To determine the probability of rolling a sum of 9 or higher with two six-sided dice, we first need to identify all the possible outcomes when rolling those dice. Each die has 6 faces, so there are a total of 36 combinations (6 sides on the first die multiplied by 6 sides on the second die).
Next, let’s identify the successful outcomes where the sum is 9 or higher:
- For a sum of 9: (3,6), (4,5), (5,4), (6,3) – total of 4 outcomes
- For a sum of 10: (4,6), (5,5), (6,4) – total of 3 outcomes
- For a sum of 11: (5,6), (6,5) – total of 2 outcomes
- For a sum of 12: (6,6) – total of 1 outcome
When we add all these successful outcomes together, we have:
4 (for 9) + 3 (for 10) + 2 (for 11) + 1 (for 12) = 10 successful outcomes.
Now, to find the probability, we use the formula:
Probability = (Number of successful outcomes) / (Total number of possible outcomes)
So, the probability of rolling a sum of 9 or higher is:
Probability = 10 / 36 = 5 / 18
This means the probability that the sum is 9 or higher when rolling two six-sided dice is 5/18.