The pooled sample is tested, with two results and actions:

(i) if there is no virus detected, then all persons contributing to the pool are considered negative, or,

(ii) if the pooled sample tests positive, then all persons contributing to the pool are re-tested individually to find out which one or more of them caused the pooled sample to be positive.

N is the number of individuals in the targeted population to be tested. Let the unknown prevalence (probability) of disease in this population be . Suppose the N persons in the population are split into K "pools" with n people in each pool, and so N = Kn, with n 2. Assume Yi to be the number of tests required from the n persons in pool i,i = 1, 2, . . . , K. Let T denote the total number of tests required in the population, i.e., T = ^K_i=1Yi.

Find the expected number of tests in the population E[T] in terms of , N, n. (Hint: first find E[Yi], then use K = N/n)