Thread 23317920

Did we ever settle on what's the right answer to this question, /pol/?

>>23317920 (OP)
It's 1/3 silver.
You're equally likely to have pulled any of the three gold balls.
And of those three cases, only one was in the box shared with a silver ball.

>>23317921
That's one way to look at it. I originally thought it was 1/2 but after thinking about it for a while I think it's 1/3, the way I look at it is:

You originally had 3 gold balls and 3 silver balls, and you were equally likely to draw any of these 6 balls. What you know given the draw of a gold ball, and given that you have to draw the next ball from the same box, is that you drew your ball from a total of 4 balls, out of which 3 were gold and 1 silver, and that your next draw is going to be from a total of 3 balls out of which 2 are gold and 1 is silver.

>>23317920 (OP)
50/50
if the box had 1 gold, then it eliminates the double silver box as a possibility.

>>23317920 (OP)
There are two types of people who believe it's 1/2:
>People who just heard the problem for the first time
>People who learned the correct answer and refuse to give up their original answer
The latter inevitably ends up at the argument that you're supposed to disregard the random choice of box when it says "it's a gold ball".
However, this ignores the fact that you cannot recreate this answer in experiments. The only way to recreate it is to randomly pick a box with gold balls in it and then randomly pick one of the gold balls from that box, despite the fact the problem says you can't see into the boxes.
i.e., you have to ignore the rest of the problem actually says for such an ambiguous statement as "it's a gold ball". You are working backwards from your original answer and not actually reading what the problem actually says.
It also ignores the fact that this is not how statistics problems are laid out. You're not told that one choice is random and then asked to disregard that random choice later by an ambiguous statement. That just wouldn't be a practical way to pose problems.

the gold ball you picked is either from box 1, box 1, or box 2
chances for the other coin to be silver is 0% for box 1, 0% for box 1, 100% for box 2
therefore chance is 1/3

>>23317920 (OP).

3/5? Since you removed a single gold ball.

>>23317923
That's what I thought at first. I thought it was a semantic problem and not a mathematics problem. However after thinking about it I think it's 1/3.

I think the fault in the thinking that you have and that I had initially, is that we think in terms of you drew from either of the first two boxes in the picture, and the next draw will be from either of these two boxes again. But this is not the case. We don't have two boxes. We only have ONE box, the box you drew from the first time, and while we know that it's either box 1 or 2 in the pic, we don't know WHICH of those it is.

I was thinking that because I'm holding a gold ball in my hand, therefore I know that my next draw cannot be from the box which has two silver balls, but rather is going to be from either of the other two boxes.

My thinking is that the fault is in thinking in terms of having two boxes, and thinking you're going to be drawing from either the first or the second of these two. You don't have two boxes. You only have the one box you picked up. Therefore you can't think in terms of two boxes at all, you have to think only in terms of the balls that are in the two boxes which you know your box is one of. So you originally had 3 gold balls and 3 silver balls, and you were equally likely to draw any of these 6 balls. But what you know given the draw of a gold ball, and given that you have to draw the next ball from the same box, is that you drew your ball from a total of 4 balls, out of which 3 were gold and 1 silver, and that your next draw is going to be from a total of 3 balls out of which 2 are gold and 1 is silver.

>>23317920 (OP)
They added more balls.

If you ignore all irrelevant information, the question is simple.

>>23317925
It's interesting to see diverse paths of thinking arriving at the same conclusion.

>>23317930
His reasoning is wrong, though.

>>23317929
It's not irrelevant, the frequency of gold balls in one box influences the probability that we chose that box.
If you believe the question itself wants us to disregard our random box choice, see: >>23317924

It's twice as likely that you're in the box with two gold, so 1/3 chance you'll pull a silver.

>>23317931
explain

>>23317934
Your answer would change if the first box had 3 gold balls.

>>23317920 (OP)
I would've guessed 1/2. But reading the explanation, it makes sense you are more likely to get the gold ball. Because if you picked the second box chances are 50 percent you would've picked the silver ball, and you would've never continued. Meanwhile if you choose the first box there is 100 percent chance you continue. So right off the bat, you are more likely to have the first box and not the second one, they are not equally likely.

>>23317920 (OP)
the only way to phrase this, so ppl stop being stupid.

