> They could ask her, "when you wake up, how likely will you think that the coin was heads?" and get the same (correct) response of 1/3. Exactly. Let's stretch

> They could ask her, "when you wake up, how likely will you think that the coin was heads?" and get the same (correct) response of 1/3. Exactly. Let's stretch the example to the extreme, if you get heads you get woken once, if you get tails you get woken 1 million times. Now say you run this experiment 10 times and you happen to get 5 heads and 5 tails. You'd be woken up 5 million and 5 times. And with each wakening, the chance of the coin having been heads isn't 50%, if you'd say and guessed it was heads every time you wouldn't get half of them right, you'd be statistically wrong about 5 million times out of the 5m and 5 times. The correct answer is 1 in a million, and if you'd guessed tails on every awakening instead you'd be wrong on average only once in a million. It's this chance to be correct or incorrect in your answer when waking that would inform the question that was posed 'When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads', which then would be 1/3.