were contaminated with campylobacter, 15% with salmonella, and 13% with both. a) Whats the probability that a tested chicken was not contaminated with either kind of bacteria? b) Are contamination with the two kinds of bacteria disjoint? Explain. c) Are contamination with the two kinds of bacteria independent? Explain.

26. Birth order, finis. In Exercises 6 and 12 we looked at the birth orders and college choices of some Intro Stats students. For these students: a) Are enrolling in Agriculture and Human Ecology disjoint? Explain. b) Are enrolling in Agriculture and Human Ecology independent? Explain. c) Are being firstborn and enrolling in Human Ecology disjoint? Explain. d) Are being firstborn and enrolling in Human Ecology independent? Explain.

27. Mens health, again. Given the table of probabilities from Exercise 9, are high blood pressure and high cholesterol independent? Explain.

28. Politics. Given the table of probabilities from Exercise 10, are party affiliation and position on the death penalty independent? Explain.

29. Phone service. According to estimates from the federal governments 2003 National Health Interview Survey, based on face-to-face interviews in 16,677 households, approximately 58.2% of U.S. adults have both a landline in their residence and a cell phone, 2.8% have only cell phone service but no landline, and 1.6% have no telephone service at all a) Polling agencies wont phone cell phone numbers because customers object to paying for such calls. What proportion of U.S. households can be reached by a landline call? b) Are having a cell phone and having a landline independent? Explain.

30. Snoring. After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30. a) What percent of the respondents were under 30 and did not snore? b) Is snoring independent of age? Explain.

31. Montana. A 1992 poll conducted by the University of Montana classified respondents by sex and political party, as shown in the table. Is party affiliation independent of the respondents sex? Explain.

32. Cars. A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Is country of origin independent of type of driver?

33. Luggage. Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65. a) Are the first flight leaving on time and the luggage making the connection independent events? Explain. b) What is the probability that her luggage arrives in Denver with her?

34. Graduation. A private college report contains these statistics: 70% of incoming freshmen attended public schools. 75% of public school students who enroll as freshmen eventually graduate. 90% of other freshmen eventually graduate. a) Is there any evidence that a freshmans chances to graduate may depend upon what kind of high school the student attended? Explain. b) What percent of freshmen eventually graduate?

35. Late luggage. Remember Leah (Exercise 33)? Suppose you pick her up at the Denver airport, and her luggage is not there. What is the probability that Leahs first flight was delayed?

36. Graduation, part II. What percent of students who graduate from the college in Exercise 34 attended a public high school?

37. Absenteeism. A companys records indicate that on any given day about 1% of their day-shift employees and 2% of the night-shift employees will miss work. Sixty percent of the employees work the day shift. a) Is absenteeism independent of shift worked? Explain. b) What percent of employees are absent on any given day?

38. Lungs and smoke. Suppose that 23% of adults smoke cigarettes. Its known that 57% of smokers and 13% of nonsmokers develop a certain lung condition by age 60. a) Explain how these statistics indicate that lung condition and smoking are not independent. b) Whats the probability that a randomly selected 60-year-old has this lung condition?

39. Absenteeism, part II. At the company described in Exercise 37, what percent of the absent employees are on the night shift?

40. Lungs and smoke again. Based on the statistics in Exercise 38, what's the probability that someone with the lung condition was a smoker?

41. Drunks. Police often set up sobriety checkpoints roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. If the officer does not suspect a problem, drivers are released to go on their way. Otherwise, drivers are detained for a Breathalyzer test that will determine whether or not they will be arrested. The police say that based on the brief initial stop, trained officers can make the right decision 80% of the time. Suppose the police operate a sobriety checkpoint after 9 p.m. on a Saturday night, a time when national traffic safety experts suspect that about 12% of drivers have been drinking. a) You are stopped at the checkpoint and, of course, have not been drinking. Whats the probability that you are detained for further testing? b) Whats the probability that any given driver will be detained? c) Whats the probability that a driver who is detained has actually been drinking? d) Whats the probability that a driver who was released had actually been drinking?

42. No-shows. An airline offers discounted advancepurchase fares to customers who buy tickets more than 30 days before travel and charges regular fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage of the advance-purchase fares. The no-show rate among people who paid regular fares is 30%, but only 5% of customers with advance-purchase tickets are no-shows. a) What percent of all ticket holders are no-shows? b) Whats the probability that a customer who didnt show had an advance-purchase ticket? c) Is being a no-show independent of the type of ticket a passenger holds? Explain.

43. Dishwashers. Dan's Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3% of the dishes he washes. (He, of course, will need a new job soon. . . .) You go to Dan's for supper one night and hear a dish break at the sink. What's the probability that Chuck is on the job?

44. Parts. A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only 70% of the connectors needed. The company must also purchase connectors from two other suppliers, 20% from supplier B and the rest from supplier C. The rates of defective connectors from B and C are 2% and 4%, respectively. You buy one of these components, and when you try to use it you find that the connector is defective. What's the probability that your component came from supplier A?

45. HIV testing. In July 2005 the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were (correctly) positive, while for people without HIV 98.5% of the tests were (correctly) negative. A clinic serving an at-risk population offers free HIV testing, believing that 15% of the patients may actually carry HIV. What's the probability that a patient testing negative is truly free of HIV?

46. Polygraphs. Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no agreement, about the reliability of polygraph tests. Based on this research, suppose that a polygraph can detect 65% of lies, but incorrectly identifies 15% of true statements as lies.