>>23317921
fpbp

>>23317920 (OP)
If you're a adherent of the Talmud, 1/3. If you're not a hook nose, it's 50/50. Jewish math dictates that when flipping 3 coins (with clipped edges) previous events count towards future outcomes. Humans know that previous events can identify a trend, but only have limited bearing on future outcomes; flipping a coin is always 50/50 no matter how many you flip. You also aren't picking a ball, you picked a box. You picked a box and then grabbed a gold ball. There's 2 boxes with gold balls, you're in one of them.

>>23317924
>>23317932
There is no probability for something that can never happen. You NEVER choose the box with only the silver balls.
You stupid leafs can't read.

>>23317924
I'm not following. I think I saw your posts in the previous threads. I agreed with you then that there was ambiguity and that it was a semantic issue. However I thought then that the answer was 1/2. I now think the answer is 1/3 and that there is no ambiguity and that it's not a semantic issue. You think it's 1/3 and you think there is ambiguity and that it's a semantic issue. What do you think is ambiguous? See my thoughts after changing my mind here: >>23317927

>>23317920 (OP)
25.5

>>23317937
E and F are not part of the question.

>>23317928
>>23317935
the gold ball you picked is either from box 1, box 1, box 1, box 1, box 2, or box 2
box 1 has 0/3 remaining silver
box 2 has 2/3 remaining silver
0,0,0,0,2/3,2/3
therefore chances are 4/18, or 2/9

>>23317921
agree with your reasoning

>>23317943
the question literally asks "'will be marked D, E or F?' which for E and F would be 0%, so add that to the total possible outcomes to get the final answer.

>>23317940
I never mentioned the box with only silver balls nor is it relevant to any of my explanations.

>>23317928
2/9

>>23317920 (OP)
The problem with this here is the image, doesn’t serve the problem justice. Just look up Bertrand’s Box paradox and learn. 1/3 boxes each with varying probability equates to 2/3. The paradox is that it also equates to 1/2 depending on the reasoning used. Both answers are correct because it is a paradox you ding dongs

>>23317923
It eliminates picking the gold/silver box and then picking silver first in the same way and for the same reason as it eliminates the double silver.

It is twice as likely that you pulled a gold first by picking the box with two golds in it. The gold/silver box is less likely as an explanation for the ball in your hand. Ergo, 2/3 & 1/3 split.

>>23317929
Nice pic
That's just how it is, I refuse to give in to stupid math concepts that rely on useless information

If you were to conduct this experiment in reality it would be 50% after the initial gold ball was drawn

>>23317920 (OP)
2/3 boxes have matching balls. 1/3 boxes have dissimilar balls. If the question asks if my balls will match then the answer has to be 2/3. When the question asks if my balls don't match then it has to be 1/3.

In this case the answer is 1/3 since they want dissimilar balls.

>>23317939
See
>>23317932

>>23317943
There is 0 probability that the balls could ever be E or F. You might as well be asking if balls G and H could be chosen as well. You have to pay attention to where the actual question is. (The sentence with the question mark.)

>>23317944
2/9 is the correct answer, but your reasoning is slightly flawed. The amount of gold balls in box 1 doesn't matter beyond the point that there are more than 2, and there are also no silver balls in the box with them. What we care about is the likelihood of pulling a gold ball, which is 100%. Reducing the amount of gold balls in box one to 2, or increasing it to be arbitrarily high would not change the answer.

>>23317949
>both answers are correct
Impossibru, just perform the experiment many times and see what proportion of the time you get the desired outcome. It CANNOT be that they are "both correct". There will be only one frequency.

t. frequentist who hates rationalist scum

>>23317954
Questions can have premises. You don't ignore everything that came before because of sentence structure. That would require that many problems were posed as run-on sentences.

>>23317947
>the frequency of gold balls in one box influences the probability that we chose that box
No, it doesn't. We can't see inside the boxes so it has no effect.
We choose one of the first two boxes. We remove a gold ball. At this point, only a gold or a silver ball remains.
You're making this more difficult than it is.

