if you choose the answer to this question at random,
So I assume the questioner has set up this question, in which all the possible correct answers are given in the 4 choices below. I think I have that straight so far. If you choose the answer to this question at random.
Ok, so lets choose either A,B,C,D at random. Do it now and stop, because that is what the questions is asking. We have chosen at random. I am assuming that we are picking with our eyes closed, but actually, it doesnt matter how you pick, and you'll see why later.
Presumably, we dont know the answer, just that it is one of the 4 numbers, but, oh wait, two are the same, so there are only THREE possible answers. Therefore, once we have picked one of the four, we either have a 25, 50, or a 60. One of those three is correct, I am assuming. We have one number in hand, what is the chance that we have the right one? Well, obviously, it is 1 in 3, or 33.3333%.
The question does NOT ask you "what are your chances of picking the right answer at random", it asks "what are your chances of, having picked an answer at random, that you are correct". Slight difference leads to totally different result. Thus the correct answer, which also goes for the "slightly more diabolical version". 33.333% what is the chance it will be correct
or 0, 25, 33, 50, or 100... depending on what assumptions you make.