solved by a program

not too hard if programming is allowed...1/9 minutes is my answer. not sure how to get it by hand though. I think it will be tough since the program returns a total number of 12766 distinct states.

btw the problem statement is not very clear in my opinion. basically it asks to estimate a time period "STARTING AT ANY POINT OF TIME", not "STARTING FROM THE BEGINNING OF THE EXPERIMENT" (in that case the answer will be simple, 12 minutes). It confused me for quite a few minutes.