Chapter 5

A computer-supply retailer purchased a batch of 1,000 CD-R disks and attempted to format them for a particular application. There were 857 perfect CDs, 112 CDs were usable but had bad sectors, and the remainder could not be used at all. a. What is the probability a randomly chosen \(\mathrm{CD}\) is not perfect? b. If the disk is not perfect, what is the probability it cannot be used at all?

With each purchase of a large pizza at Tony's Pizza, the customer receives a coupon that can be scratched to see if a prize will be awarded. The odds of winning a free soft drink are 1 in \(10,\) and the odds of winning a free large pizza are 1 in \(50 .\) You plan to eat lunch tomorrow at Tony's. What is the probability: a. That you will win either a large pizza or a soft drink? b. That you will not win a prize? c. That you will not win a prize on three consecutive visits to Tony's? d. That you will win at least one prize on one of your next three visits to Tony's?

For the daily lottery game in Illinois, participants select three numbers between 0 and \(9 .\) A number cannot be selected more than once, so a winning ticket could be, say, 307 but not 337 . Purchasing one ticket allows you to select one set of numbers. The winning numbers are announced on TV each night. a. How many different outcomes (three-digit numbers) are possible? b. If you purchase a ticket for the game tonight, what is the likelihood you will win? c. Suppose you purchase three tickets for tonight's drawing and select a different number for each ticket. What is the probability that you will not win with any of the tickets?

Several years ago Wendy's Hamburgers advertised that there are 256 different ways to order your hamburger. You may choose to have, or omit, any combination of the following on your hamburger: mustard, ketchup, onion, pickle, tomato, relish mayonnaise, and lettuce. Is the advertisement correct? Show how you arrive at your answer.

IIt was found that 60 percent of the tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing. Forty percent visited Xi'an with its magnificent terracotta soldiers, horses, and chariots, which lay buried for over 2,000 years. Thirty percent of the tourists went to both Beijing and Xi'an. What is the probability that a tourist visited at least one of these places?

A new chewing gum has been developed that is helpfu to those who want to stop smoking. If 60 percent of those people chewing the gum are successful in stopping smoking, what is the probability that in a group of four smokers using the gum at least one quits smoking?

Reynolds Construction Company has agreed not to erect all "look-alike" homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways can the exterior and interior plans be offered to potential home buyers?

A new sports car model has defective brakes 15 percent of the time and a defective steering mechanism 5 percent of the time. Let's assume (and hope) that these problems occur independently. If one or the other of these problems is present, the car is called a "lemon." If both of these problems are present, the car is a "hazard." Your instructor purchased one of these cars yesterday. What is the probability it is: a. A lemon? b. A hazard?

The state of Maryland has license plates with three numbers followed by three letters. How many different license plates are possible?

There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are female, of which only one is over 60 . a. What is the probability that a candidate is over 60 and female? b. Given that the candidate is male, what is the probability he is less than \(60 ?\) c. Given that the person is over \(60,\) what is the probability the person is female?

Tim Bleckie is the owner of Bleckie Investment and Real Estate Company. The company recently purchased four tracts of land in Holly Farms Estates and six tracts in Newburg Woods. The tracts are all equally desirable and sell for about the same amount. a. What is the probability that the next two tracts sold will be in Newburg Woods? b. What is the probability that of the next four sold at least one will be in Holly Farms? c. Are these events independent or dependent?

.A computer password consists of four characters. The characters can be one of the 26 letters of the alphabet. Each character may be used more than once. How many different passwords are possible?

A case of 24 cans contains 1 can that is contaminated. Three cans are to be chosen randomly for testing. a. How many different combinations of 3 cans could be selected? b. What is the probability that the contaminated can is selected for testing?

A puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column. The puzzle asks the reader to match each president with his vice president. If you make the matches randomly, how many matches are possible? What is the probability all 10 of your matches are correct?

Two components, \(A\) and \(B\), are in series. (Being in series means that for the system to operate, both components \(A\) and \(B\) must work.) Assume the two components are independent. What is the probability the system works under these conditions? The probability \(A\) works is .90 and the probability \(B\) functions is also .90 .

During the 1970 s the qame show Let's Make a Deal had a long run on TV. In the show a contestant was given a choice of three doors, behind one of which was a prize. The other two doors contained a gag gift of some type. After the contestant selected a door, the host of the show then revealed to them one of the doors from among the two not selected. The host asked the contestant if they wished to switch doors to one of those not chosen. Should the contestant switch? Are the odds of winning increased by switching doors?