Question

You and your friend are rolling number cubes. Each cube has 6 sides with the numbers 1 to 6. If a sum of 7 is rolled, your friend gets a point. However, you get a point if either one of the sums listed below is rolled. Which pair of numbers would make the game fair?
2 and 12
2 and 5
12 and 8

Answer 1

Sum ---- Combinations
2 --------- 1
3 --------- 2
4 --------- 3
5 --------- 4
6 --------- 5
7 --------- 6
8 --------- 5
9 --------- 4
10 ------- 3
11 ------- 2
12 ------- 1

7 has 6 combinations.
Now,
2 and 12 ---- 1+1 = 2
2 and 5 ------1+4 = 5
12 and 8 ---- 1+5 = 6

12 and 8 would, therefore, make the game fair.