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Vaniver comments on Conservation of Expected Evidence - Less Wrong

68 Post author: Eliezer_Yudkowsky 13 August 2007 03:55PM

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Comment author: Vaniver 07 May 2012 11:56:01PM *  3 points [-]

P(H) = P(H|E)P(E) + P(H|~E)P(~E)

P(H)*(P(E)+P(~E))=P(H|E)P(E) + P(H|~E)P(~E)

P(H)P(E)+P(H)P(~E)=P(H|E)P(E) + P(H|~E)P(~E)

P(H)P(~E)=(P(H|E)-P(H))*P(E) + P(H|~E)P(~E)

0=(P(H|E)-P(H))*P(E) + (P(H|~E)-P(H))*P(~E)

The trick is that P(E)+P(~E)=1, and so you can multiply the left side by the sum and the right side by 1.