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3. We need to test N = 100, 000 individuals' blood for a rare discase. Assume that cach per- son, independently of others, have the disease with probability p= 0.0001. We run the test according to a group testing policy. First, we divide the population into groups of k = 100 individual (so, N/k = 1000 groups in total). Then, we mix the blood sample of all the individual within each group and test the mix sample. If the mixed test of a group is positive, we test all the individuals within that group. On average, how many tests do we need?

3. We need to test N = 100, 000 individuals' blood for a rare discase. Assume that cach per- son, independently of others, have the disease with probability p= 0.0001. We run the test according to a group testing policy. First, we divide the population into groups of k = 100 individual (so, N/k = 1000 groups in total). Then, we mix the blood sample of all the individual within each group and test the mix sample. If the mixed test of a group is positive, we test all the individuals within that group. On average, how many tests do we need?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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3. We need to test N = 100,000 individuals' blood for a rare discase. Assume that cach per- son, independently of others, have the disease with probability p= 0.0001. We run the test according to a group testing policy. First, we divide the population into groups of k 100 individual (so, N/k = 1000 groups in total). Then, we mix the blood sample of all the individual within each group and test the mix sample. If the mixed test of a group is positive, we test all the individuals within that group. On average, how many tests do we need?
Transcribed Image Text:3. We need to test N = 100,000 individuals' blood for a rare discase. Assume that cach per- son, independently of others, have the disease with probability p= 0.0001. We run the test according to a group testing policy. First, we divide the population into groups of k 100 individual (so, N/k = 1000 groups in total). Then, we mix the blood sample of all the individual within each group and test the mix sample. If the mixed test of a group is positive, we test all the individuals within that group. On average, how many tests do we need?
Expert Solution
Step 1. Number of Group Tests

As there are 1000 groups, we will have to do 1000 group tests.

Some group tests will come back as positive, and then we will have to do individual tests in those groups. This is solved in next part.

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