IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events
Two independent lives aged 60 and 65 have survival probabilities over one year of 0.98 and 0.96 respectively. What is the probability that exactly one of them survives to the end of the year?
Exactly one survivor means either the first survives and the second dies, or the reverse. Adding 0.98 x 0.04 and 0.96 x 0.02 gives 0.0392 + 0.0192 = 0.0584.
- A0.0588
- B0.0392
- C0.0196
- D0.9408
- 0.0780Correct
Explanation
P(only first survives) = 0.98 x 0.04 = 0.0392. P(only second survives) = 0.96 x 0.02 = 0.0192. Sum = 0.0584. Check against options: 0.0780 is not this. The correct sum is 0.0584.
Did you get it right without looking?
One question tells you little. A timed set on Valuing cashflows contingent on multiple transition events shows your real accuracy, how long you take and where you lose marks.
More Valuing cashflows contingent on multiple transition events questions
- In a continuous-time multiple state model for a policyholder, the states are Healthy (H), Sick (S) and Dead (D). The policy pays a sickness …
- A policy has sum assured Rs 30,000 payable immediately on death and premiums of Rs 1,200 per year paid continuously. At a certain time the p…
- In a continuous-time Markov jump model with states H (healthy), S (sick) and D (dead), the transition intensity from H to S at age x is defi…
- A three-state model (Healthy, Sick, Dead) is used. Annual effective interest is 5%. A policy pays Rs 10,000 at the end of a year if the life…
- For a policy paying Rs 60,000 immediately on death, with continuous premiums of Rs 1,500 per year, the policy value at time 10 is Rs 20,000.…
- For a life policy with sum assured ₹80,000, level premiums of ₹1,500 per annum paid continuously, δ = 0.04 and μ = 0.02 at the current age, …