Understanding the Problem
The problem presents a scenario where we need to calculate the probability of rolling a number greater than 2 on a die, given that one of the outcomes is a boy. This scenario appears to mix two different concepts: probability and gender, which may be confusing. However, we can focus on the die's outcomes for clarity.

Sample Space of a Die
- A standard die has six faces: 1, 2, 3, 4, 5, and 6.

Favorable Outcomes
- The numbers greater than 2 on a die are: 3, 4, 5, and 6.
- Thus, there are **4 favorable outcomes**.

Total Outcomes
- The total outcomes when rolling a die are **6** (1, 2, 3, 4, 5, 6).

Calculating the Probability
- The probability \( P \) of rolling a number greater than 2 is given by the formula:
\[ P(\text{number > 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
- Therefore:
\[ P(\text{number > 2}) = \frac{4}{6} = \frac{2}{3} \]

Conclusion
- The occurrence of a boy does not alter the probability associated with the die roll.
- Hence, the probability of rolling a number greater than 2 is **\(\frac{2}{3}\)**.
This calculation remains consistent regardless of any external factors like gender, as they do not influence the outcomes of rolling a die.