It is known that 5 of the population has disease A which can

It is known that 5% of the population has disease A, which can bediscovered by means of a blood test. Suppose that N (a largenumber) people are tested. The blood sample of k people arepooled together and analyzed. (Assume that N=nk, with n aninteger.) If the test is negative, all of the persons in thepool are healthy and only one test is needed. If the test ispositive, each of the k persons must be tested separately and atotal of k+1 tests are needed.

For a fixed k, what is the expected number of tests needed?

[(0.95)^k][1] +[1-(0.95)^k][k+1] = (0.95)^k + k + 1 -k(0.95)^k - (0.95)^k =[1-(0.95)^k][k]+1

n{[1-(0.95)^k][k]+1}

It is known that 5 of the population has disease A which can

Solution

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