A Math Problem for Cretans

This math question has been floating around the interwebs recently:

The answer may initially seem obvious, a rather straightforward application of probability. But if you look at it more closely you’ll see that it’s the type of question that Epimenides might ask if he was a statistics professor. Think you know the answer?

(Hint: Over on The Volokh Conspiracy, the first commenter provides the best answer (i.e., the answer that I agree with).)