Having a prior opinion is about having some previous understanding of the subject being discussed. If more data were to be provided to you then you might reason differently. Not because you are changing your mind or flip-flopping (like politicians say), but because you are a thinker and coherent individual. You will analyse the new data with fresh eyes and challenge the old data with it. Its all part of the scientific approach. Don't you agree?
Being given new information on a subject I know about which contradicts my understanding might make me change my mind. Just showing me that I apparently answered the question differently wouldn't, for the obvious reason that I know about the subject.
If I don't have any previous understanding of the subject then I wouldn't be able to give an immediate opinion on it. If pressed, I might choose to answer a question on the spur of the moment, but my choice would be mainly random. If it was mainly random then the magic trick described here would probably work, but it wouldn't really mean anything as it was a mainly random choice in the first place.