To determine whether or not they have a certain disease, 150 people are to have their blood tested. However, 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, 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 0.04 for all people, independently of each other, and compute the expected number of tests necessary for each group.

Question

Mathematics

Jaron Snow

21 September, 22:15

To determine whether or not they have a certain disease, 150 people are to have their blood tested. However, 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, 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 0.04 for all people, independently of each other, and compute the expected number of tests necessary for each group.

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Answers (1)

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Bria · Answer 1

The answer is 75 tests for 150 people.

Step-by-step explanation:

Firstly, with 150 people, we can divide into 15 groups; and the probability of disease is 0.04, there are 6 persons who possibly get disease.

Therefor, the maximum number of groups with an individual getting disease is 6. Then, 6 * 11 tests = 66 tests required.

15 groups - 6 groups with disease = 9 groups of negative with 9 tests.

In conclusion, there are 75 tests required.