Assume that for to determine whether or not they have a certain disease in the city of Wuhanco, 600 people are to have their blood tested. Yet, rather than testing each individual separately, it has been decided first to group the people in groups of 10. The blood samples of the 10 people in each group will be pooled and analyzed together. If the test is negative, then one test will suffice for the 10 people (we are assuming that the pooled test will be positive if and only if at least one person in the pool has the disease); whereas, if the test is positive each of the 10 people will also be individually tested and, in all, 11 tests will be made on this group.Assume the probability that a person has the disease is 0.09 for all people, independently of each other. Compute expected total number of tests necessary for the entire population of 600 people.
Assume that for to determine whether or not they have a certain
disease in the city of Wuhanco, 600 people are to have their blood tested. Yet, rather than
testing each individual separately, it has been decided first to group the people in groups of 10.
The blood samples of the 10 people in each group will be pooled and analyzed together. If the
test is negative, then one test will suffice for the 10 people (we are assuming that the pooled
test will be positive if and only if at least one person in the pool has the disease); whereas, if the
test is positive each of the 10 people will also be individually tested and, in all, 11 tests will be
made on this group.Assume the probability that a person has the disease is 0.09 for all people,
independently of each other. Compute expected total number of tests necessary for the entire
population of 600 people.
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