You are not being asked the probability of a coin flip. You are a being asked the probability of a coin flip given that it woke you up. Simple Bayesian statisti

You are not being asked the probability of a coin flip. You are a being asked the probability of a coin flip given that it woke you up. Simple Bayesian statistics. You don't know which of the three scenarios your in (Heads: 1st wake up, Tails: 1st Wake up or Tails: 2nd wake up). Given that there are three possible scenarios you are in, when finding myself in a scenario, I would give each scenario equal weight. There's my devil's advocate view. I can see what you're saying though. Edit: Additionally, even though the awakenings are not in the same 'stream of consciousness' if one tails waking happen, they both happen. They are linked even if you're trying to view them in isolation.