Seems I asked my last questions poorly and it got a bad response. Okay so basically here's the problem and I will explain how I am trying to do it. 
You roll 1 fair die repeatedly until you either [get a 1 followed immediately by a 2] or [you get a 2 followed immediately by a 2]. What is the probability that a [1 immediately followed by a 2] is rolled before a [2 immediately followed by a 2]?

These are my thoughts on the question:

At first I thought they were equally likely. Like I thought "if you roll a 1 then you have a 1/6 chance of rolling a 2 and same thing if you roll a 2 you have a 1/6 chance of rolling another 2, but then I realized that rolling a 1 means that if you roll a 2, that 2 doesn't count towards rolling another 2. I.e. the 1,2 outcome cuts into the 2,2 outcome so there is some dependence going on and I don't know how to account for that.

Maybe I'm over thinking it. Please help!