This is not your standard multiple choice question we are dealing with here. Most multiple choice questions do not involve a random sample.

I have understood what you are doing since TheMadFool made his first post, it was incorrect then and it incorrect now.

And if you are so right, then whey do you need an alternative example to prove it? What is wrong with using the question in the OP? I think your examples is you deflecting.

You were not asked what the capital of France is. That is an entirely different question. You changed the question.

I think there have been too many redefined examples already and I don't think they are helping at all. In fact I think that's what is mixing you up, I would suggest you focus on the actual question. Furthermore I already gave you my comments on this example of yours, they have not changed and this post did not convince me otherwise, so I don't see any reason to repeat myself, and I'll refer you to my prior post.

I do this.

I consider the it's-subjective-arguments, in cases like these, nothing but a cop-out and I actually end up losing more respect for a person than someone willing to stand by their argument.

I clearly disagree with that.

Not in this context.

If your "solution" involves reshaping the question or changing the sample space, then you are wrong. And the mods can get mad at me for saying so, and delete another one of my posts, but that's the truth of it. If you have to redefine the parameters in order to be right, then not only are you wrong, but you are deceiving yourself. That is not philosophy, not by a long shot and if that is the standard that passes on these forums, then I have to question if I belong here at all.

When figuring probability repeated values are very important, if you remove them then you will misrepresent the distribution. Repetition is not a valid reason to remove a datum. What you are doing is changing the sample space and it should be a clue to you, that in order for your numbers to come out that you have to change the data.

I think you just can't admit that you were wrong.

The question is not how many are in the list. You people are confusing yoursleves because you all keep changing the parameters of the question with your nonsense examples. It is the dumbest thing I have ever seen.

If we took a random sample from your sample space it would be Paris 75% of the time and London 25%. If I was a betting man I'd bet on Paris.

You are not paying attention to the sample space that the actual random sample is taken from. It is not a 50/50 chance. They would have to be equally distributed for it to be 50. So your chance of being correct if you choose Paris is 75%. As the question in the OP is not how many are in the list, it ask what are your chances of being correct when one is selected at random.

Stop changing the question, stop changing the sample space and learn how to read.

Actually, the thread has been very useful to me. I learned a lot about the people participating in it.

Ya, I don't really care what you think about me.

My argument over this 33% nonsense is already on the table and then some. I am not going to rehash the same crap over and over again. If you want to know how I will response then read my past posts, as I am still very much right.

You really live up to your name.

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

I got your goat, didn't I.

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

You make me glad I am me.

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

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

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

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.

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

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

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

The only way you could have a 33% chance is if each outcome has an equal chance of being selected. Clearly, after 10000 samples, they don't.

Just because you decided there were three choices that does not mean they have the same likelihood of occurring.

It is more than clear that you are "only half paying attention".

This is our question:

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%

This is our sample space: 25, 50, 60, 25

One of those will be choose at random.

OK, following along now? Everyone got that much?

Now using R I took 10,000 random samples of that sample space and put that into a bar graph.

Here is the graph:

https://ibb.co/iaE5rT

Here is the code:

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')


Now I'll do same with some of your examples:

Michael said rock, paper, scissors, let's try that:

The sample space:

A. Rock
B. Paper
C. Scissors
D. Paper

https://ibb.co/ifBtBT

TheMadFool,

Sample space:

2 red balls, 1 blue and 1 black.

https://ibb.co/ceOC5o

Do I need to keep going?

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.

I sure would love to gamble with some of you.

Would the 33% geniuses care to explain how 25% goes from having a greater probability to having an equal probability; from having one to one odds then going to a one to two odds?

Spin it however you want, but the math doesn't lie. 25% has a greater probability and it cannot just magically go to having an equal probability. If you try and shove it into three then you are not accounting for the second 25%, which is what gives it a greater likelihood.

The people saying 33% are demonstrating a fundamental misunderstanding of basic probability.

33% is not a valid answer no matter how you slice it. It completely ingores the distribution. I am sorry but that is just incorrect math, there is no point to aruge on that front because it is just wrong.

The random event is for four slots, which means 25 is weighted more than the others. It cannot have an equal chance as the others no matter how you scale it.

I think it is one of them most helpful post I have ever made.

Maybe you should thinking about it longer than 3 or 4 minutes.

To be honest, I think the 60% version generates more discussion.

The act of choosing 50% or 25% makes one of those answers correct, but they are not correct until you pick one of them. If you pick 50% then 25% is the correct answer, and if you choose 25% then 50% is the correct answer.

There are two correct answers you just can't pick them.

If you wish to equate facts with truth, go for it; however, a scientific fact merely means the thing in question currently meets the standards to be called a fact. It is a classification and they are never final. They change all the time, and sometimes they are also wrong altogether.