Two dices are rolled, list all possible sample spaces. When adding in each parenthesis, which one got the highest odds?

Each die has 6 faces, so when two dice are rolled, there are $6 \times 6 = 36$ possible outcomes. The sample space $S$ is:

$$S = \begin{Bmatrix} (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), \\ (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), \\ (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), \\ (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), \\ (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), \\ (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) \end{Bmatrix}$$

The sum of the two dice can range from $1+1=2$ to $6+6=12$.

• Sum of 2: (1,1) - 1 way
• Sum of 3: (1,2), (2,1) - 2 ways
• Sum of 4: (1,3), (2,2), (3,1) - 3 ways
• Sum of 5: (1,4), (2,3), (3,2), (4,1) - 4 ways
• Sum of 6: (1,5), (2,4), (3,3), (4,2), (5,1) - 5 ways
• Sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) - 6 ways
• Sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2) - 5 ways
• Sum of 9: (3,6), (4,5), (5,4), (6,3) - 4 ways
• Sum of 10: (4,6), (5,5), (6,4) - 3 ways
• Sum of 11: (5,6), (6,5) - 2 ways
• Sum of 12: (6,6) - 1 way

The sum with the highest number of ways has the highest odds. From the frequencies above, a sum of 7 has 6 possible combinations, which is more than any other sum.

The sum that got the highest odds is $\boxed{\text{7}}$.