By the replacement for the (1), we have:

It instance of Bayes’ Theorem works closely with the straightforward situation in which you have a couple hypotheses H and you can J which can be mutually private and you can jointly thorough, and you may in which you’re looking \(\Pr(H \middle Age)\), that is, the probability you to definitely H holds true offered proof E. Exactly what it exemplory instance of Bayes’ Theorem really does is give you to definitely having a means of figuring one possibilities, so long as you to understands, first, \(\Pr(H)\) and \(\Pr(J)\)-which is, the latest a priori logical likelihood of \(H\) and you may \(J\)-and get, next, \(\Pr(Age \middle H)\) and \(\Pr(E \mid J)\)-which is, the new analytical odds of \(E\) offered, correspondingly, only \(H\) and simply \(J\).

But now Draper brings up a few substantive claims. The foremost is that a good priori probability of the new theory out-of apathy isnt lower than the new a beneficial priori odds of theism, to make sure that we have

Draper’s 2nd substantive allege is that the conjunction of propositions throughout the fulfillment and you may pain to which Draper pertains, and you may that is depicted by \(O\)’ is much more likely to be true when your hypothesis away from apathy is valid than just in the event that theism is valid. So we keeps

However, so long as \(\Pr(T)\) and \(\Pr(O \middle T)\) are not equal to zero-that’s seriously affordable-(5) and (6) are rewritten since the

(more…)