This question comes from a discussion on reddit.
One user asked a question:
Given $p=0.05$ in one study, what is the likelihood of $p \ge 0.05$ if the same study was repeated under the exact same condition in the same population?
With a set of possible answers: 5%, 10%, 50%, 95% and 99%.
The most common and most accepted answer seemed to be that you don't have enough information to tell.
However this seems wrong. My reasoning is the following:
0.05 is an arbitrary p-value. So the question really asks - when you obtain a p-value, what's the probability that the second p-value will be greater than the first one? And when rephrased that way 50% looks like an obvious answer.
The question is - what is the correct answer and how to derive it in a more rigorous way?