What is the chance you randomly guess the correct answer? a) 25%, b) 60%, c) 25%, d) 50%.
This is a common "pop probability" question and I want to have my say at what the answer is. By all means, think about it and try to reach a conclusion for yourself. Hint: I think there's a very clear correct answer.
Ready? Here goes.
The solution
If you somehow haven't heard this before, the obvious answer of 25% is wrong because both a) and c) are 25%, so there is a 50% chance of guessing that. But, the answer of 50% is also wrong because then there's only one of those so the chance of guessing is... 25%. An infinite loop. There: a contradiction. Which means there is no correct answer. Like saying "G holds if and only if G doesn't hold".
Except... that's not quite right. It's not actually a contradiction. There are two true statements: if the answer is 25%, then the chance of guessing it is 50% and if the answer is 50%, then the chance of guessing it is 25%. This kinda looks like a contradiction, but it isn't! It would be if 25% and 50% where the only allowed answers, but they're not!
So let's try more answers. There is one more obvious case to inspect: if the answer where 60%, then the chance of guessing it is 25%. This also isn't a solution. So that leaves us with a set of cases which are so "trivial" you might not have thought of them. What is the chance of guessing 42% as an answer? Or 33%? Or 69% or 3% or pi% or literally whatever other number there is? The chance is 0%.
What is the chance of guessing 0%, then? 0%
The solution is 0%.
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This one comes to the same conclusion as me.
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PS: Note that if you changed one of the answers that isn't 25% (either b or d) to 0% then there would actually be no answer (and if you changed either a or c, then the answer would be 25%)