A large number N of people are subjected to a blood investigation. This investigation can be organized in two d) ways. (1) The blood of each person is investigated separately. In this case N analyses are needed. (2) The blood of k people are mixed and the mixture is analysed. If the result is negative, then this single analysis is sufficient for k persons. But if it is positive, then the blood of each one must be subsequently investigated separately, and in toto for k people, k+1 analysis are needed. It is assumed that the probability of a positive result (p) is the same for all people and that the results of the analysis are independent in the probabilistic sense. )What is the probability that the analysis of the mixed blood of k people is positive? What is the expectation of the number of analysis necessary in the second method of testing? For what k is the minimum expected number of necessary analysis attained?

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