The Wizard will bank this bet: 1/6 vs 1/11

[arcimede$]

Arc let me clue you in on the English language. The key phrase "at least" means this:

There is a 2 on one die, or there is a 2 on both dice.

True but not the complete picture. There is a 2 on one die (the red one), or there is a 2 on the other die (the blue one) or there is a 2 on both of them.

That is what "at least" means. It does not mean the #2 can jump from one die to another.

No one said it did. Back to the red/blue dice. The 2 can be on the red die or the blue die. That is what "at least one die" means. If the 2 is on the red die then the blue die can be 1-6, that gives you 6 possibilities. If the 2 is on the blue die then the red die can have 1-6, that also gives you 6 possibilities. Since the 2-2 is a duplicate we eliminate one and you are left with 11 possible results.

This has all been explained to you multiple times.