IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives
Two lives (x) and (y) have independent future lifetimes. Over the next year, the probability that (x) survives is 0.90 and the probability that (y) survives is 0.80. What is the probability that at least one of the two lives is alive at the end of the year?
The probability is 0.98. With independent lives, both dying has probability 0.10 × 0.20 = 0.02, and the chance that at least one survives is the complement. The figure 0.72 is only the probability that both are alive.
- A0.72
- B0.98Correct
- C0.90
- D0.28
- 0.26
Explanation
At least one survives is the complement of both dying. P(both die) = 0.10 × 0.20 = 0.02, so the required probability is 1 − 0.02 = 0.98. The value 0.72 is the probability that both survive (the joint-life case), not the last-survivor case.
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