To determine the probability of rolling a sum of 5 or lower with two six-sided dice, we first need to consider the possible outcomes when two dice are rolled.
Each die has 6 sides, so when rolling two dice, there are a total of 6 x 6 = 36 possible outcomes.
Next, let’s identify the combinations that yield a sum of 5 or lower:
- Sum of 2: (1, 1) – 1 combination
- Sum of 3: (1, 2), (2, 1) – 2 combinations
- Sum of 4: (1, 3), (2, 2), (3, 1) – 3 combinations
- Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) – 4 combinations
Now, we can count the total number of combinations that result in a sum of 5 or lower:
- 1 (sum of 2)
- 2 (sum of 3)
- 3 (sum of 4)
- 4 (sum of 5)
This leads us to a total of 1 + 2 + 3 + 4 = 10 favorable outcomes.
Now, to find the probability, we use the formula:
Probability = (Number of favorable outcomes) / (Total outcomes)
Thus, the probability of rolling a sum of 5 or lower is:
Probability = 10 / 36 = 5 / 18
In decimal form, this is approximately 0.2778, or about 27.78%.
So, the final answer is:
The probability of rolling a sum of 5 or lower with two fair six-sided dice is 5/18 or about 27.78%.