To find the probability of rolling two dice and obtaining a sum of 6, we first need to understand the total possible outcomes when rolling two dice, and then identify the specific outcomes that yield a sum of 6.
When we roll two six-sided dice, each die has 6 faces. Therefore, the total number of possible outcomes when rolling both dice can be calculated as:
- Total outcomes = 6 (from die 1) × 6 (from die 2) = 36
Next, let’s determine the favorable outcomes that yield a sum of 6. The combinations of two dice that add up to 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
Counting these combinations gives us:
- 1 + 5
- 2 + 4
- 3 + 3
- 4 + 2
- 5 + 1
Thus, there are a total of 5 favorable outcomes.
Now, to find the probability, we use the formula:
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
Substituting in our values, we get:
- Probability = 5 / 36
Therefore, the probability of rolling a sum of 6 when two dice are rolled is 5/36. This can also be approximated as 0.1389, or about 13.89% when expressed as a percentage.