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Jonathan_Graehl comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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She knew from the start that she is twice as likely to be asked when it is tails. So, her estimate of the chances of her being awakened facing tails should be bigger from the beginning.
I couldn't decide exactly you meant by "twice as likely to be asked (woken) when it's tails" either. I'm going to guess that you're averaging evenly over Monday and Tuesday, in which case I agree. After marginalizing over M/T, P(wake|heads)=1/2 and P(wake|tails)=1.