Answer: 0.199

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.

Author: Tanishq Prabhu