When in doubt, pick B.
What a coincidence. Those are the odds of me winning the lottery too! Either I will win or I won’t.
I heard someone say this in earnest once. “It’s 50/50, really”. A little part of my brain melted and leaked away that day.
If you have a zero percent chance of answering it correctly, then you are wrong.
See, now, the question says If. It doesn’t say you have to answer randomly. I’m parsing the question as though it were:
(Where the answere would be B, obviously.)
I like “100%” as the answer. There’s nothing saying I have to choose from the choices presented to me, and this answer is recursively correct as well- if you always choose 100%, you’ll be right 100% of the time, right? The only problem is I didn’t choose it at random…
That won’t work, because if you parse the question that way you don’t know that 25% is the correct answer, and therefore A and D are correct, and therefore will be chosen half the time.
It’s not like the OP asked for epirical v. theoretical probability!
edit: Apparently the OP didn’t even ask the right question. D’oh!
The answer to the question:
“If you choose an answer to this question at random, what is the chance you will be correct?”
Is 0%. The implication is that I am choosing a percentage from 0% to 100% uniformly at random. There are infinitely many choices, so my chance of choosing any particular one is 0%. In probability, something that has a 0% chance of happening may still be possible.
If the question is:
“If you choose an answer to this question at random from A, B, C, and D, what is the chance you will be correct?”
Then there is no correct answer.
I’m not following. Can you elaborate?
Is there any way we can apply fuzzy logic to this question, sort of like saying that Epimenides’ statement is half-true?
I’d guess this is just a clever joke, but I was (ETA: even before Chronos’s post) trying to think if there were a way to assign probabilities to each possibility, and have a consistent results. So
P(25%) = x
P(50%) = y
P(60%) = z
x+y+z = 1
Then the probability of randomly guessing correctly is
p(correct) = x/2 + y/4 + z/4
If p(correct) has to be 0.25, 0.5, or 0.6, then
p(correct) = 2x+y+z has to be 1, 2, or 2.4
Then, since x+y+z=1, we get x = 0, 1, or 1.4, and it can’t be 1.4, so either
x = 1, y=z=0
or
y+z = 1, x=0
And then I’m stuck.
Even after you’ve reinterpreted the problem to remove the self-referential element, B is not correct.
If the correct answer to Alice’s question is “25%,” then she will be correct if she picks A or D, and wrong if she picks B or C, so her chances are 50%.
If the correct answer is “50%,” then Alice will only be correct if she picks B, giving her a 25% chance. The same goes for “0%.”
So B is correct if “25%” was the correct answer to Alice’s question. But you don’t know that.
Here’s how I see it, though I’m crap at these sorts of logic puzzles, so I may be wrong:
If all the answers were different, with the correct answer present, there would be a 1 in 4 chance (25%) of picking the correct answer by choosing randomly.
Since this answer is represented twice, the chance of choosing it randomly is doubled (50%)
And since the question is asking what her chances are of picking the correct answer, not asking what the correct answer actually is, then B (50%) represents her chances of choosing the correct answer (25%) randomly given the duplication of the correct answer.
But if the correct answer is duplicated, changing the chances of choosing, it, then the chance itself has changed, thereby changing the correct answer and the chances of choosing it.
And there my head explodes.
If you change C to anything but 0% then 0% becomes the logically consistent correct answer. A random pick of one of the 4 solutions will necessarily be wrong (as the correct answer is 0%) and we are done. All other solutions are self contradictory.
With C itself being 0% this is no longer an option. In that case it just becomes one of those undetermined self referential thingies that doesn’t need to have a logically consistent solution.
Similar to
Is the statement “this statement is false” true or false.
and
“What is the lowest positive integer that can’t be described in English in fewer than one hundred letters?”
If there was one I could describe it as
“the lowest positive integer that can’t be described in English in fewer than one hundred letters”, and yet there are more than 26^100 positive integers.
You can assign imaginary truth values, a la Spencer-Brown…
Every statement in this thread is wrong.
In order to choose an answer to this riddle at random I’d have to weigh up the four possibles. So, there would be 1/4th of a chance I’d choose the right one.
A.) in my opinion.
I don’t see an infinite amount of choices. You are given four absolutes.
D) is also 25%.
This is wrong, only some of the statements on this thread are wrong.