Let the probability that a person aged x years will survive I year be denoted by P_x, whereas q_x = 1 - P_x is the probability that he will die within a year. Consider a board of directors, consisting of a chairman and 5 members; all of the members are 60, the chairman is 65. Find the probability, in terms of q₆₀ and q₆₅, that within a year (i) no members will die, (ii) not more than 1 member will die, (iii) neither a member nor the chairman will die, (iv) only the chairman will die. Evaluate these probabilities under the assumption that 960 = 0.025 and q₆₅ = 0.040.