Yet, this is just an issue of possibilities idea
Because of the replacement in (1), we have:
Which illustration of Bayes’ Theorem works with the easy circumstances where you have a couple of hypotheses H and J which might be collectively exclusive and polske datingsider you will as one thorough, and in which you’re searching for \(\Pr(H \mid Elizabeth)\), that’s, the probability you to definitely H holds true considering facts Elizabeth. Exactly what that it exemplory case of Bayes’ Theorem really does is provide one with a means of calculating one to likelihood, provided that you to definitely knows, firstly, \(\Pr(H)\) and you will \(\Pr(J)\)-that is, brand new a great priori analytical probabilities of \(H\) and you can \(J\)-and then have, next, \(\Pr(Elizabeth \mid H)\) and you may \(\Pr(Age \middle J)\)-that’s, the new analytical odds of \(E\) provided, correspondingly, merely \(H\) and just \(J\).
However now Draper introduces a few substantive says. The foremost is your a good priori likelihood of brand new theory out-of apathy is not less than brand new a priori likelihood of theism, to make certain that i have
Draper’s second substantive claim is the fact that the conjunction out-of propositions from the pleasure and you will soreness to which Draper refers, and you will which is depicted of the \(O\)’ is more probably be correct whether your hypothesis regarding apathy is true than just if theism is valid. So we enjoys
However, provided that \(\Pr(T)\) and you may \(\Pr(O \middle T)\) aren’t equal to zero-which is surely very reasonable-(5) and you will (6) shall be rewritten as the
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