The phrasing of the question is When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
It's not actually asking for a strategy about guessing the correct answer, or how many times you'll be right or wrong.
It think whether you are a halfer or a thirder is going to depend on how you interpret the question.
If you see it as asking about the frequency at which "Heads" will the right answer, then it's clearly 1/3. But that's not what the question actually asks (probably - all language is interpreted).
It's not actually asking for a strategy about guessing the correct answer, or how many times you'll be right or wrong.
It think whether you are a halfer or a thirder is going to depend on how you interpret the question.
If you see it as asking about the frequency at which "Heads" will the right answer, then it's clearly 1/3. But that's not what the question actually asks (probably - all language is interpreted).