quote:

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 a priori probability doesn’t change, but this is an after the fact probability with relevant knowledge. To take a very simple example if you can see that the coin has come up tails the probability that it came up heads is zero.

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So what is being asked? What is the probability of tails? or what are the probabilities of scenarios? They are not the same question

It is the probability of heads to the girl in her situation.

Or to put it another way, it’s the probability that she would be right if she guesses that the coin came up heads.

If she guesses heads she will be right in one of the three equally likely (to her) scenarios. If she guesses tails she will be right in two of them.

So if she guesses heads she will be right 1/3 of the time. Therefore the probability that the coin came up heads - to her in that situation - is 1/3.