Of the replacing for the (1), you will find:
Which example of Bayes’ Theorem works together the straightforward situation in which you’ve got one or two hypotheses H and you may J which might be mutually private and you may jointly exhaustive, and where you’re selecting \(\Pr(H \mid E)\), which is, your chances one to H is true offered proof Elizabeth. Exactly what which exemplory instance of Bayes’ Theorem really does are render one that have a means of calculating you to chances, provided you to knows, to begin with, \(\Pr(H)\) and \(\Pr(J)\)-which is, brand new a good priori analytical probabilities of \(H\) and you may \(J\)-while having, second, \(\Pr(Elizabeth \middle H)\) and \(\Pr(Age \middle J)\)-that’s, the new analytical likelihood of \(E\) provided, correspondingly, just \(H\) and only \(J\).
However Draper brings up two substantive says. The foremost is that an excellent priori likelihood of the fresh new hypothesis out-of indifference is not less than the latest a good priori odds of theism, in order for i have
Draper’s 2nd substantive allege is that the combination out-of offres regarding fulfillment and aches to which Draper relates, and you can that is illustrated from the \(O\)’ is much more more likely true if the hypothesis from indifference holds true than simply in the event that theism is true. So we keeps