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

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 96% accurate and one in one thousand men of his age has this disease. What is the probability he has the disease? When this question was put to a group of student doctors, 80% of them answered “96%”. He now plans to sell up all his assets, quit his job on the spot and live in Bora Bora in the time he has left. Is this a rational decision? Explain. (Hint: research conditional probability).

Math   Statistics-And-Probability   
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Answer #1

Probability that the man has the disease= 1/1000 = 0.001

Thus, probability that the man does not have the disease= 999/1000 = 0.999

Probability that the test is accurate= 96/100 = 0.96

Thus, probability that the test is not accurate= 4/100 = 0.04

Probability ( man has disease | test is positive ) = P ( man has disease) * P ( test is positive | man has disease) / [ P ( man has disease) * P ( test is positive | man has disease) + P ( man does not have disease) * P ( test is positive | man does not have disease) ]

= (0.001*0.96) / [ (0.001*0.96) + (0.999*0.04) ]

= 8/341

= 2.3%

Thus, the probability that the man does have the disease given that the test is positive is a meager 2%. It is a very bad decision to sell everything and leave.

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