To date, this is just a question of chances idea
By the replacing in (1), we have:
So it example of Bayes’ Theorem works together the easy case where one has two hypotheses H and J which might be mutually personal and you may as you thorough, and in which you’re trying to find \(\Pr(H \middle Age)\), that’s, the possibility one to H is valid given proof E. Just what this exemplory instance of Bayes’ Theorem do are offer one with a way of figuring you to definitely possibilities, provided that knows, firstly, \(\Pr(H)\) and you may \(\Pr(J)\)-which is, brand new an effective priori analytical possibilities of \(H\) and you can \(J\)-while having, 2nd, \(\Pr(E \middle H)\) and you can \(\Pr(E \middle J)\)-that is, brand new logical odds of \(E\) given, respectively, merely \(H\) and only \(J\).
However now Draper brings up one or two substantive says. The first is that a great priori probability of the hypothesis from apathy is not below the newest good priori probability of theism, with the intention that you will find
Draper’s second substantive allege is the fact that combination of offres about satisfaction and you will aches that Draper pertains, and you can that’s portrayed because of the \(O\)’ is far more likely to be true in case your hypothesis away from indifference holds true than simply in the event that theism is valid. (more…)