Multiple correct type !

The solution presented is very simplistic. I guess the problem was a little ambiguous. Ok, a LOT ambiguous. I assumed that the student doesn't know how many correct answers there are - I've taken these tests and the question asks to mark all answers that apply, they do not state how many that is. Since the question says the student will answer randomly, I assumed he will choose one of the 15 possible ways he can color the answers. Now, the question itself will only have 1, 2, 3 or 4 correct answers. The problem also states that as long as the student marks ALL the correct answers he will get the points, so if he marks incorrect answers in addition to correct ones, he should still get the points, as per the problem conditions! An obvious strategy is to color all answers correct every time, but we'll assume the student doesn't know that. Anyway, you have to look at the probabilities of the student answering the question correctly in each of the 4 scenarios separately and then add them together. If the question only has one correct answer, the student will get it right 8 times out of 15. How is that? Well, if he colors only one answer, that's 1 out of 4 correct. If he chooses to color two answers, he will get the correct answer in 3 out of 6 ways, etc. Do that for each scenario of correct answers, and you will calculate that he answers the question correctly the first time 13/45 = 28.8% of the time. Now, here is where it gets complicated. If he gets the question wrong, will he try a completely different answer, or will he still do it randomly, chancing the same exact answer? If he excludes the answer he just tried, this problem becomes near impossible, because we need to account for the answer the student excluded as well as how many correct answers the question actually has, because the probabilities change with each variable. Since the problem states he answers at random, I'll assume maybe he is doing a re-test and forgot what he answers the first time, so he'll just do it randomly again. For that the probability will be: 13/45 + 32/45*( 13/45 + 32/45 * 13/45 ) = 64.04%............. 3/15? Are you kidding me? Am I the only one confused by this question?