# Question: 3 mortal disease there is a rare and deadly disease...

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3 Mortal Disease

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 PhD degree from Waseda University. Two doctors claim that they can diagnose Nerditosis.

1. Doctor X received his degree from Harvard Medical School. He practices at Massachusetts General Hospital and has access to the latest scanners, lab tests, and research. Suppose you ask Doctor X whether you have the disease. 2 • 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 P(E), the probability that Doctor X makes a mistake.

2. “Doctor” Y received his genuine degree from a fully-accredited university for $49.95 via a special internet offer. He knows that Nerditosis strikes 1 person in 1000, but is a little shaky on how to interpret this. So if you ask him whether you have the disease, he’ll helpfully say “yes” with probability 1 in 1000 regardless of whether you actually do or not. Let D be the event that you have the disease, and let F be the event that the diagnosis is faulty. Use the Total Probability Law to compute P(E), the probability that Doctor Y made a mistake.

3. Which doctor is more reliable?