Fine, so kill that portion of the post.
The enumeration of candidate throws stands. There are 36 equally probable dice throws. Of these, there are 11 specific throws where someone who looked at the outcome would say, "At least one of the dice is a 2." (as posed in the original problem).
Of these 11 possible outcomes, only 1 satisfies the criteria.
If you wish to discuss this further, run the suggested trial and post the results. (it's a short trial, so "anything can happen", but odds favor a result near 1/11)