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2.72 For a certain population of employees, the percentage passing or failing a job competency exam,
listed according to sex, were as shown in the accompanying table. That is, of all the people
taking the exam, 24% were in the male­pass category, 16% were in the male­fail category, and
so forth. An employee is to be selected randomly from this population. Let A be the event that
the employee scores a passing grade on the exam and let M be the event that a male is selected.
Sex
Outcome Male (M) Female (F) Total
60
36
Pass ( A) 24
40
24
Fail ( Ac) 16
100
60
40
Total
a Are the events A and M independent?
b Are the events Ac and F independent?
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AP 04.08.13.notebook
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2.86 Suppose that A and B are two events such that P ( A) = .8 and P(B) = .7.
a Is it possible that P( A ∩ B) = .1? Why or why not?
b What is the smallest possible value for P( A ∩ B)?
c Is it possible that P( A ∩ B) = .77? Why or why not?
d What is the largest possible value for P( A ∩ B)?
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2.130 A study of Georgia residents suggests that those who worked in shipyards during World War II were subjected to a significantly higher risk of lung cancer (Wall Street Journal, September 21, 1978). It was found that approximately 22% of those persons who had lung cancer worked at some prior time in a shipyard. In contrast, only 14% of those who had no lung cancer worked at some prior time in a shipyard. Suppose that the proportion of all Georgians living during World War II who have or will have contracted lung cancer is .04%. Find the percentage of Georgians living during the same period who will contract (or have contracted) lung cancer, given that they have at some prior time worked in a shipyard.
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2.125 A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the
individuals who actually have the disease. Also, if a person does not have the disease, the test
will report that he or she does not have it with probability .9. Only 1% of the population has the
disease in question. If a person is chosen at random from the population and the diagnostic test
indicates that she has the disease, what is the conditional probability that she does, in fact, have
the disease? Are you surprised by the answer? Would you call this diagnostic test reliable?
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2.124 A population of voters contains 40% Republicans and 60% Democrats. It is reported that 30% of the Republicans and 70% of the Democrats favor an election issue. A person chosen at random from this population is found to favor the issue in question. Find the conditional probability that this person is a Democrat.
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