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MIT6_042JF10_rec18

# MIT6_042JF10_rec18 - 6.042/18.062J Mathematics for Computer...

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6.042/18.062J Mathematics for Computer Science November 17, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 18 1 Nerditosis There is a rare and deadly disease called Nerditosis which afflicts about 1 person in 1000. One symptom is a compulsion to refer to everything— fields of study, classes, buildings, etc.— using numbers. It’s horrible. As victims enter their final, downward spiral, they’re awarded a degree from MIT. Two doctors claim that they can diagnose Nerditosis. 1. Doctor X received his degree from Harvard Medical School. He practices at Mas- sachusetts General Hospital and has access to the latest scanners, lab tests, and re- search. Suppose you ask Doctor X whether you have the disease. If you have Nerditosis, he says “yes” with probability 0.99. If you don’t have it, he says “no” with probability 0.97. Let D be the event that you have the disease, and let E be the event that the diagnosis is erroneous. Use the Total Probability Law to compute Pr { E } , the probability that Doctor X makes a mistake.

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