This was similar to my intuition also. She will wake up in the end no matter what regardless of how many times she has been woken up before, so how does her wakefulness add any new information? If there was a scenario where she would never wake up, then her being awake would actually mean something, but that isn't the question.

I can't see how this a problem of conditional probability. Isn't it just "what is P(heads)"? Am I missing something?