In probability, I often have trouble determining which situations to take as distinct outcomes for calculation. For instance, if we have a die with its faces numbered $1, 2, 2, 3, 3, 6$ and we roll it twice.
We get $2$ on the first roll and $3$ on the second. Again rolling it twice we get $2$ and $3$. But the $2$ we got the second time is not the same $2$ as the first one. Its the other $2$ inscribed on the face of the die (the die has two $2$'s).
So, for the purpose of calculating the probability that the sum of the two rolls in a die will be a certain number $4$, say, will these two situations constitute distinct outcomes?
This is just a simplified, distilled example of a persistent problem I face in probability. Is there any way to think about outcomes that can make this clearer?