A large number N of people are subjected to a blood investigation. This investigation can be organized in two 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?
A large number N of people are subjected to a blood investigation. This investigation can be organized in two 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
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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