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My dice | |||||||
---|---|---|---|---|---|---|---|
Your dice | 1 | 2 | 3 | 4 | 5 | 6 | |
1 | 2 | 3 | 4 | 5 | 6 | 7 | |
2 | 3 | 4 | 5 | 6 | 7 | 8 | |
3 | 4 | 5 | 6 | 7 | 8 | 9 | |
4 | 5 | 6 | 7 | 8 | 9 | 10 | |
5 | 6 | 7 | 8 | 9 | 10 | 11 | |
6 | 7 | 8 | 9 | 10 | 11 | 12 |
Imagine that I change my dice slightly by replacing the 2 with an 8.
Can you choose numbers for the faces of your dice so that the two dice still perform in exactly the same way when thrown as a pair (ie so that the probability of getting a sum of $2$ is still $\frac1{36}$, the probability of getting a sum of $3$ is still $\frac2{36}$, and so on)?