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In group testing for a certain disease, a blood sample was
Chapter 2, Problem 18E(choose chapter or problem)
Problem 18E
In group testing for a certain disease, a blood sample was taken from each of n individuals and part of each sample was placed in a common pool. The latter was then tested. If the result was negative, there was no more testing and all n individuals were declared negative with one test. If, however, the combined result was found positive, all individuals were tested, requiring n+1 tests. If p = 0.05 is the probability of a person’s having the disease and n = 5, compute the expected number of tests needed, assuming independence.
Questions & Answers
QUESTION:
Problem 18E
In group testing for a certain disease, a blood sample was taken from each of n individuals and part of each sample was placed in a common pool. The latter was then tested. If the result was negative, there was no more testing and all n individuals were declared negative with one test. If, however, the combined result was found positive, all individuals were tested, requiring n+1 tests. If p = 0.05 is the probability of a person’s having the disease and n = 5, compute the expected number of tests needed, assuming independence.
ANSWER:
Answer :
Step 1 of 2 :
Given,
In group testing for a certain disease, a blood sample was taken from each of n individuals and part of each sample was placed in a common pool. The latter was then tested. If the result was negative, there was no more testing and all n individuals were declared negative with one test. If, however, the combined result was found positive, all individuals were tested, requiring n+1 tests.
Where, p = 0.05 and n = 5
The claim is to compute the expected number of tests needed.
Let X follows binomial distribution
X~B(n,p)
P(x) = , x = 0, 1, 2, ……, n.