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 March 11th, 2011, 09:15 PM #1 Newbie   Joined: Mar 2011 Posts: 3 Thanks: 0 Challenging Probability and Statistics Questions! It is known that 5% of the members of a population have disease A, which can be discovered by a blood test. Suppose that N ( a large no.) people are to be tested This can be done in 2 ways : 1. Each person is tested separately , or 2. the blood samples of k people are pooled together and analyzed. ( Assume that N =nk , with n an integer) If the test is -ve , all of them are healthy ( that is , just this 1 test is neeeded) if the test is +ve , each of the k persons must be tested separately ( that is , a total of k+1 tests are needed) Questions: a) For the fixed k, what is the expected no. the tests needed in option 2. b) Find the k that will minimize the expected no. of tests in option 2. c) If k is selected as in part b, on the average how many tests does option 2 save in comparison with option1? March 12th, 2011, 02:23 PM   #2
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 Originally Posted by GreenBamboo It is known that 5% of the members of a population have disease A, which can be discovered by a blood test. Suppose that N ( a large no.) people are to be tested This can be done in 2 ways : 1. Each person is tested separately , or 2. the blood samples of k people are pooled together and analyzed. ( Assume that N =nk , with n an integer) If the test is -ve , all of them are healthy ( that is , just this 1 test is neeeded) if the test is +ve , each of the k persons must be tested separately ( that is , a total of k+1 tests are needed) Questions: a) For the fixed k, what is the expected no. the tests needed in option 2. b) Find the k that will minimize the expected no. of tests in option 2. c) If k is selected as in part b, on the average how many tests does option 2 save in comparison with option1?
I'll show you how to do a. See if you can do the rest. If you test k people, the probability that none are infected is .95^k (=P). Therefore the expected number of tests is P + (k+1)(1-P).

There is something wrong with the problem statement for b, since k=1 is the obvious answer, but it seems wrong for the underlying problem. March 13th, 2011, 07:44 AM #3 Newbie   Joined: Mar 2011 Posts: 3 Thanks: 0 Re: Challenging Probability and Statistics Questions! for question (a), the answer given is assume the number of expected no. of test for population which means we need to use N=nk. for the number of people in sample k have disease A is (k * (1-0.95^k)) is it? the number of test is k + 1, so is 1+(k * (1-0.95^k))? Tags challenging, probability, questions, statistics ,

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