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Example 3.3 Consider men who need to undergo surgery because they are suffering from a particular disease. The surgery is complicated and there is a probability of only 50% that they will survive for a year following surgery. If they do survive for a year, then they are fully cured and their future mortality follows the Australian Life Tables 200002, Males, from which you are given the following values: lg] = 39777, f51 = 39015, fm = 77946. Calculate (a) the probability that a man aged 60 who is just about to have surgery will be alive at age T0, (b) the probability that a man aged 60 who had surgery at age 59 will be alive at age T0, and (c) the probability that a man aged 60 who had surgery at age 53 will be alive at age TU. likalIIpIE 3.11 A select survival model has a select period of three years. Its ultimate mortality is equivalent to the US Life Tables, 2002, Females. Some I; values for this table are shown in Table 3.5. You are given that for all ages I 21: 65, FLY] = H.999, P[_rl]+1 = 0.993, p[_g_g]+g = 0.997. Calculate the probability that a woman currently aged TU will survive to age T5 given that (a) she was select at age 67-", (b) she was select at age 63, (c) she was select at age 69, and ({1} she is select at age \"l0