@Jeremiah

Your answer to this question will go far toward clearing things up.

I’m thinking of a number. It’s either 1, 2 or 3. If you randomly choose a number from the list below, what are the odds that it’ll be the one I have in mind?

1, 2, 3, 1


If your answer is not 33%, I must question your mathematical literacy. If it is 33%, then we’re not arguing about the same thing.

You really live up to your name.

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.

@Jeremiah

There he is. Good timing, was just checking one last time. I am a fool, but I know intelligence when I see it. I will keep my thoughts about you to myself. Good day, sir.

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

This thread :

Person A ask : "Conundrum : What can swallow a man, and be swallowed by him"?
Person B answers : euh, I don't know, a piranah?
Person A replies : You fool, the only answer is "pride".
Person B object : yeah, I mean, classically perhaps, but you asked me a question, and I gave you an answer that fitted the parameters.
Person A : What are you, defective?
repeat

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

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 — Jeremiah

How many cities are in this list?

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

4 or 2? I say 2. So if I'm asked to pick a city at random from that list, I think it reasonable to flip a coin and select Paris if it's heads or London if it's tails. The question is ambiguous as to the sample space.

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.

I'm not changing the sample space. I'm saying that there is room to disagree over what is the sample space. You say that the sample space is the rows in the list (of which there are 4); I say that the sample space is the cities (of which there are 2).

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

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. — Jeremiah

One what? One answer? But what counts as an answer? If I were to ask you for the capital city of France, and then list A) Paris, B) Paris, C) Paris, and D) London, you might say that there are 4 answers (A, B, C, or D) but I'm saying that there are only 2 answers (Paris or London).

Repetitions aren't different answers. They're all one answer. Paris repeated 99 times is still just one answer, not 100 answers.

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.

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.

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. — Jeremiah

Oi oi, look in the 'math and motives' thread and see what you think.

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. — Jeremiah

It is in some contexts.

You don't always need repeated values corresponding to a single parameter to get a sensible estimate for that parameter; look at Gelman's analysis of the radon data...

Not in this context.

Not in this context. — Jeremiah

That's up to interpretation.

I clearly disagree with that.

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.

What if one stands by the subjectivity? The argument being subjective is not subjective.

I do this.

What you are doing is changing the sample space — Jeremiah

No, I'm disagreeing over what is the sample space.

There are two cities in this list, not four:

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

If I'm asked what the capital city of France is, and given the list above as choices, I only have two possible answers (Paris or London), not four. A, B, and C are the same answer. So if I'm asked to pick an answer at random, and if there are only two answers (which there are: Paris or London) then I have a 50% chance of picking Paris.

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.

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

The principle behind there being 2 answers, not 4, is the same. In your question there are 3 answers, not 4. So if I'm asked to pick an answer at random my sample space has 3 elements, not 4. The actual question is irrelevant, so your responses are just deflections.

If in a real life multiple choice quiz there are duplicates - e.g A) Paris, B) Paris, C) Paris, and D) London - and I don't know the answer then I will pick an answer at random, and the rational thing to do at this point is to flip a coin to choose between either Paris or London. It certainly wouldn't be rational to give more weight to Paris just because it appears more times. That's ridiculous. So if I'm to pick an answer from your question at random I'm not going to give more weight to 25% just because it appears twice.

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.

And if you are so right, then whey do you need an alternative example to prove it? — Jeremiah

Because you don't seem to understand it with your question, so I'm providing an alternative that should make the reasoning clearer. There are only two answers to the question, even though Paris appears three times, so an answer picked at random has a 50% chance of being Paris. There are only three answers to your question, even though 25% appears twice, so an answer picked at random has a 33.33% chance of being 25%.

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