Step 1: Total possible outcomes when rolling a die.
A standard die has six faces, numbered 1 through 6. Thus, there are 6 possible outcomes when rolling a die.
Step 2: Number of favorable outcomes.
The objective is to determine the probability of rolling a number greater than 4. The numbers on a die that exceed 4 are 5 and 6. Consequently, there are 2 favorable outcomes.
Step 3: Probability calculation.
Probability is calculated as the ratio of favorable outcomes to total possible outcomes:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3}
\]
Answer: The probability of rolling a number greater than 4 is \( \frac{1}{3} \).