I think the problem is in the phrasing of the question: <i>When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?</i><p>That&#x27;s not a precise probability question.<p>More significantly the question (whatever it might be) is <i>potentially</i> asked more than once.<p>So, if the question is &quot;what is the probability that the coin-flip was Heads?&quot; (which I think it the most likely interpretation) then it&#x27;s 1&#x2F;2<p>But if the question is &quot;what is the probability that you are being woken up because the coin was Heads&quot; then it&#x27;s 1&#x2F;3<p>Asking me what I &quot;should believe about the outcome&quot; is (intentionally, I suppose) blurring the question so that it disguises the fact that there are actually 2 different questions in play.