Assume a testing clinic in a major metropolitan area—one with millions of residents, even in the 1950s and 60s—needed to test 1000 patients for measles on any given day. Assume blood is drawn from each of the 1000 patients, but rather than running each blood sample through a test individually (the tests were very expensive 70 years ago), the clinic employs a sample batching technique as follows: Phase 1: First, batch blood samples into groups of 5. The blood samples of the 5 people in each group will be pooled and analyzed as a single sample. If the test is positive—that is, at least one person in the group has measles—continue to Phase 2. Otherwise, deliver negative test results to all five people in the group. 200 of these pooled tests are performed. Phase 2: Individually test each of the 5 samples in the pool to deliver negative and positive test results to each of the 5 people. Suppose that the probability that a person has measles is 0.04, independently of others, and that the test has a 100% true positive rate and 0% false positive rate. Using this strategy, compute the expected total number of blood tests (individual and pooled) that need to be performed between both phases. Express your answer to the nearest integer.

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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Assume a testing clinic in a major metropolitan area—one with millions of residents, even in the 1950s and 60s—needed to test 1000 patients for measles on any given day. Assume blood is drawn from each of the 1000 patients, but rather than running each blood sample through a test individually (the tests were very expensive 70 years ago), the clinic employs a sample batching technique as follows:

Phase 1: First, batch blood samples into groups of 5. The blood samples of the 5 people in each group will be pooled and analyzed as a single sample. If the test is positive—that is, at least one person in the group has measles—continue to Phase 2. Otherwise, deliver negative test results to all five people in the group. 200 of these pooled tests are performed.
Phase 2: Individually test each of the 5 samples in the pool to deliver negative and positive test results to each of the 5 people.

Suppose that the probability that a person has measles is 0.04, independently of others, and that the test has a 100% true positive rate and 0% false positive rate. Using this strategy, compute the expected total number of blood tests (individual and pooled) that need to be performed between both phases. Express your answer to the nearest integer.

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