Suppose there are 10 multiple choice questions in an science class quiz. each question has four possible answers, and only one of them is correct. what is the probability of having two correct answers if a student attempts to answer every question at random

The probability should still be 2 out of 10 even if it's random. No matter what he's just trying to get 2 questions right. Other than it being completely random. So 2/10 or 1/5. That's what I would say. If they say different you could argue that more information is needed.