Answer: B. $\text{0.29}$

Explanation:1. Understand the problem: We are given a table showing the distribution of people in a city by age group. We need to find the conditional probability that a randomly selected person is greater than $\text{65}$ years old, given that the person is at least $\text{18}$ years old.

2. Extract proportions from the table (Source [334]): - Less than $\text{18}$ years old: $\text{27}\%$ - $\text{18-40}$ years old: $\text{24}\%$ - $\text{41-65}$ years old: $\text{28}\%$ - Greater than $\text{65}$ years old: $\text{21}\%$ The sum of these proportions is $\text{27} + \text{24} + \text{28} + \text{21} = \text{100}\%$.

3. Define the events: Let A be the event that the selected person is greater than $\text{65}$ years old. Let B be the event that the selected person is at least $\text{18}$ years old. We want to find $P(A|B)$, the probability of A given B.

4. Calculate $P(B)$, the probability that the person is at least $\text{18}$ years old: This includes the age groups $\text{18-40}$, $\text{41-65}$, and Greater than $\text{65}$. $P(B) = \text{Proportion(18-40)} + \text{Proportion(41-65)} + \text{Proportion(Greater than 65)}$ $P(B) = \text{24}\% + \text{28}\% + \text{21}\% = \text{73}\%$ or $\text{0.73}$.

5. Calculate $P(A \cap B)$, the probability that the person is greater than $\text{65}$ years old AND at least $\text{18}$ years old: If a person is greater than $\text{65}$ years old, they are automatically at least $\text{18}$ years old. So, the event "A and B" is the same as event A ("person is greater than $\text{65}$ years old"). $P(A \cap B) = \text{Proportion(Greater than 65)} = \text{21}\%$ or $\text{0.21}$.

6. Calculate the conditional probability $P(A|B)$: $P(A|B) = \dfrac{P(A \cap B)}{P(B)}$ $P(A|B) = \dfrac{\text{0.21}}{\text{0.73}}$.

7. Perform the division: $\dfrac{0.21}{0.73} = \dfrac{21}{73}$. $21 \div 73 \approx 0.2876712...$

8. Compare with the given options and find the closest: [A] $\text{0.21}$ [B] $\text{0.29}$ [C] $\text{0.73}$ [D] $\text{0.22}$ (from PDF source, assuming this was intended) The calculated probability $\text{0.2876712}...$ is closest to $\text{0.29}$.

9. Conclusion: The probability of selecting a person who is greater than $\text{65}$ years old, given that the person is at least $\text{18}$ years old, is closest to $\text{0.29}$. This matches option [B].