 It has been argued that, seen as an inductive argument, PI is fallacious: it commits the base-rate fallacy (cf. Lewis 2001). If in the past there have been many more false theories than true ones, (if, in other words, truth has been rare), it cannot be concluded that there is no connection between success and truth. Take S to stand for Success and not-S to stand for failure. Analogously, take T to stand for truth of theory T and not-T for falsity of theory T. Assume also that the probability that a theory is unsuccessful given that it is true is zero \((\textrm{Prob}({\textrm{not-}S}\mid T)=0)\) and that the probability that a theory is successful given that it is false is 0.05 \((\textrm{Prob}(S\mid {\textrm{not-}T})=0.05)\). Assume that is, that there is a very high True Positives (successful but true) rate and a small False Positives (successful but false theories) rate. We may then ask the question: How likely is it that a theory is true, given that it is successful? That is, what is the posterior probability \(\textrm{Prob}(T\mid S)\)?