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Chapter 4: Q1 (page 155)
Notation When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do and represent ?
represents the probability of selecting an adult having blue eyes.
represents the probability of selecting an adult without blue eyes.
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In Exercises 21鈥�24, use these results from the 鈥�1-Panel-THC鈥� 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 results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)
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?
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 29 and 30, find the probabilities and indicate when the 鈥�5% guideline for cumbersome calculations鈥� is used.
Medical Helicopters In the same study cited in the preceding exercise, among the 47,637 patients transported by helicopter, 188 of them left the treatment center against medical advice, and the other 47,449 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice?
At Least One. In Exercises 5鈥�12, find the probability.
Births in China In China, where many couples were allowed to have only one child, the probability of a baby being a boy was 0.545. Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out of this policy was begun in 2015.)
Probability of At Least One Let A = the event of getting at least 1 defective iPhone when 3 iPhones are randomly selected with replacement from a batch. If 5% of the iPhones in a batch are defective and the other 95% are all good, which of the following are correct?
a. = (0.95)(0.95)(0.95) = 0.857
b. P(A) = 1 - (0.95)(0.95)(0.95) = 0.143
c. P(A) = (0.05)(0.05)(0.05) = 0.000125
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