IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives
For independent lives (x) and (y), 10 p_x = 0.90 and 10 p_y = 0.80. What is the probability that exactly one of the two lives is alive at the end of 10 years?
The probability is 0.26. Exactly one survives if x lives and y dies (0.90×0.20=0.18) or x dies and y lives (0.10×0.80=0.08), and these add to 0.26. It equals the last survivor probability 0.98 minus the joint-life probability 0.72.
- A0.26Correct
- B0.72
- C0.98
- D0.18
- 0.28
Explanation
Exactly one alive = 0.90×0.20 + 0.10×0.80 = 0.18 + 0.08 = 0.26. Check: last survivor = 0.90+0.80−0.72 = 0.98, and 0.98 − 0.72 = 0.26. The value 0.28 comes from the mistake of computing 1 − 0.72.
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