Via BayesianBiologist  : An excellent explanation of the fallacy that most people have about, P-value

What we really want is the probability of hypotheses given our data (written as P(H | D) ), which we can obtain by applying Bayes rule.

What we get from a p-value is the probability of observing something as extreme or more than our data, under the null hypothesis ( written as P(x>=D | Ho) ).  Isn’t that awkward? No wonder it is so commonly misrepresented.