Ok, so here's the deal with this question. It states "If you choose an answer to this question at random..." It must be stated that there really is no question to answer so, we are forced to make some assumptions and, depending on what you assume, your answers will be different.
If you assume that the answers given are irrelevant, a red herring as it were, then you cannot answer the question since we do not know what the correct answer is and the odds of getting the correct answer are different depending on which you choose.
For Example, replace the percentages with some other thing:
A) Cat
B) Dog
C) Bird
D) Cat
Obviously your chance of guessing cat is double the chance of guessing the others, but since we don't know, from the question, what the correct answer is, we cannot calculate the odds.
If you assume that the choices given are meant to be your options then you have a 0% chance of getting the correct answer since none exists. You have a 50% chance of guessing "25%" which automatically makes it an invalid answer and, of course, the other answers are wrong because 50% and 60% do not equal the odds either. I would argue that this is the approach that requires the least assuming and/or reading into the problem.
If you assume that the question is asking something like "Given a set of four solutions, only one being correct. What are the odds you will guess the correct solution at random? Select from the options below." In this case the correct answer is 25% and you have A or D to choose from. This is what many here are doing. They are answering the question independent of the answers provided, then applying the answers after the fact.
"Oh! one out of four is 25%! But I have two 25% answers, therefore the answer is 50%!" (Most first graders will tell you that 25% does not equal 50%.)
You could get all philosophical and assume that since there really is no definite question, as if the question were as vague as "what am I thinking of?" Your odds here would be one in infinity of guessing the answer correctly or 1/infinity. **WARNING MATH** The limit of x (your possible solutions) approaches infinity your odds become zero. In other words, one divided by a REALLY big number become, the same as makes no difference, zero.
I'm going to guess that the purpose of this question is to start all kids of discussions like this. It really is a good critical thinking exercise. I agree with Tank-Ace, there really is not enough information to definitely prove one way or the other what the answer is, we need more. BUT, the path with the fewest assumptions will give us an answer of 0%.
