Financial Risk Manager Part 1

To calculate the probability that the dead client was between 66 and 99 years old, we need to use Bayes' theorem:

$P(A|B) = \frac{P(B|A) \times P(A)}{P(B)}$

Where:

• Event A: Client was between 66-99 years old
• Event B: Client died

From the table:

• P(Dying|66-99) = 0.14
• P(66-99) = 0.12

First, calculate the marginal probability of dying: $P(\text{Dying}) = (0.04 \times 0.10) + (0.05 \times 0.29) + (0.10 \times 0.49) + (0.14 \times 0.12) = 0.004 + 0.0145 + 0.049 + 0.0168 = 0.0843$

Now apply Bayes' theorem: $P(66\text{-}99|\text{Dying}) = \frac{P(\text{Dying}|66\text{-}99) \times P(66\text{-}99)}{P(\text{Dying})} = \frac{0.14 \times 0.12}{0.0843} = \frac{0.0168}{0.0843} = 0.1993$

The probability is approximately 0.199, which corresponds to option B.