• Jeremiah
    1.4k
    Does this problem have a solution? Is it a paradox or other?

    Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct?

    A) 25%
    B) 50%
    C) 60%
    D) 25%
  • unenlightened
    2.5k
    If the correct answer is 25%, then the correct answer is 50%.
    If the correct answer is 50% or 60% then the correct answer is 25%

    Therefore, the correct answer is 0% which is correct because it is not a choice on offer. If one could choose it, randomly or deliberately, it would be wrong. It's an amusing self-referential paradox, but I don't see anything special about it. It would have been more amusing, and neater, if one of the options (C) had been 0%

    One expects there to be a right answer on offer, but there may not be.

    2 + 2 = ?

    A) 3
    B) 203
    C) 42
    D) 8.73

    Expect to get low marks in such tests, however hard you revise.
  • StreetlightX
    2.7k
    There's no criterion for correctness, so there's no possible answer.
  • noAxioms
    585
    There's no criterion for correctness, so there's no possible answer.StreetlightX
    But there is. It asks about the odds of guessing correctly.

    Therefore, the correct answer is 0% which is correct because it is not a choice on offer.unenlightened
    I agree, and the consistency of this makes it not a paradox. Choice C should probably have been 0% instead of 60%. Then it would be a paradox I think.
  • noAxioms
    585
    Heh
    Thought of a variation of the original one:

    If you choose an answer to this question at random, what is the chance you will be correct?

    A) 25%
    B) 50%
    C) 100%
    D) 50%

    Each answer is correct (not necessarily in the same way), so are any of them really?
  • TheMadFool
    2.3k
    I don't get it.

    There are only 3 choices 25%, 50% and 60%.

    Random selection would be a chance of 1/3=33.33%.
  • StreetlightX
    2.7k
    It asks about the odds of guessing correctly.noAxioms

    Guessing what correctly though? Guessing the answer yes, but... to what? The question... which is... about the odds of guessing correctly. It's a weird little circle.

    The self-reference of the indexical 'this' hides the fact that there is no actual question to which a chance of answering corresponds.

    The two 25%s are a trick, a distraction. The question is unanswerable from the very beginning.
  • noAxioms
    585
    Guessing what correctly though?StreetlightX
    of correctly guessing the answer giving the correct odds.
    Yes, circular, but that doesn't mean there's no actual question.
  • noAxioms
    585
    Sorry. See edit
  • StreetlightX
    2.7k
    Once circularity is admitted, the game is up. The question is a verbal Penrose staircase:

    Penrose_stairway.gif
  • noAxioms
    585
    It is not necessarily invalid for a question to be circular.

    How many letters does the correct answer have?
    • two
    • three
    • four
    • five
  • Jeremiah
    1.4k


    There are four possible outcomes. That part never changes. The fact that two of the possible outcomes contain the same values does not change that there are four possible outcomes. We just increase our chances of being correct if the desired outcome is 25% since it is two of the four possible outcomes.
  • Jeremiah
    1.4k


    0% is not a possible outcome, which means there is a 0% chance of it being 0%.
  • Jeremiah
    1.4k
    The problem as I see is that the outcome changes the solution and I not sure if I would consider that truly circular.
  • noAxioms
    585
    The problem as I see is that the outcome changes the solution and I not sure if I would consider that truly circular.Jeremiah
    Of course it is circular. Perhaps there is a paradox that is not, but I cannot think of one offhand.

    The question concerns the answer to the question. That's a circle, or more formally, self-referential.

    You ask about the odds of correctly guessing the answer giving the correct odds of correctly guessing the answer giving the correct odds of correctly guessing the answer giving the correct odds of correctly guessing the answer ....

    0% is not a possible outcome, which means there is a 0% chance of it being 0%.Jeremiah
    If none of the choices is correct, then the correct answer is simply not among the choices. 0% is the answer since it cannot be chosen. This itself is not paradoxical. Hence my comment that (C) should have been 0%, not 60. That forces the paradox.
  • Jeremiah
    1.4k


    0% is not a possible outcome for the answer, therefore it cannot be chosen. Furthermore you are not wrong until after the chance event.

    The idea that is it circular is just your perspective. There is a single chance event, one and only one. That is not a circle.

    I considered the 0% version before making this thread, it really makes no difference at all as C is nothing but filler to give us four possible outcomes. The only reason to use the 0% version is to end moot arguments about how multiple choice questions work.

    Also odds are not the same thing as chance.
  • Jeremiah
    1.4k
    I think some of you are not getting it.

    There is only one purposed chance event. It does not loop back on itself, it is not a circle and, as long as you don't say C), then you are not wrong until after the chance event, only then can you be wrong.
  • noAxioms
    585
    There is only one purposed chance event. It does not loop back on itself, it is not a circle and, as long as you don't say C), then you are not wrong until after the chance event, only then can you be wrong.Jeremiah
    ????

    You're wrong no matter what you choose. There is thus zero percent chance of choosing correctly, which is what the question asks. That the thing is self-referential doesn't seem to change that. It's not a paradox as written.
  • StreetlightX
    2.7k
    How many letters does the correct answer have?

    two
    three
    four
    five
    noAxioms

    This too is unanswerable.
  • Jeremiah
    1.4k


    OK I'll try this one more time then that is it, as you don't seem to even comprehend what I am saying at all. Disagreeing is one thing, but not comprehending all together is quite another.

    I fully understand what you are saying, that no matter what you pick you'll be wrong, but this is not an essay question where you get to put in your own answers, this is a multiple-choice question and you can only select from the available options and 0% is not in those available options, so it cannot be selected. If you can't understand that simple concept then you are not worth anymore of my time.

    And the only reason you saw this as a circle is the same reason humans tend to think of time as linear, that is how your brain is processing the information, but it is not a circle.
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