Financial Risk Manager Part 1
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A life assurance company insures individuals of all ages. A manager compiled the following statistics of the company's insured persons:
| Age of insured | Mortality (Probability of death) [arbitrary] | Portion of company's insured persons |
|---|---|---|
| 16 – 20 | 0.04 | 0.10 |
| 21 – 30 | 0.05 | 0.29 |
| 31 – 65 | 0.10 | 0.49 |
| 66 – 99 | 0.14 | 0.12 |
If a randomly selected individual insured by the company dies, calculate the probability that the dead client was in age range 21-30.
Explanation:
This is a conditional probability problem using Bayes' theorem. We want to find P(Age 21-30 | Death).
Given:
- P(Age 16-20) = 0.10, P(Death|Age 16-20) = 0.04
- P(Age 21-30) = 0.29, P(Death|Age 21-30) = 0.05
- P(Age 31-65) = 0.49, P(Death|Age 31-65) = 0.10
- P(Age 66-99) = 0.12, P(Death|Age 66-99) = 0.14
Using Bayes' theorem: [P(B_2|B) = \frac{P(B_2) \times P(B|B_2)}{\sum_{i=1}^{4} P(B_i) \times P(B|B_i)}]
Calculation: [P(B_2|B) = \frac{(0.29 \times 0.05)}{(0.29 \times 0.05) + (0.10 \times 0.04) + (0.49 \times 0.10) + (0.12 \times 0.14)}]
[= \frac{0.0145}{(0.0145 + 0.004 + 0.049 + 0.0168)}]
[= \frac{0.0145}{0.0843} = 0.172]
Therefore, the probability that a randomly selected deceased client was in the age range 21-30 is 17.2%._