91Ó°ÊÓ

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. What's 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.

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 employer-sponsored 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.

If you draw a card at random from a well-shuffled deck, is getting an ace independent of the suit? Explain.

The local animal shelter in Exercise 22 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.

According to estimates from the federal government's 2010 National Health Interview Survey, based on face-to-face interviews in 16,676 households, approximately \(63.6 \%\) of U.S. adults have both a landline in their residence and a cell phone, \(25.4 \%\) have only cell phone service but no landline, and \(1.8 \%\) 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.

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 30 or less and did not snore? b. Is snoring independent of age? Explain.

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?

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 freshman's chances to graduate may depend upon what kind of high school the student attended? Explain. b. What percent of freshmen eventually graduate?

A company's 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?

An airline offers discounted "advance-purchase" 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. What's the probability that a customer who didn't show had an advance- purchase ticket? c. Is being a no-show independent of the type of ticket a passenger holds? Explain.