A blood test is being performed for n = NV . kindividuals by pooling the samples for kpeople, and analyzing [them together. If the test is negative, this pooled test suffices for all k individuals. If the test is positive, we test each of the kpersons separately, i.e., we carry out a total of k + 1tests. Suppose that we create /Vdisjoint groups of people and use the pooling method. Let A, =i-th person has a positive result, and assume Pr (A; ) = p, independently, i = 1, . . . , n. 6a. Let Bj denote the event of a positive pooled sample, for the j-th pooled sample consisting of samples from a batch of k individuals. For p = 0.01, k = 4 and n = 40, find Pr (Bj ) . Give your answer using two decimal places. 6b. Let X = # of tests What is the expected number of tests necessary, E(X)? For p = 0.01, k = 4 and n = 40, find E(X). Give your answer using one decimal place