This multiple choice probability puzzle has been causing arguments for years

Originally published at: https://boingboing.net/2024/01/25/this-multiple-choice-probability-puzzle-has-been-causing-arguments-for-years.html

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A. 25% – assuming one of the options is the correct answer, and you choose at random.

Edit: wait a minute, just noticed that D is also 25%. So make that C. 50%

Edit 2: Ummmmm… :thinking:

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Yeah… I think you see the issue now.

ETA:

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The answer is always D.

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The answer seemed so obvious at first; but…

5d011e87250000a013dc5766

My brain is no way capable of working this out :older_man:

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Insufficient info to reach a conclusion.

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Unless the question is, “Which one is Ant and which one is Dec”?

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Is it a seven per cent solution?

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I see the riddle as a slightly-altered version of the classic “Is the answer to this question ‘No?’” (provided of course the question may only be answered “yes” or “no”). Change all the answers of the given riddle to 0%, and you’ve reduced it to the above.

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I’m going with C.

I thought I’d worked out why, but I’ll have to get back to you on that.
In a year or so.

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There isn’t even a question. “Correct” isn’t defined. If you try to expand it so that it’s something like, “If you choose an option at random, what are the odds that the percentage chosen matches…”

Matches what? Matches the odds of choosing the percentage of the odds of choosing the percentage of the odds of…

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I think it is a three pipe problem.

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The answer is 0%

Randomly, you pick 25%, but A and D are correct then was a resulting 50% chance so it is incorrect.

Randomly you pick 50%, which is incorrect because it had a 25% chance of being picked.

Randomly you pick 0%, which is correct because your chance of picking it is 25% but it has a 0% chance of being accurate and 0% times 25% equals 0%.

0%

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If you assume that there’s only 1 right answer, and you have a 1 in 4 (25%) chance of randomly choosing the right one out of A, B, C, or D, then A and D are both correct (your chances of being right are 25%), so there’s a 50% chance that you’ll pick one of the 2 correct answers out of the 4. Therefore C is the correct answer.

Alternatively, A and D are both the correct percentage chance of choosing correctly, and if you have to have only 1 right answer, those both can’t be right. B is wrong because there can’t be 0 percent chance of picking the right answer out of 4 choices if 1 of them is correct. That just leaves C, 50%.

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I fuckin’ knew it!

No idea how, because I understood very little of your theory, soz.

ETA: I have read your post several times now and I think I’m beginning to get it.
Still, Booyah, first guess!

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vsTS8X4-592274204

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That illustration is giving me a migraine.

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Can I ask the audience?

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What if there are zero right answers?

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The question doesn’t state that the pool of answers is limited to those 4 choices. Just that a random answer is picked. OK, “potato” is a random answer.

What are the odds of “potato” being correct? Uh… divide by zero error. Maybe?

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