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PhilGoetz comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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If you don't need to condition on it, why is it in the story?
The question asked in the story is "Sleeping Beauty, what is p(heads | you are awake now)?"
Someone is going to complain that you can't ask about p(heads) when it's already either true or false. Well, you can. That's how we use probabilities. If you are a determinist, you believe that everything is already either true or false; yet determinists still use probabilities.
"On Sunday she is given a drug" is also in the story. Does it follow that it is imperative to explicitly condition on that as well?