The sleeping beauty problem....?

[The Question]

We plan to put Beauty to sleep by chemical means, and then we'll flip a (fair) coin. If the coin lands Heads, we will awaken Beauty on Monday afternoon and interview her. If it lands Tails, we will awaken her Monday afternoon, interview her, put her back to sleep, and then awaken her again on Tuesday afternoon and interview her again.The (each?) interview is to consist of the one question: what is your credence now for the proposition that our coin landed Heads?When awakened (and during the interview) Beauty will not be able to tell which day it is, nor will she remember whether she has been awakened before.She knows the above details of our experiment.What credence should she state in answer to our question? Is the answer 1/2 or 1/3?

[Cirric]

Hi. 1/2. There is only one coin toss.

[cdmillstx]

If I interpret this bizarre setup correctly, then when she finds herself being interviewed, there are three possibilities:1) it's Monday and it landed heads2) it's Monday and it landed tails3) it's Tuesday and it landed tailsIt's a fair coin, so the probability of #1 and #2 are equal; #3 occurs if and only if #2 occurs, so the probability of #2 and #3 are equal.Since all three are equally probable and only one has the coins landing heads, the answer is 1/3.This is an odd restatement of other well-known questions that restrict the problem space to 3/4 of the possible outcomes, such as:You two children are in a house and at least one is a boy. You knock on the door and a boy answers. What is the probability that the other child is a boy?(Answer: 1/3)