To find the probability of rolling a number greater than 5 with a single 9-sided die, we first identify the possible outcomes on the die, which are the numbers 1 through 9:
1, 2, 3, 4, 5, 6, 7, 8, 9
Next, we determine the numbers greater than 5. The numbers greater than 5 on this die are:
6, 7, 8, 9
This gives us a total of 4 favorable outcomes.
Next, we calculate the total number of possible outcomes when rolling a 9-sided die, which is 9.
The probability \( P \) of rolling a number greater than 5 can be calculated using the formula:
\[ P(\text{greater than 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{9} \]
Therefore, the probability of rolling a number greater than 5 is:
\[ \frac{4}{9} \]