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

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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(d) 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. • For what k is the minimum expected number of necessary analysis attained?
Transcribed Image Text:(d) 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. • For what k is the minimum expected number of necessary analysis attained?
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