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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 21–24, 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 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?
In Exercises 17–20, refer to the accompanying table showing results from a Chembio test for hepatitis C among HIV-infected patients (based on data from a variety of sources).
Positive Test Result | Negative Test Result | |
Hepatitis C | 335 | 10 |
No Hepatitis C | 2 | 1153 |
Positive Predictive Value Find the positive predictive value for the test. That is, find the probability that a subject has hepatitis C, given that the test yields a positive result. Does the result make the test appear to be effective?
In Exercises 9–12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.
47 girls.
In Exercises 29 and 30, find the probabilities and indicate when the “5% guideline for cumbersome calculations” 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?
Probability from a Sample Space. In Exercises 33–36, use the given sample space or construct the required sample space to find the indicated probability.
Three Children Using the same sample space and assumption from Exercise 33, find the probability that when a couple has three children, there are exactly two girls.
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