Bernoulli's fallacy is common in current statistical applications, where studies are often not reproducible. The problem is that investigators ask the wrong question. One formulates a hypothesis and then asks whether the sample data is consistent with that hypotheses. But what is really needed is to find which hypothesis is suggested by the data.
One has to ask how likely is the hypothesis. Being consistent with an improbable hypothesis is not useful and can be very misleading. One need to state the prior probability of the hypothesis and consider alternatives. Bayesian methods are more appropriate than frequentist for many applications
