Not a paradox...here is a proof that it is 1/3 Let P(T) = probability that coin landed on tails, P(H) = probability that coin landed on heads. Let "1st" denot

Not a paradox...here is a proof that it is 1/3 Let P(T) = probability that coin landed on tails, P(H) = probability that coin landed on heads. Let "1st" denote the event that it is the first time you are awaken, "2nd" the second time. Note that P(T|1st) = 1/2 (if you were told that this is the first time you were woken up, it's equally likely that the coin landed heads or tails). And of course, P(T|2nd) = 1 By the definition of conditional probability, 1/2 = P(T|1st) = P(1st|T)P(T)/P(1st) = (1/2)P(T)/P(1st) Hence P(T) = P(1st) = P(T)1/2 + P(H) = P(T)1/2+(1-P(T)) = 1 - P(T)/2 -> P(T) = 2/3