x <- c("25", "50", "60", "25")
x2 <- sample(x, 10000, replace = TRUE, prob = NULL)
library(ggplot2)
x2 <- as.data.frame(x2)
ggplot(x2, aes(x=x2)) + geom_bar(fill="blue") + xlab('Values') + ylab('Count')

...

Where is the equal 33% between the three choices? 10,00 samples and it is not there. If it was an equal 1/3 chance the bars should be even, but they are not. — Jeremiah

I'm suggesting that this is a viable way to select an answer at random:


Which gives:

https://ibb.co/n0joBT

Michael's right that c) should be 0% to really make it a paradox through and through.

But Jeremiah is right that when you are given 4 options to choose AT RANDOM (your selection then can't be based on knowing that A and D are the same) the probability would never be 33%.

That being said, I'm pretty sure none of these misunderstandings mean you need to get snarky, Jeremiah. It's just math and logic.

All you did was created a new vector with three values instead of four.

Newp. The chance of selecting one of the 3 choices is different from the chance of selecting the correct answer choice. Look at my profile image. The compound event is (1/4)(1/3) + (1/4)(1/3) + (1/2)(1/3) = 1/3. Circularity aside, this is an easy problem guys. We don’t need R.

Trust me, I am trying very hard to not be snarky, but I can only repeat myself so many times in polite manners.

That's the point. The question doesn't say that I have to pick one of A, B, C, or D at random. It just says pick "an answer" at random. I might interpret "an answer" to mean "a unique value", of which there are three: 25%, 50%, and 60%.

No, you changed the sample space. There are two 25% not one.

No, you changed the sample space. There are two 25% not one. — Jeremiah

What is the capital city of France?

A. Paris
B. Paris
C. Paris
D. Paris

You say there are 4 answers (A, B, C, and D). I say there is 1 answer (Paris) repeated three times.

There are 4 answer choices, each 25% likely to get picked. There are 3 unique possibilities, each 33% likely to be correct. Whatever the distribution of your sample, the chance of being right is still 33%.

Whatever the distribution of your sample, the chance of being right is still 33%. — Fool

Only if one of the answers actually is correct, but none of them are.

Granted. That’s not at issue, right?

Granted. That’s not at issue, right? — Fool

None of the answers provided in the original question are correct, so the chance of being right is 0%.

Yeah, thought we were all on board with that.

A, B, C, D is not the sample space I used in my code. You remember that?

My sample space was: 25, 50, 60, 25. We'll call this sample space 1.

You remember that? Or do I need to quote myself? It sure the heck was not A, B, C, D.

Now when you used the unique function you changed that sample space to: 25, 50, 60. We'll call this sample space 2.

So when I ran the sample command it sampled from sample space 1.

When you ran the sample command it sampled from sample space 2.

That is what happened, and it is in black and white.

Now the question of interest is: 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%

It has a sample space of: 25, 50, 60, 25. Now wait, that looks a lot like my sample space, sample space 1. While sample space 2, your sample space, is missing a value. Hmm... that can't be, as the random event for the question is for the sample space of the question. How could this possibly happen? Oh I know, you are doing it wrong.

Why don't you run the code correctly this time, with the correct sample space and stop trying to save face. I am sorry, but this is just beyond sad.

However interested these little puzzles maybe, this one is certainly not worth the time you are losing upon it, and above all doesn't justify your attitude here.

You presented this as a conundrum. By definition, conundrum are hard to answer satisfyingly, possibly impossible. You don't get to pretend you have a clearly obvious answer afterward.

If we take the question at its veiled-face value, the odds of guessing correctly actually turns out to be 3/8

We have at least a 1/4th chance of being right, and on top of that we have the scenarios of guessing A and the answer being D (making us correct) and the scenario of guessing D and the answer being A (also making us correct).

The odds of choosing A but the answer turning up D is (1/4*1/4) (in other words, 1/16 possible outcomes fits this win condition) and the same holds true for the scenario of guessing D and the answer being A

So the full odds are (1/4+1/16+1/16) which works out to (3/8) or 37.5%

If you don't believe me run the experiment yourself (it's Processing.js)



Since 37.5% isn't a possible answer, 0% of the time the correct answer will be guessed.

Since the correct answers to questions are normally not determined by random dice rolls which include redundant options (weighting the dice) we would normally calculate 33% as the outcome because we don't ascribe causal value to the existence of redundant options in multiple choice questions. (we also assume one of the answers is correct)

I have the same attitude everywhere, it has nothing to do with "here".

Just ran the experiment in a spreadsheet. The outcome is in my profile image. Before any iterative process of revising the actual correct answer, the abstract solution is 33%.

@VagabondSpectre I hadn't considered how to structure the iterative game. That's an interesting take.

So much for philosophy, I suppose it had a nice go while it lasted.

Do you even have an answer for me?

Blithering about us not getting it isn't helpful. As I've just shown mathematically and proven experimentally (with your interpretation of sampling), the odds of guessing the correct answer to that question are 37.5%. That's the product of your "conundrum". If we assume that the question is self-referential (you seem to maintain that it is not) then it becomes unanswerable because 37.5% (or 33% under a sensical interpretation of what multiple choice questions are) is not an option.

do you have a different solution in mind?

Are you able to explain the understanding that we lack instead of just telling us we're stupid?

If we do the weighted selection (with the redundant option being rolled for in the answer algorithm, not the guess algo), then 37.5 percent is indeed the result.

Imagine selecting option D on a test but your teacher/professor arguing that A was the correct choice; since they're the same they would have no choice but to mark it correct. If you made the 1/4 guess you would be right 37.5 percent of the time.

I have explaind it well enough, and if you cannot grasps it by now then that is your problem not mine.

It's evident you have not explained it well at all. By continuously saying this instead of responding properly you make it amply clear.

It's not us, it's your inability to explain.

You make me glad I am me.

You make me glad I am not you. To each their own.

Good luck with your conundrum.

Ya, I don't think you could handle being me either.

What are the odds you describe yourself correctly in the following question:

A: wise
B: foolish
C: foolish
D: foolish
E: foolish
F: foolish
G: foolish
H: foolish
I: foolish

I got your goat, didn't I.

You're refusing to participate and engage in the topic of your own creation and you've been lazy and insulting towards good-faith replies.

If by "got my goat" you mean to say you've frightened it and every other goat away with your jackassery, then yes.

If you are trying to shame me, it won't work.