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jimrandomh comments on Formalization is a rationality technique - Less Wrong
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For the argument to be wrong, only one of its subarguments has to be wrong. So the correct equation is
P(whole argument is wrong) = 1 - P(first subargument is right) * P(second subargument is right | first argument is right)
If the arguments are chained together, then this is true, but the original poster was talking about independent lines of reasoning leading to the same conclusion. For arguments which are truly independent, then his formulation is correct.
Alrighty, I gotcha.