OnceDear your logic is fine, but you are not answering the original question. The original question makes it clear that at least one of the two dice is a two. And once again (how many times, Lord, how many times?) given that information you only have to consider the six faces on the other die.
Tell your buddies over on the Wizard's forum who enjoy insulting me and the others here who also say it's 1/6 that we appreciate your logic but your logic does not answer the question and the conditions posed in the question.
And frankly, I wish the original poster would come out of the bushes, desert, closet, Siberia, or wherever else he might be to clarify why he asked the question that way? I don't know if it was in error, an accident, or intentional to mislead? But whatever he did and whatever his motive, he sure created a mess out of a simple exercise.