Logic Puzzle

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

A) 25%
B) 50%
C) 0%
D) 25%

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35 Comments

  1. B),

    Random simulations will result in 25% of picking each answer.

    25% – A is “correct”
    25 % – B is “wrong”
    25% – C is “wrong”
    25% – D is “correct”

    Therefore, you’re 50% to pick the correct answer, and so B is correct. But if B is correct, then you’re only 25% likely to pick the actual correct answer, and so the answer is a and d. But if A and D are correct, then you’re 50% likely to pick the correct answer, and so B is the correct answer….HEAD EXPLODES.

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  2. The most common way to create a paradox is with a self referential statement like this one. Self referential statements are not “logical statements.” They don’t have either a value of true or false. Same is true about statements about the future. (Self referential statements are usually implicit statements about the future.) “The Broncos will win their first regular season game” is not at this time true or false (unless you believe in predestination). It has a probability of being true. “If you pick the answer at random” is the same idea.

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  3. They should have posed this question to Colossus. Perhaps that would have prevented the machine from being the VOICE OF WORLD CONTROL. Or maybe it would have resulted in this:

    ACTION WILL BE TAKEN.

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  4. If I choose one of four possible answers at random, what is the chance that I will choose one of the four answers at random?

    If I do X, what is the chance that I have done X? 100%, by definition.
    ____________________

    Actually, after spending hours trying to suss this out with long explanations, I think I’ve condensed it pretty well.

    The puzzle is unanswerable.

    If there is a 25% chance of choosing the correct answer, then it can’t be A or D, because there is a 50% chance of selecting either of those two.

    If there is 50% chance of choosing the correct answer, then it can’t be B, because there is a 25% chance of selecting it.

    If there is a 0% chance of choosing the correct answer (even though there is no correct answer), then it can’t be C, because there is a greater than 0% chance of selecting it — 25%

    My head hurts.

    This lie takes the cake.

    Excuse me, one of my hands is clapping.

    A monk asked Obama: “Does a dog have Buddha Nature?”

    Obama barked back: “Yum!”

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  5. Now, after doing a search and looking at different wordings of the puzzle elsewhere, I should qualify that I interpret the question to mean that the answer is supposedly among the four options, and that there is an equal chance of hitting any one of them.

    Here’s one discussion of a similar problem, with “60%” as answer C, and the author seems to interpret it similarly — favoring the conclusion that the answer would be 0%, but that there would be no solution if C were 0% — described in conclusion #3 on this page: http://understandinguncertainty.org/probability-paradox

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  6. This problem is conditional on what the correct answer is. The way I see it the answers themselves are inconsequential and also misleading. Recast the question thus:

    If you choose an answer to this problem at random, what is the chance that you will be correct?
    I am assuming that “the problem” is not actually stated here.

    1) a
    2) b
    3) c
    4) a

    The probability is dependent on the correct answer. If the correct answer is “a” then the probability is 50%. If “b” or “c” the probability is 25%. That is, you can only figure the probability if you know what the correct answer is.

    How’s that?

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  7. If you try arguing the probability of the other answers being right then you are falling into a trap. You are actually figuring the probability of the them being picked.

    Since there can be no correct answer, the only correct answer is C. 0%. And the universe now implodes.

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  8. It could be argued that choosing an answer at random is not an attempt to make a determination at all and can therefore not be correct. Any agreement between an unintentional mark and reality is happenstance or coincidence. You may get credit in a test but so would a monkey– a chinese monkey.
    The answer is c because a random answer doesn’t address the question.
    IF you didn’t even read the question, how can you be correct?

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