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).
In my use of the words ‘every week’ I am implicitly—I take that back, I am explicitly supposing that every week the procedure is repeated.
So we would obtain an indefinitely long sequence of awakenings, of which 1⁄7 are in the evening and 6⁄7 in the morning.
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).