Chapter 4: Q4 (page 143)
Subjective Probability Estimate the probability that the next time you turn on a light switch, you discover that a bulb does work.
An estimate of the probability that the next time the bulb will glow when the light switch is turned on is equal to 0.998.
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Surge Protectors Refer to the accompanying figure showing surge protectors p and q used to protect an expensive television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.985 probability of working correctly when a voltage surge occurs.
a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? (Do not round the answer.)
b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television? (Do not round the answer.)
c. Which arrangement should be used for better protection?
In Exercises 9–20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.
McDonald’s | Burger King | Wendy’s | Taco Bell | |
Order Accurate | 329 | 264 | 249 | 145 |
OrderNotAccurate | 33 | 54 | 31 | 13 |
Fast Food Drive-Thru Accuracy If two orders are selected, find the probability that both of them are not accurate.
a. Assume that the selections are made with replacement. Are the events independent?
b. Assume that the selections are made without replacement. Are the events independent?
Redundancy. Exercises 25 and 26 involve redundancy.
Redundancy in Computer Hard Drives It is generally recognized that it is wise to back up computer data. Assume that there is a 3% rate of disk drive failure in a year (based on data from various sources, including lifehacker.com).
a. If you store all of your computer data on a single hard disk drive, what is the probability that the drive will fail during a year? continued 158 CHAPTER 4 Probability
b. If all of your computer data are stored on a hard disk 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 disk drives, what is the probability that all three will fail during a year?
d. Describe the improved reliability that is gained with backup drives
In Exercises 21–24, refer to the sample data in Table 4-1, which is included with the Chapter Problem. Assume that 1 of the 555 subjects included in Table 4-1 is randomly selected.
Positive Test Result (Test shows drug use) | Negative Test Result (Test shows no drug use) | |
Subject Uses Drugs | 45 (True Positive) | 5 (False Negative) |
Subject Does Not Use drugs | 25 (False Positive) | 480 (True Negative) |
Drug Testing Job Applicants Find the probability of selecting someone who uses drugs. Does the result appear to be reasonable as an estimate of the “prevalence rate” described in the Chapter Problem?
Exclusive Or The exclusive or means either one or the other events occurs, but not both.
a. For the formal addition rule, rewrite the formula for P(A or B) assuming that the addition rule uses the exclusive or instead of the inclusive or.
b. Repeat Exercise 11 “Fast Food Drive-Thru Accuracy” using the exclusive or instead of the inclusive or.
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