A man goes to see his medical doctor to find out whether or not he has a deadly

Question

A man goes to see his medical doctor to find out whether or not he has a deadly disease. The test is positive. The test is 95% accurate and one in one thousand men of his age has this disease. What is the probability he has the disease? He decides to seek a second opinion but the results are exactly the same. When this question was put to a group of doctors. 80% of them answered "95%". He now plans to sell up all his assets, tell his boss what he really thinks of her, quit his job on the spot and live in Mauritius in the time he has left. Is this a rational decision? Explain.

Explanation / Answer

First put the data in the table as shown below

Prob that he has disease/test is positve = P(he has disease and test positive)/P(test positive)

=0.95/1.00 = 0.95

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Since 80% of doctors answered yes, his decision is rational

Disease No disease Positive 0.95 949.05 950 Negative 0.05 49.95 50 1 999 1000

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