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gjm comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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Pr(heads|alive) / Pr(tails|alive) = {by Bayes} Pr(alive|heads) / Pr(alive|tails) = {by counting} (99/100) / (1/100) = {by arithmetic} 99, so Pr(heads|alive) = 99/100. Seems reasonable enough to me.