This was the only part of this question that wasn\'t alreadyanswered. Each of 50

Question

This was the only part of this question that wasn't alreadyanswered. Each of 500 soldiers in an army company independently has acertain disease with probability 1/1000. This disease willshow up on a blood test, and to facilitate matters, blood samplesfrom all 500 soldiers are pooled and tested. Suppose now thatthe blood test yields a positive result. One of the 500people is Jones, who knows that he has a disease. (d) Because the pooled test was positive, the authorities havedecided to test each individual separately. The firsti - 1 of these tests were negative, and the ithone - which was Jones - was positive. Given the preceedingscenario, what is the probability, as a function of i,that any of the remaining people have the disease? This was the only part of this question that wasn't alreadyanswered. Each of 500 soldiers in an army company independently has acertain disease with probability 1/1000. This disease willshow up on a blood test, and to facilitate matters, blood samplesfrom all 500 soldiers are pooled and tested. Suppose now thatthe blood test yields a positive result. One of the 500people is Jones, who knows that he has a disease. (d) Because the pooled test was positive, the authorities havedecided to test each individual separately. The firsti - 1 of these tests were negative, and the ithone - which was Jones - was positive. Given the preceedingscenario, what is the probability, as a function of i,that any of the remaining people have the disease?

Explanation / Answer

Make sure you understand how I'm interpreting yourquestion. I believe that you are given that Jones has the disease. Sopooling all 500 soldiers and getting a positive result tells younothing, because you already know that Jones has the disease. If that is the case, then P(at least one of i people has the disease) = 1 - P(none ofthe i people has the disease)     = 1 -(0.99)i
Send me a PM if you think I have misinterpreted the question, Mike

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