In some settings there are not enough COVID-19 test kits and pooled testing is used in which multiple samples from different people are combined in a "pool." The pooled sample is tested, with two possibilities: 1. If negative, then all people in the pool are negative or 2. If the pool tests positive, then all people who contributed are tested individually Suppose there are N individuals in the targeted population to be tested and the unknown prevalence of Covid-19 infection in this population be . Suppose the N people in the population are split into K "pools" with n people in each people so N = Kn and n 2. Let Y; represent the number of assays required for n persons in pool i, i = 1,2,3,... K. Let T represent total assay required T = Y 1. Find an expression for the expected number of assays in this population in terms of , N. n (Note: Use K = N/n) 2. If R = E[T]/N is the ratio of expected number of assays needed wih pooling compared to assaying all N persons individually, calculate R assuming = 0.001 for n = 10,30,50,100 (Note: R should be independent of N) 3. Determine the optimal number of individuals to pool when = 0.001 (ie. minimise R with = 0.001 and find n)