Originally Posted by 1in11 View Post
Knowing which die shows a 2 gives us 6 possibilities for the combination of the two dice: 2-1, 2-2, 2-3, 2-4, 2-5, 2-6.

Knowing only that at least 1 die shows a 2 gives us 11 possibilities for the combination of the two dice: 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 1-2, 3-2, 4-2, 5-2, 6-2.

This is why it is an important issue, as they are two fundamentally different conditions.
That's what's called an incessant need to take theory to a more complicated, unnecessary level. The OP's question clearly eliminates one of the die from the calculation--random or not. Putting the other die back into the issue would lead to an F from any math professor at any university.