To find the probability that Rebecca rolls a number greater than 3 on a standard 6-sided die, we first need to identify the total possible outcomes and the favorable outcomes.
A standard 6-sided die has the numbers: 1, 2, 3, 4, 5, and 6.
The total number of outcomes when rolling the die is:
\[ 6 \]
Next, we need to determine the favorable outcomes where the rolled number is greater than 3. The favorable outcomes are:
\[ 4, 5, 6 \]
This gives us a total of:
\[ 3 \text{ favorable outcomes} \]
Now, we calculate the probability using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{3}{6} = \frac{1}{2} \]
Thus, the probability that Rebecca rolls a number greater than 3 is:
\[ \boxed{\frac{1}{2}} \]