Earlier quoted context omitted.
The answer to that question is obviously 0% Now, what would be the answer to the same question with the answer options: A) 20% B) 40% C) 60% D) 20% E) 0%
Your answer above is incorrect in a very funny way. "At random" implies an uninformed prior, but the question presupposes there's a correct answer, as 0% is missing. 0% and 100% are indefensible for any uninformed prior. There are two answers giving the correct probability for uniform prior. One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of…
Given uniform random none of the answers is correct:
25%) There's a 50% chance of choosing this answer
50%) There's a 25% change of choosing this answer
60%) There's a 25% chance of choosing this answer
If you're allowed to pick your own random distribution then any answer is equally valid. Say we pick one of the 25% answers 25% of the time, and the other ones uniformly:
25%) There's a 25% chance of picking this, as defined by our random distribution.
50%) 37.5% chance
60%) 37.5% chance
But if we instead pick our distribution so we pick the 60% answer 60% of the time and the others uniformly we've suddenly got this answer:
25%) ±27% chance
50%) ±13% chance
60%) 60% chance
So depending on if you interpret random as "uniform random" or as "whichever random distribution you like" either none of the answers are right or you can pick any answer to be right.