You do not need to pick at all for the paradox to exist. If either A or D is correct, the other is also correct, and the random odds of selecting the correct answer should have been 50%. This is a contradiction. Neither A nor D can be the correct answer.

If B is correct, the random odds of selecting it is only 25% - a contradiction, so B cannot be correct. Likewise, if C is correct, there is a 25% chance of randomly picking C. C is also not correct.

None of the four answers is correct, so there is a 0% chance of randomly picking the correct answer. C is correct, contradiction, C is not correct, C is correct, is not, is too, etc.

The paradox is resolved by knowing the the scantron answer key has A selected. D is not sufficiently identical to A in javascript, so only the students that randomly guessed the correct answer will get credit.

Because the paradox can only be resolved with either A or D as the selected answer, well informed students picking randomly would have a 50% success rate.