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Suppose we need to infer the occurrence of a rare disease in a population of N people. If the blood of every person is tested, obviously N tests will have to be done. An alternate strategy is to pool all the blood samples into groups of k (Mix the blood samples of k people. Assume N and k are such that N k is an integer). Each pooled sample is then tested. If it is negative, all k people in the group are concluded to be free from the disease. If it is positive, each person in the group must be retested, ultimately requiring k + 1 tests being done on that particular group. Suppose the probability of any one person having a positive test is p. What will be the expected number of tests under the pooling plan? can someone pls help. the way i thoght abt this question is that with prob p (k+1) tests are being done.but i am unable to complete it .

Suppose we need to infer the occurrence of a rare disease in a population of N people. If the blood of every person is tested, obviously N tests will have to be done. An alternate strategy is to pool all the blood samples into groups of k (Mix the blood samples of k people. Assume N and k are such that N k is an integer). Each pooled sample is then tested. If it is negative, all k people in the group are concluded to be free from the disease. If it is positive, each person in the group must be retested, ultimately requiring k + 1 tests being done on that particular group. Suppose the probability of any one person having a positive test is p. What will be the expected number of tests under the pooling plan?
 
can someone pls help. 
the way i thoght abt this question is that 
with prob p (k+1) tests are being done.but i am unable to complete it .

Grade:12th pass

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