The whole question relies on probability unless you say it's an impossible answer due to infinite iterations during the question.
The only things we know about the question are the number of possible outcomes: 4, having to choose a possible outcome
Pick out or select (someone or something) as being the best or most appropriate of two or more alternatives
and randomly selecting an answer,
Made, done, happening, or chosen without method or conscious decision
thus, unless you look at additional evidence for random decisions made on a multiple choice test, there is, as you've said a 1 in 4 or 25% chance of randomly picking an answer whether it be right or wrong. Now the probability of choosing 25% is both A and D out of 4 possible outcomes, therefore 50%, resulting as said: Answer B.
Though I do agree these questions or paradox's as some people see it do always create a discussion.
(Reminds me of another paradox I heard)
Mr&Mrs Smith have two children. At least one of them is a boy. What is the probability both children are boys?
