(b) You wish to pick at least two of each symbol, but no more than 5 hearts
and 6 spades? (10%)

五、Most medical tests occasionally produce incorrect results, called false positives and false negatives. When a test is designed to determine whether a patient has a certain disease, a false positive result indicates that a patient has the disease when the patient does not have it. A false negative result indicates that a patient does not have the disease when the patient does have it. When large-scale health screenings are performed for diseases with relatively low incidence, those who develop the screening procedures have to balance several considerations: the per-person cost of the screening, follow-up costs for further testing of false positives, and the possibility that people who have the disease will develop unwarranted confidence in the state of their health. Consider a medical test that screens for a disease found in 5 people in 1,000. Suppose that the false positive rate is 3% and the false negative rate is 1%. Then 99% of the time a person who has the condition tests positive for it, and 97% of the time a person who does not have the condition tests negative for it. (a) What is the probability that a randomly chosen person who tests positive for the disease actually has the disease? (10%)

(b) What is the probability that a randomly chosen person who tests negative for the disease does not indeed have the disease? (10%)

六、Solve the recurrence relation an-6an-1-7an-2 =0 for n≧5 where a3 = 344 and a4 = 2400. (10%)

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