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.

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Community

TTanishq

0.172

0.04

0.168

0.145

Explanation:

This is a conditional probability problem using Bayes' theorem. We want to find P(Age 21-30 | Death).

Given:

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%.

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