One gloomy day in 1982 a boat carrying N asylum-seeking married couples left a port near Haiphong (a place in northern Vietnam) and headed for Hongkong. (a) It was known that the Hongkong government was prepared to take in a total of M (< 2N) refugees and repatriate all those who were in excess of the quota. Assume that the M refugees who were granted asylum were selected randomly. (i) What is the expected number of repatriated couples? (ii) What is the expected number of couples who became separated as a result of this selection procedure? (b) Assume now that the Hongkong government adopted a new policy under which each Vietnamese arrival had a right to try his/her fortune by tossing a fair coin once. If the coin came up "heads", the refugee would be granted asylum; otherwise he/she would be repatriated. What are your answers to questions (i) and (ii) in part (a)? (c) Find the ranges of M for which the new policy was "more humanitarian", (i) in the sense that more refugees were expected to stay in Hongkong under the new policy; (ii) in the sense that fewer couples were expected to separate under the new policy.