The Sleeping Beauty Problem

The question the experimenters ask is "what is the probability of heads?". There is only one answer she could give.The paper then goes on to change the question to "what are the probabilities of each of the three scenarios?". That is not the same question at all.I don't understand the problem in having two different answers. There is no problem. There is no comparison. They are two different questions from two separate frames of reference. I don't understand the consternation SciAm is hyping here.

I can see that. But, the probability of heads/tails is .5 no matter how many scenarios you attach to each outcome and no matter what the girl may or may not know when.The problem is surreptitiously transitioned from a question of the outcome of a binary state to a question of probabilities of multiple states. They are not the same.So what is being asked? What is the probability of tails? or what are the probabilities of various scenarios from the girl's reference frame? They are not the same question.What am I missing?

Yes, I know all that ... if ... the question was for this smart girl to give her perspective and not the physical reality of a coin flip.I didn't take the question to be that though I can see where that question arises.Excellent explanation, PaulK.

The operative words being "from SB's point of view".She doesn't know if this is her first or 69th awakening. All she knows is she is awake and there are 99 ways for that to happen if the coin was tails and only one way for that to happen if the coin was heads. Yeah, 99 to 1 for tails. In her mind, flipping a heads is the least probable event explaining her being awake.Interesting.