So far, this is simply a question of likelihood principle
Of the replacing from inside the (1), we have:

This instance of Bayes’ Theorem deals with the simple situation where one has one or two hypotheses H and you will J which might be mutually personal and together exhaustive, and you can where a person is in search of \(\Pr(H \middle Elizabeth)\), that is, the possibility you to H is true given proof Elizabeth. Exactly what this illustration of Bayes’ Theorem really does is offer that that have a means of figuring one to chances, provided that one to knows, first and foremost, \(\Pr(H)\) and you may \(\Pr(J)\)-which is, the new a good priori analytical probabilities of \(H\) and you can \(J\)-and have, 2nd, \(\Pr(E \mid H)\) and you will \(\Pr(Age \middle J)\)-that’s, the latest logical probability of \(E\) provided, respectively, only \(H\) and simply \(J\).
The good news is Draper raises one or two substantive says. The very first is your an excellent priori likelihood of this new hypothesis away from indifference isnt below brand new an excellent priori odds of theism, in order for you will find
Draper’s second substantive claim is the fact that the conjunction off offres regarding fulfillment and discomfort to which Draper refers, and you may that’s illustrated because of the \(O\)’ is much more apt to be correct in the event the hypothesis regarding apathy is true than just in the event that theism is valid. So we provides
But so long as \(\Pr(T)\) and \(\Pr(O \middle T)\) aren’t equal to zero-that is undoubtedly very affordable-(5) and you can (6) shall be rewritten as
So we feel the influence you to, considering the facts about satisfaction and you may soreness described by the \(O\)’, theism is more probably be incorrect rather than become true. (altro…)