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? 12 and 8 12 and 10 2 and 5 2 and 12

Answer 1

12 and 8

Explanation:

The following 6 outcomes add 7: {1, 6}, {2,5}, {3,4}, {4,3}, {5,2} and {6,1}

The following 1 outcome adds 12: {6, 6}

The following 5 outcomes add 8: {2,6}, {3,5}, {4,4}, {5,3} and {6,2}

Therefore the pair 12 and 8 would make the game fair, because both players have 6 favourable outcomes