4-2 Addition Rule and Multiplication Rule 169 19. Texting and Alcohol If four different high school drivers are randomly selected, find the probability that they all drove when drinking alcohol. 20. Texting and Alcohol If four different high school drivers are randomly selected, find the probability that they all texted while driving. In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive (incorrect) results; among 157 negative results, there are 3 false negative (incorrect) results. (Hint: Construct a table similar to Table 4-1 on page 159.) 21. Testing for Marijuana Use a. How many subjects are included in the study? b. How many of the subjects had a true negative result? c. What is the probability that a randomly selected subject had a true negative result? 22. Testing for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested negative or used marijuana. 23. Testing for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested positive or did not use marijuana. 24. Testing for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject did not use marijuana. Do you think that the result reflects the general population rate of subjects who do not use marijuana? Redundancy. Exercises 25 and 26 involve redundancy. 25. Redundancy in Computer Hard Drives It is generally recognized that it is wise to backup computer data. Assume that the following refer to use of Western Digital model WD60EFRX hard drives, which have an annual failure rate of 3.66% (based on data from Backblaze, Inc.). a. If you store all of your computer data on a single hard drive, what is the probability that the drive will fail during a year? b. If all of your computer data are stored on a hard drive with a copy stored on a second hard disk drive, what is the probability that both drives will fail during a year? c. If copies of all of your computer data are stored on three independent hard drives, what is the probability that all three will fail during a year? d. Describe the improved reliability that is gained with backup drives. 26. Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure. a. What is the probability that your single battery-powered alarm clock works successfully when you need it? b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail? c. If you use a battery-powered alarm clock and a smartphone alarm clock and an electric alarm clock, what is the probability that they all fail? What is the probability that they don’t all fail? Express both of these answers using eight decimal places. d. What configuration gives you the best chance to wake up for something really important?
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