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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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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.
• What is the expectation of the number of analysis necessary in the second method of testing?
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. • What is the expectation of the number of analysis necessary in the second method of testing?
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