Your statements 1 and 2 are correct, blount2000. Whether or not you saw 2-2 when at least one of the two dice is a 2 one-sixth of the time doesn't matter. Frankly, when you roll two dice the chance of getting 2-2 is 1/36.

The original question and the question to be answered is simply this: if you have at least one 2 showing, what are the odds for the second die to be a 2 as well. And that is the same as rolling one die with a 2 showing 1/6 times.

If you are not seeing 2-2 with one 2 showing one-sixth of the time you're just like me. Like I said, that would be a 1/36 chance.