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timtyler comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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Probabilities are subjective. From Beauty's POV, if she has just awakened to face an interview, then p(H)=1/3. If she has learned that is Friday and the experiment is over, (but she has not yet been told which side the coin came down), then she updates on that info, and then p(H)=1/2. So, the value of p(H) depends on who is being asked - and on what information they have at the time.