It is known that 5% of the members of a population have disease A, which can be discovered by a bloodtest. 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 seperately( that is, a total of k+1 tests are needed).
Question: Find the k that will minimize the expected number of tests in option 2.