When rolling two dice, the total number of possible outcomes is:
$ \displaystyle 6 \times 6 = 36 $
To find the probability of getting a sum more than 9, we count the favorable outcomes where the sum is 10, 11, or 12.
Possible outcomes:
- Sum = 10: (4,6), (5,5), (6,4) → 3 outcomes
- Sum = 11: (5,6), (6,5) → 2 outcomes
- Sum = 12: (6,6) → 1 outcome
Total favorable outcomes = $ \displaystyle 3 + 2 + 1 = 6 $
Probability:
$ \displaystyle P(\text{sum} > 9) = \frac{6}{36} = \frac{1}{6} $
Thus, the probability of getting a sum more than 9 is $ \displaystyle \frac{1}{6} $.