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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?

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. What's 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?

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. What's 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?

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.

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) What's the probability he has neither employersponsored health insurance nor a retirement plan? b) What's 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.

According to estimates from the federal government's 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 won't 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.

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. A certain company believes that \(95 \%\) of its job applicants are trustworthy. The company gives everyone a polygraph test, asking, "Have you ever stolen anything from your place of work?" Naturally, all the applicants answer \({ }^{\prime} \mathrm{No}\)," but the polygraph identifies some of those answers as lies, making the person ineligible for a job. What's the probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy?