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Jonathan_Graehl comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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Huh? If tails, then Beauty is (always) woken on Monday. Why do you have probability=1/2 there?
(likewise for Tuesday)
The probability represents how she should see things when she wakes up.
She knows she's awake. She knows heads had probability 0.5. She knows that, if it landed heads, it's Monday with probability 1. She knows that, if it landed tails, it's either Monday or Tuesday. Since there is no way for her to distinguish between the two, she views them as equally likely. Thus, if tails, it's Monday with probability 0.5 and Tuesday with probability 0.5.
Okay, I now understand what you mean by that tree.