This only produces a paradox if you fall for the usual fallacy that “at random” necessarily means “with uniform probability”.

For example, I would pick an answer at random by rolling a fair cubic die and picking a) if it rolls a 1, c) on a 2, d) on a 3 or b) otherwise so for me the answer is b) 50.

However, as it specifies that you are to pick at random the existence and value of the correct answer depends on the specific distribution you choose.