>>23317928
out of 12 possible balls, you grabbed 1 of the 6 out of 12. labeling the 1st 6 balls with A,B,C,D,E, and F respectively, let put every possible combination possible.
A means you can grab B, C, or D
B means you can grab A, C, or D
C means ABD
D means ABC
E means FGH
F means EGH

so 6 possible initial gold ball draws, and out of those 6, only 2 possible draws lead to the other possibilities including a silver ball marked with either G or H.

so including all possible outcomes, the max is out of 18, and 6 were the desired outcome.
6/18

reduced/simplified to 1/3

>>23317924
its 50% 50% no matter how much you try to jew this

>>23317920 (OP)
>polniggers try to discover probability theory

There are literal niggers who outsmart you guys

>>23317957
>You don't ignore everything that came before because of sentence structure
This problem starts with a sequence of events that happen every single fucking time. That means no probability.
The only question and probability happens once you're left with 1 box with a gold ball, and one box with a silver ball.
You're inventing a problem that doesn't exist because you have poor reading comprehension.

>>23317920 (OP)
>lust provoking image
>time wasting question

>>23317958
>No, it doesn't.
Yes, it does. It makes the double-gold box more likely as an explanation as to how a gold ball got into our hand first.

>>23317923
The silver silver box is a red herring regardless. It's just to fuck with you.

>>23317956
>doesnt know what a paradox is
The data shows 2/3 is the answer. But now it isn’t a paradox. The answer to OP is either/or because it is worded in a way up for interpretation.

>>23317955
>The amount of gold balls in box 1 doesn't matter
There are 3 boxes. Each box contains 2 balls. One box contains 6 million gold balls, another box contains 2 silver balls, and the final box contains one gold ball and one silver ball.
You pick box at random. You put your hand in and take a ball from that box at random. It's a gold ball. What is the probability that the next ball you take from the same box will be silver?

>>23317958
Yes it does influence the probability, not because we didn't choose the ball/box randomly but because we have limited information. We know it is a gold ball, so we know it's one of the two boxes, but we don't know which one.
If one of the boxes had 1000 silver balls in it and one gold ball, and the other box had 1001 gold balls in it, would you still be just as confident that the gold ball came from the box with silver balls in it? If not, how many silver balls have to be in the box for the chance to be 50/50?

>>23317954
idk why you quoted yourself.
anyways, youre assuming that you only ever drew A and never drew B as your initial ball.
why is that?
if you draw A, then the other is B
if you drew B the other is A
if you drew C, the other is D

out of the 3 possibilities, only 1 lead to drawing either a silver D, silver E, or silver F.

>>23317966
>the data
no it doesnt

>>23317951
This is testable you know.

>>23317920 (OP)
50%. your only options on your draw are 1 gold or 1 silver. you cannot draw the first gold of the gold/silver box or the gold/gold box as you have already drawn those when you picked the box. autism test btw

>>23317964
>Yes, it does. It makes the double-gold box more likely as an explanation as to how a gold ball got into our hand first.
It says you pick a gold ball every single time. There is no "more likely" here. There is no probability at this point.
Your brain is inventing stuff that doesn't exist.

>>23317929
The initial gold ball had a 2/3 chance of coming from the box with both golds. This is like saying your chance of winning the lottery is 50/50 because there are only two outcomes (win or lose).

>>23317967
1/3, same as the original question.
The first step in the problem is choosing one of the 3 boxes at random. Please spend a moment to convince yourself that the amount of balls in a box does not increase its likelihood of being picked.

>>23317962
>a sequence of events that happen every single fucking time
Yes, the sequence of events happens every time, no interpretation of the events disputes that. The question is how we got to that state.
The 1/3 chance is if the ball was chosen randomly and poses the question at a point with limited information. The 50/50 chance interpretation can only work if the ball was chosen by "fate", that is you were guaranteed to draw a ball in the "gold" category.
The "fated" answer asks that we ignore the premise and convention at an arbitrary point because of ambiguous wording.

>>23317973
>Given that A, what is the probability of B
It's called conditional probability and it's an entire field of study on its own

>>23317951
And if I were to run the 100m dash with a 120mph wind at my back, I'd be faster than Usain Bolt. We don't use "reality" to determine the truth.

>>23317969
>anyways, youre assuming that you only ever drew A and never drew B as your initial ball.
No I'm not. The question says a gold ball. It could be A, B, or C.
>if you draw A, then the other is B
>if you drew B the other is A
>if you drew C, the other is D
Literally no part of this has to do with the probability question. I don't think you understand this.

