To determine whether or not they have a certain disease, 6 people are to have th

Question

To determine whether or not they have a certain disease, 6 people are to have their blood tested. However, rather than testing each individual separately, the blood samples will be pooled and then the pooled blood sample will be tested. If the test is negative, one test will suffice for the 6 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 6 people will also be individually tested and, in all, 7 tests will be made on this group. Assume the probability that a person has the disease is 0.06 for all people, independently of each other, and compute the expected number of tests necessary for the group.

Explanation / Answer

Let us suppose that X~B(n,p). Then the expected number of tests necessary for this group are6*0.06=0.36. the probablity is 0.36.

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