Statistics Mindfuck

On Saturday I googled ‘cool mindfuck things to read online’ (I was in a hotel with my 2-year-old and needed something to do between her bedtime and mine, and there was no bar). I found the following:

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%

I read about halfway through the comments and there were a few categories of answers,  all of them poorly explained:

1. 25%
2. 50%
3. 60%
4. 0%
5. 33%
6. 37.5%
7. It’s a paradox.

I think the paradox answer is least wrong, but first let’s discuss why the others are more wrong.

25% would be correct if it wasn’t listed twice, but since it is, you have a 50% chance of picking it randomly. If 50% is correct, however, you only have a 25% chance of choosing it. Thus, neither A, nor B, nor D can be correct.

Some argued that 50% is correct because “you’re either right or wrong.” This logic reflects such a profound misunderstanding of statistics that I wouldn’t even know where to begin explaining how wrong it is.

60% was justified as: the 50% choice is really two 25% choices, giving us 5 total options, 3 of which may be correct. What? No. You have to take the question as it’s given to you.  Otherwise you can just make up whatever answer you want and call it correct.

Zero is incorrect because it’s not a listed choice. Some argued that it’s not really a multiple choice question, but that’s bullshit because there are 4 choices right after the question mark. You can’t ignore the info in the question and then take information from somewhere else and then proclaim that you solved the problem. But even if 0% was added as a choice it becomes an even bigger mindfuck because you would have a 25% chance of picking it.

33 and 37 are out because they aren’t listed as choices (see above).

“It’s a paradox” isn’t a choice either, but I’ll explain why I think it’s the least wrong. First, the definition of a paradox is… ha! Fuck that. I’m not looking that shit up. I think it means a problem that appears to have a solution, but the solution becomes wrong as soon as you find it.

Take Russell’s paradox, as poorly explained by me based on what I remember from reading about it over ten years ago. A set is a group of things, often numbers, that meet the definition of the set. [1, 2, 3…] is the set of all integers; [1, 3, 5, 7, 11…] is the set of all prime numbers, etc. The Russell set is defined as the set of all sets that don’t contain themselves.

Let’s suppose that you were putting the Russell set together. You would be putting all the sets that don’t contain themselves into the Russell set and then you would say ‘hang on,  the Russell set doesn’t contain itself,  it belongs in the Russell set.’ But then the Russell set would contain itself, so you would have to take it out.  But then it wouldn’t contain itself so you’d put it back in. And so on ad infinitum or whatever.

In the present question, you can only pick one answer randomly out of 4 choices, so the odds would be 25%. But 25% is listed twice,  which means there’s a 50% chance of picking it. So you pick 50%, but there’s only a 25% chance of picking that one randomly. So you’re back to 25% being correct. That looks a lot like Russell’s paradox to me. That doesn’t make “it’s  a paradox” a correct answer, but it is a correct statement, which distinguishes it from any numerical answer.

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