For any such finite sequence of awakenings, there would (when viewed from the outside) be a 50% chance for a particular week of waking up in an evening, and a 50% chance for a particular week of waking up in the mornings - you can then assign a uniform distribution for particular weeks, getting a 1/6 probability of a particular morning in a tails week. If you pick an awakening randomly on that distribution, you have a 1/2 probability it's an evening and a 1/12 probability it's any particular morning (ETA: out of the week).