Please answer in details and provide a brief explanation. Thank you.

8. It is known that 5% of a population have disease A, which can be discovered by blood test. Suppose that N (a very large number) people are to be tested. This can be done in two ways: (1) Each person is tested separately; (2) the blood samples of k people are pooled together and analyzed (assume that N = nk, with n being an integer). If the test result is positive, each of the k persons must be tested separately (that is, totally k + 1 tests are needed). (a) For k being xed, what is the expected number of tests needed (per person) in (2)? (b) Find the value of k that will minimize the expected number of tests in (2) (c) How many tests does (b) save in comparison with (1) to screen the whole population with N people