Answer the following questions, kindly help

Question 12.1 A life insurance company uses the three-state illness-death model as described above to calculate premiums for a 3-year sickness policy issued to healthy policyholders aged 60. S, denotes the state occupied by the policyholder at age 60+7, so that So = a and S, = a, i ord for 1 = 1, 2, 3. The transition probabilities used by the insurer are defined in the following way: Poots = P(S, = k IS, = j) For / =0, 1, 2, it is assumed that: P6047 =0.9 ai P60+ = 0.08 ia P 60+1 =0.7 ii P60+1 = 0.25 What is the probability that a new policyholder is: (a) ill at exact age 62? (b) dead at exact age 62?Question 12.3 (Tricky) You are using the three-state illness-death model to price various sickness policies. Using the notation defined in Section 1, write down an expression for the expected present value of each of the following sickness benefits for a healthy life aged 30. (i) $3,000 pa payable continuously while ill, but ceasing at age 60. (ii) 13,000 pa payable continuously throughout the first period of illness only, but ceasing at age 60. (iii) E3,000 pa payable continuously while ill provided that the life has been ill for at least one year. Again, any benefit ceases to be paid at age 60