Answer:
2 and 5
Explanation:
Let's list all the possible combinations of numbers that would result in you winning:
1 + 6 = 7
2 + 5 = 7
3 + 4 = 7
4 + 3 = 7
5 + 2 = 7
6 + 1 = 7
There are six combinations that would result in you winning. To make the game fair, the probability of each outcome should be equal.
Since each cube has 6 sides with numbers 1 to 6, the total number of possible outcomes is 6 * 6 = 36.
The probability of your friend winning (rolling a sum of 7) is 6/36, which simplifies to 1/6.
To make the game fair, you should also win with a probability of 1/6. Since there are six combinations that result in you winning, each combination should have a probability of 1/6.
However, we can see that the combinations (1, 6) and (6, 1) are essentially the same, as they result in the same sum. Similarly, (2, 5) and (5, 2), as well as (3, 4) and (4, 3), are equivalent pairs.
Considering this, we can choose one representative pair from each set of equivalent pairs. Let's choose (1, 6), (2, 5), and (3, 4) as the representative pairs.
Therefore, the pair of numbers that would make the game fair is (1, 6), (2, 5), and (3, 4).