When rolling two dice what is the probability of the sum being 4?

Answer 1

Listing all possible outcomes:
Dice 1 Dice 2 Sum
1 1 2
1 2 3
1 3 4
1 4 5
1 5 6
1 6 7
2 1 3
2 2 4
2 3 5
2 4 6
2 5 7
2 6 8
3 1 4
3 2 5
3 3 6
3 4 7
3 5 8
3 6 9
4 1 5
4 2 6
4 3 7
4 4 8
4 5 9
4 6 10
5 1 6
5 2 7
5 3 8
5 4 9
5 5 10
5 6 11
6 1 7
6 2 8
6 3 9
6 4 10
6 5 11
6 6 12

Only 3 out of the possible 36 combinations turned out to have a sum of 4. So that is 1/12

The faster mental way:
You know a standard dice has 6 sides.
In this problem, there are two die. So that means you have to multiply 6 x 6. That is 36.
So there are 36 possible outcomes.
You know 1 + 3 = 4, 3 + 1 = 4, and 2 + 2 = 4. Those are the only 3 equations that have all positive numbers that have a sum of 4 (Zero is not positive nor negative).
You have your answer. 3/36. In simplest form, it is 1/12.