A debate over some simple probabilities

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

Who is right about this simple probability problem?

You are right, sir.
9
24%
You are mistaken. Your friends are absolutely correct.
24
65%
You're both wrong! I'll tell you why!
0
No votes
You're both right. Let me explain...
4
11%
 
Total votes: 37

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Woxor
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Postby Woxor » Mon Jun 04, 2007 2:59 pm UTC

evilbeanfiend wrote:glossing over ignoring previous rolls is all very well but so many people make mistakes about that (e.g. "number 43 has come up every 3 weeks in a row in the lottery, so it must be less likely it will come up now!" except it isn't) so i'm not surprised the op's friends seem to be concerned that this sort of mistake is being made (even though it isn't) hence their instance that the first table was 'a given'.

Yes, exactly. The friends know enough probability to know what the common misconception is, but (according to the OP) they were too stubborn to hear him out on his technicality. They should have agreed and argued that it was irrelevant instead of saying he was wrong, but I'm guessing they weren't mathematicians.

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Gelsamel
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Postby Gelsamel » Mon Jun 04, 2007 3:00 pm UTC

That's fine and all, but while it is 'defensible' you're making up arguments for his friends from nowhere.

Unless I misread, nowhere did the OP say they were claiming his situation was irrelevant, or did they argue theirs was more relevant. What I read at least is just that they thought that he answered question 1 wrong.

Anyway, I think question 1 is way more relevant/meaningful to the situation then 3.
"Give up here?"
- > No
"Do you accept defeat?"
- > No
"Do you think games are silly little things?"
- > No
"Is it all pointless?"
- > No
"Do you admit there is no meaning to this world?"
- > No

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evilbeanfiend
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Postby evilbeanfiend » Mon Jun 04, 2007 3:44 pm UTC

Gelsamel wrote:
Anyway, I think question 1 is way more relevant/meaningful to the situation then 3.


q1 is saying 'what if we didn't know what table we sat at last time ...' where as q3 is all 'dude, but we do know what table we sat at last time'.

id pick 3 for relevance. but i think you can pretty much argue for any position in this.

Woxor wrote:They should have agreed and argued that it was irrelevant instead of saying he was wrong

true my argument does involve having irrelevant = wrong, but meh, close enough.

think im done playing devils advocate on this one now.
in ur beanz makin u eveel

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Woxor
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Postby Woxor » Mon Jun 04, 2007 7:44 pm UTC

Gelsamel wrote:That's fine and all, but while it is 'defensible' you're making up arguments for his friends from nowhere.

Unless I misread, nowhere did the OP say they were claiming his situation was irrelevant, or did they argue theirs was more relevant. What I read at least is just that they thought that he answered question 1 wrong.

If we're going to play that game, it doesn't matter what their arguments were; he asked if they were "right," and based on the question and context that he described, they were. There is an interpretation of the question that is more correct than the others, and that's what I've been arguing.

They then went on to be wrong about a straw man question that the OP created to defend himself. No one's a real winner here.

Gelsamel wrote:Anyway, I think question 1 is way more relevant/meaningful to the situation then 3.

Despite its qualitative nature, the relevance issue here is not one of those things where everyone has an equally valid opinion. There is no mathematical relevance to the 1/2500 chance because every table combination has that chance. The fact that they sat at two given tables is not the most notable feature, and is not what prompted the question. Others and I have given many arguments to this effect; your interpretation is more or less objectively wrong.

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Azquelt
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Postby Azquelt » Mon Jun 04, 2007 9:20 pm UTC

Woxor wrote:Despite its qualitative nature, the relevance issue here is not one of those things where everyone has an equally valid opinion. There is no mathematical relevance to the 1/2500 chance because every table combination has that chance. The fact that they sat at two given tables is not the most notable feature, and is not what prompted the question. Others and I have given many arguments to this effect; your interpretation is more or less objectively wrong.


No it isn't. What prompted the question was sitting next to the bins twice. The state of confusion isn't helped by the fact that that wasn't the question that was originally asked.

Also of note is that this argument assumes that the table was chosen at random both times. This is unlikely to be the case because a) people are bad at picking randomly and b) Unless the restaurant is always full, it's likely that some tables are occupied more often than others (e.g. because they're not next to the bins) and you can only choose an unoccupied table.

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hencethus
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Postby hencethus » Mon Jun 04, 2007 9:29 pm UTC

Just for the record, I wasn't trying to save face by changing the question. I didn't change the question at all, I was just asking a different question than my friends were. I acknowledged that the 1 in 50 solution was the correct answer for the question they were asking, but they could not (or would not) grasp the concept that I was trying to convey.

I'll recreate the situation in dialog using only one friend and a coin flip:

*my friend flips a coin twice, and it lands on heads both times*

Friend: Hey, what are the odds of that?

Me: 1 in 4.

Friend: No, 1 in 2.

Me: Yes, there's a 1 in 2 chance that the coin will land on the same side twice in a row, but only a 1 in 4 chance that it will land on heads twice in a row.

Friend: No, it's always 1 in 2. Go back to school and take a statistics course. Idiot.


(And I realize that this wasn't all made clear initially.* Sorry. But hey, it's sparked some interesting discussion.)

*Edit: Actually, it kind of was (but no worries):
hencethus wrote:One of my friends even used an analogy, saying that by my logic, if he flipped a coin I would have a 1 in 4 chance of guessing correctly on which side it would land.

I tried to explain that while the odds of choosing correctly were 1 in 2, the odds of him flipping heads and me randomly guessing heads specifically was only 1 in 4 (and that the same was true for tails).

Another one of my companions again insisted that I was wrong, and suggested that I go back to school and take a statistics course.

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Woxor
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Postby Woxor » Mon Jun 04, 2007 10:15 pm UTC

Azquelt wrote:No it isn't. What prompted the question was sitting next to the bins twice.

It would take a pretty big stretch to get that even from all the posts the OP has made, let alone the first one. He did say
hencethus wrote:It was right by the trash bins, which I why I remembered that it was the same table in the first place. I hate sitting by the trash.
but only in his fifth post, and just because he remembered the trash doesn't mean that that was the interesting part, particularly as it relates to the wording of the original question asked. He hasn't said that he told his friends anything about the trash at all.

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SpitValve
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Postby SpitValve » Mon Jun 04, 2007 10:25 pm UTC

I say you're both right, you're just not making it clear that you're talking about different things. You'd naturally assume that you're talking about the odds of being in the same place twice, unless there's something special about the place where you were sitting, so I say the fault is yours for not making it clear enough that you were referring to sitting in place x twice in a row, rather than sitting in any place twice in a row.

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Communicating badly and acting smug when you're misunderstood is not cleverness.

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Gelsamel
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Postby Gelsamel » Tue Jun 05, 2007 4:00 am UTC

Yeah, because he's acting smug, and he totally didn't explain himself to them.
"Give up here?"
- > No
"Do you accept defeat?"
- > No
"Do you think games are silly little things?"
- > No
"Is it all pointless?"
- > No
"Do you admit there is no meaning to this world?"
- > No


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