Some researchers are going to put you to sleep.

During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking.

When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?

If the question is about the first time you are awakened, and if you know the rules, you will think that you are awake because you are in one of three possibilities: head and awake, tail and first awake, tail and second awake. So the probabilty should be 1/3 (you are in one of three equal probability events).

Edited on January 22, 2018, 4:41 pm

Ps: I'm supposing also that there is no way to notice the first absolute awakening from any other of the series. Otherwise (if you can be sure that this is your first absolute awakening (i.e: because they didn't give you already the "oblivious drug") the possibility is 1/2.

Edited on January 22, 2018, 5:10 pm

Posted by armando on 2018-01-22 16:18:53