This is becomes a self-referential paradox. Both A and D would be correct if there were four unique answers, but since A and D are the same answer, the chance that you would choose a correct answer is 50%, which makes B correct. But if there’s only one correct answer, the odds of choosing the correct one at random goes back to 25%. And around and round you go.

There’s a lot of discussion at Richard Wiseman’s blog and more at Lifehacker, where I first saw this.