The question does not ask whether A,B,C or D is correct, but the probability that you pick the correct out of 4 answers. So the intuitive answer is 25% (not A or D, but 25% or 1/4 or 0.25).
However, the text is missing important information such as how many answers are correct or if they are all wrong. Additionally, the text does not state that you (can) pick A,B,C or D with the same probability (it only says "at random" but that does not mean anything) because the percentages may affect you.
Therefore it is not a mathematical question of probability and thus you can argument that all probalities 0-100% can be correct. Instead it's a question to fool you and to create a discussion and I guess it will always be successful.