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You want to examine N people to see if they have a certain disease. The obvious alternative is to analyze individual blood samples and see whether or not each of them has the disease. But another more efficient alternative is to divide the N people into n groups of k people each (N= nk). A blood sample is then taken from members of each group and the samples are pooled. If the combined blood sample is negative, all the members of the group are healthy, if it comes out positive, an individual analysis is done to find the sick people. Assuming that there is a probability p that the blood sample of any person is positive. a) Find the expected number of blood tests, which must be analyzed to find all the sick people. b) Determine the range of p values so that the "group test" is preferable to the "individual test".

You want to examine N people to see if they have a certain disease. The obvious alternative is to analyze individual blood samples and see whether or not each of them has the disease. But another more efficient alternative is to divide the N people into n groups of k people each (N= nk). A blood sample is then taken from members of each group and the samples are pooled. If the combined blood sample is negative, all the members of the group are healthy, if it comes out positive, an individual analysis is done to find the sick people. Assuming that there is a probability p that the blood sample of any person is positive. a) Find the expected number of blood tests, which must be analyzed to find all the sick people. b) Determine the range of p values so that the "group test" is preferable to the "individual test".

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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You want to examine N people to see if they have a certain disease. The obvious alternative is to analyze individual blood samples and see whether or not each of them has the disease. But another more efficient alternative is to divide the N people into n groups of k people each (N= nk). A blood sample is then taken from members of each group and the samples are pooled. If the combined blood sample is negative, all the members of the group are healthy, if it comes out positive, an individual analysis is done to find the sick people. Assuming that there is a probability p that the blood sample of any person is positive. a) Find the expected number of blood tests, which must be analyzed to find all the sick people. b) Determine the range of p values so that the "group test" is preferable to the "individual test".
Transcribed Image Text:You want to examine N people to see if they have a certain disease. The obvious alternative is to analyze individual blood samples and see whether or not each of them has the disease. But another more efficient alternative is to divide the N people into n groups of k people each (N= nk). A blood sample is then taken from members of each group and the samples are pooled. If the combined blood sample is negative, all the members of the group are healthy, if it comes out positive, an individual analysis is done to find the sick people. Assuming that there is a probability p that the blood sample of any person is positive. a) Find the expected number of blood tests, which must be analyzed to find all the sick people. b) Determine the range of p values so that the "group test" is preferable to the "individual test".
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