For each part below, express the given probability in actuarial notation. Then calculate its exact value using the life table and any given fractional age assumptions. a) The probability that a life aged 71 survives at least 6 years; b) The probability that the curtate future lifetime K68 equals 4; c) The probability that a life aged 65.5 survives at least 6.3 additional years, but not more than 13.7 additional years. Assume the uniform distribution of deaths as the fractional age assumption. d) The probability that a life aged 65.4 survives at least until age 71.9. Assume constant force of mortality for fractional ages. 65 88,348 66 87,551 67 86,695 68 85,776 69 84,789 70 83,726 71 82,581 72 81,348 73 80,024 74 78,609 75 77,107 76 75,520 77 73,846 78 72,082 79 70,218 80 68,248 For each part below, express the given probability in actuarial notation. Then calculate its exact value using the life table and any given fractional age assumptions. a) The probability that a life aged 71 survives at least 6 years; b) The probability that the curtate future lifetime K68 equals 4; c) The probability that a life aged 65.5 survives at least 6.3 additional years, but not more than 13.7 additional years. Assume the uniform distribution of deaths as the fractional age assumption. d) The probability that a life aged 65.4 survives at least until age 71.9. Assume constant force of mortality for fractional ages. 65 88,348 66 87,551 67 86,695 68 85,776 69 84,789 70 83,726 71 82,581 72 81,348 73 80,024 74 78,609 75 77,107 76 75,520 77 73,846 78 72,082 79 70,218 80 68,248