It is known that 5% of the members of a population have disease A, which can be discovered by a blood test. Suppose that N (a large number) people are to be tested. This can be done in two ways: (1) Each person is tested separately, or (2) the blood samples of k people are pooled together and analyzed. (Assume that N = nk, with n an integer.) If the test is negative, all of them are healthy (that is, just this one test is needed). If the test is positive, each of the k persons must be tested separately (that is, a total of k + 1 tests are needed).
a For fixed k, what is the expected number of tests needed in option 2?
b Find the k that will minimize the expected number of tests in option 2.
c If k is selected as in part (b), on the average how many tests does option 2 save in comparison with option 1?
i have solve part a...answer is E[X] = n [1 + k(1-(0.95^k)) ]
but i cant solve part b....anyone can help me???