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

Answer 1

12 and 8

Explanation:

Let's do some casework.

The probability that the sum is a 7 can be found the following way.

If the first number is a 1, the second number has to be a 6. If the first number is a 2, the second number is a 5. 3-4, 4-3, 5-2, 6-1, making a total of 6 possible ways to get a sum of 7.

There is only one way to make a 12(both dice roll a 6), and only 1 to make a 2(both dice are a 1). There are 4 possible ways to roll a 5, and 5 ways to make an 8. Since 5+1=6, the only fair dice rolls listed here are 12 and 8. Hope this helps!