The following problen was given to 60 students and doctors at the famous Hevardi

Question

The following problen was given to 60 students and doctors at the famous Hevardi Medical School (HMS): Assune there exists a test to detect a disease, say D, whose prevalence is 0.001, that is, the probability, P[D, that a person picked at raudom is suffering from D, is 0.001. The test has a false-positive rate of 0.005 and a correct detection rate of 1. The correct detection rate is the probability that if you have D, the test will say that you have D. Given that you test positive for D, what is the probability that you actually have it? Many of the HMS experts answered 0.95 and the average answer was 0.56. Show that your knowledge of probability is greater thau that of the HMS experts by getting the right answer of 0.17.

Explanation / Answer

P( Disease/Positive)= P( Positive/Disease)*P(Disease) /[P( Positive/Disease)*P(Disease) +P( Positive/NonDisease)*P(NonDisease)] = 0.001*1/[0.001*1 + 0.999*0.005]=0.1668=0.17

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