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Comment on What's the main device to hammer in a nail?

Triumph@fedia.io ⁨1⁩ ⁨day⁩ ago

All right, let's break this down.

For this question, for these available answers, choosing at random:

First glance says the correct percentage is 25%. There are four answers, you get to pick one.

However, two of the answers are 25%. This means you have a 50% chance of picking an answer that's right.

Which makes the correct answer C: 50%.

But there's only one answer that's "50%", so you have a 25% chance of picking that one.

Which makes the correct answer "25%", so you have a 50% chance of picking that one.

If we consider that "two answer" equation, we can then consider the correct percentage to be "37.5%" -- halfway between 25% and 50%. That makes the correct answer from the available answers to be B: 0%.

And you have a 25% chance of picking that one at random. So we go back to the beginning, where the correct percentage is 25%.

I think we need to get Matt Parker on this one.

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TowardsTheFuture@lemmy.zip ⁨1⁩ ⁨day⁩ ago
There is simply no solution. If you choose an answer as “correct” it is shown to be not correct, (not a 25% chance to choose 25%, not a 50% chance to choose 50%, not a 0% chance to choose 0%) showing there is no correct answer.

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- Triumph@fedia.io ⁨1⁩ ⁨day⁩ ago
  There's always a solution. Even if it's "empty set".
  
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  - TowardsTheFuture@lemmy.zip ⁨1⁩ ⁨day⁩ ago
    Sure same thing.
    
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Artisian@lemmy.world ⁨1⁩ ⁨day⁩ ago
They don’t say that the random answer is chosen uniformly (though that is the norm in the field). If we relax that, then we’re putting a distribution on these where we want:

P(correct with distribution (a,b,c,d)) = some value shown on A,B,C,D

I don’t see any assumption that we will pick using that distribution, so I think this avoids the recursion.

Unfortunately this has too many solutions. If you put a total of 0.25 weight on A and D, then the rest does not matter. If you put 0.5 weight on C, again the rest is irrelevant.

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- Triumph@fedia.io ⁨1⁩ ⁨day⁩ ago
  You've added details that aren't in the question. It's like asking what are the odds of rolling a "one" on a 1d4, and then saying "Well, if it's not a fair 1d4, then ..."
  
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  - Artisian@lemmy.world ⁨1⁩ ⁨day⁩ ago
    … I… I literally talked about this. It’s the first words.
    
    They don’t say that the random answer is chosen uniformly (though that is the norm in the field). If we relax that,…
    
    What more was needed?
    
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    Triumph@fedia.io ⁨1⁩ ⁨day⁩ ago
    
    If we relax that, ...
    
    The question is as posed. We have no indication that we should assume a different distribution of "random".
    
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Soup@lemmy.world ⁨1⁩ ⁨day⁩ ago
There’s also, I think, the weird fucky option were 75% sorta works because the 25% applies to choosing 50% and 50% applies to choosing 25% which means that as long as you don’t choose 0% you’re good?

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