I was just exposed to this puzzle:
If you choose an answer to this question at random, what is the chance you will be correct?
My answer is: 25%. But here’s just a stab at an explanation (which makes this puzzle seem similar to Newcomb’s paradox).
Either A or D is the correct answer, and your choice determines which is correct (and, consequently, which is incorrect). My initial thought is that counterfactual semantics may be of come help.
Assume there can only be one correct answer in any possible world in which an answer is chosen. So for any world in which A is chosen, A is the correct answer in that world; likewise, any world in which D is chosen, D is the correct answer in that world.
Suppose you choose A in this world (the actual world, call it W). A is thereby the correct answer W, and D is the incorrect answer. But D is correct in another possible world (say, W*) and A, incorrect. I.e., the following counterfactual is true: Had W* been actual, you would have chosen D, and D would have been the correct answer (and A would have been the incorrect answer). But it does not follow that D could have been the correct answer in W, because there can only be one correct answer per world, and you chose A in W. In other words, which answer is correct is logically posterior your choice, and that there is no correct answer prior to your choosing. That last bit may sound odd, but isn’t this exactly what we should expect if odds can be determined by random choice (i.e., there is no arbitrary choosing, there are no odds of choosing correctly)?
But I must confess that, probably, the chances of me being correct in my explanation are probably less than 25%. Enter the Paradox of the preface.