Finally, something my math degree is good for! Before I ruin it, I want to state my admiration for this brainteaser. Simple yet elegant in its ability to play on the human race's addiction to correlative logic.

Sadly, the riddle has nothing to do with statistics or math... but is rather a lesson in subjective semantics (assuming that at least one of the options is the correct answer of course). All you have to do is ask the question, "If the correct answer were (a), then would (d) also be correct?"... at which point you've solved it & there is no need for a reply.

It's a bit tricky to explain but here-goes:

• If (d) is considered incorrect if (a) is correct, then the values of each answer are irrelevant since the "25%" didn't make (a) correct... which means you have a 25% chance of getting the correct answer, but the correct answer has nothing to do with the value. (b) or (c) could just as easily be the correct answer with the same probability. In other words, the answer wouldn't be 25%, 50% or 60% ... rather the answer is simply (a).

Conversely

• If (d) is also a correct answer if (a) is correct, then there can be no value which corresponds to the probability of randomly selecting the right answer, and thus the correct answer is again arbitrary irrelevant of its value.

Simply put, there is no possible scenario where the correct answer's value matches the probability of randomly getting it right; so the value does not define the correct answer only the person who created the question does.

If there are two correct answers then the probability of getting it correct is 50%, however there is only one option for 50% therefor either 25% or 60% is also a value of a correct answer and thus again the value does not define the answer.

The same can be repeated for if there were 3 or 4 hypothetically correct answers, where since there is no '75%' or '100%' value listed the values once again cannot define the answer.

[the best way to think of it is to replace all the values with anything else, e.g. colors, and repeat the question; once you accept that the correct answer is arbitrary, the response of probabilities is irrelevant]