>>23317973
>It says you pick a gold ball every single time.
No it doesn't. It says we picked a gold ball, once, after a series of two random choices.

It doesn't say we have a magic hand that was guaranteed to draw a gold if any were in the box. We got lucky. If we picked the gold/silver box, we had to have been luckier. It is a less probable explanation.

>>23317973
if the question said u picked a box at random, and it wasnt the box with 2 silver, then it would be almost reasonable to say the question is asking if u picked between 2 choices.
but it then adds a second choice of picking a ball inside at random.
(the same as picking a prize behind a door, when u cant see, its random)
its fundamentally saying you picked one of the 3 gold balls at random, but phrased in a manner to misdirect you into focusing on the idea of picking between 2 boxes, and not on the picking between 3 balls.

>>23317971
Can't find anyone doing a test

>>23317978
No you'd just fall down from the wind fatty, that's the reality

>>23317977
This question poses ONE condition and the probability for this one condition is 1/2.

>>23317920 (OP)
Okay
I get it - the answer is 66.6% we draw Gold next
Because the first drawn ball had a HIGHER chance of coming from the GG box in the first place

>>23317979
you say i "dont understand", but when you "pick" 1 ball out of 4, and remove it from the possibilities, the possible outcomes are 3.
so the PROBABILITY is 1 out of 3, since only ONE is silver, out of the possible remaining options.

>>23317980
If you pick a gold ball every time, the initial choice of boxes was not random.
You want to factor in the probability of something that the question says never happens. You can't have it both ways.

>>23317941
The ambiguity comes from the statement "It's a gold ball". People who refuse to let go of the 1/2 answer and try to find an explanation that matches this interpretation inevitably end on an interpretation that reads this line as:
>It's a gold ball - it was always going to be a ball that was gold, not any one specific gold ball, despite any choices that were stated to be random before.
It really comes down to the word "it's" or "is" when you boil the semantic disagreement down to its core. It either IS a gold ball because you happened to draw it or it IS a gold ball because it was always going to be a gold ball.

>>23317985
NO YOU'RE ALWAYS PICKING THE SECOND BALL FROM THE **SAME BOX** YOU FUCKING RETARD

>>23317920 (OP)
You now have a 50/50 chance of plucking another yellow ball.
The fact that you produced a yellow ball means you took it from box A or B. The fact that it came from either box is of equal probability. You guys are really over thinking this.

>>23317984
To add to this
If we changed the question and allowed ourselves the option to pick one of the other boxes (or stay on the same one)
You would have a higher chance getting gold by sticking with the same box - because you more than likely chose double gold
By switching you have a 33.3% chance of getting gold

>>23317941
>>23317987
Also I'm still reading through your explanation, I don't want to misrepresent the 1/2 side, I just haven't encountered anyone yet who doesn't fall int either of the two camps for 1/2 that I initially described.

gacha question for statistic 101, reminder the faggots acting like this knowledge was worth the 15k debt they accrued and cant pay off

>>23317988
ok, i have a 6 sided with only 1-3 twice.
ill roll for A B or C.
ill do this 100 times, what do you think the percentage chances of it landing on C, for the possibility of a silver (D)?
you seem to fail to understand this.

get some die, and do the actual experiment yourself, you'll quickly see the answer. did the same shit with monty hall problem.

>>23317986
The question doesn't assume that we pull a gold every time. It assumes we are in a scenario where one box was chosen at random and then we randomly pulled a gold ball out of it.

>>23317989
the question states you also make another random choice after picking a box.
which defines 3 possibilities.

which means the final outcome is X out of 3.

>>23317992
Autists get this right on intuition.

>>23317986
>If you pick a gold ball every time, the initial choice of boxes was not random.
We don't pick a gold ball "every time". That isn't written or implied in the question.

One specific thing happened in the past to get us where we are, we don't know which explanation it is, and the question is explicit that our past choices were made Randomly - that every option we had in front of us was equally as likely as any other. We were not guaranteed to have a gold ball in our hand first on any given hypothetical attempt. We just have one now.

Think about how you would have felt if you didn't eat breakfast this morning and then try the problem again.

>>23317920 (OP)
Its 1/2.
You are stuck with either the 2 gold box, or 1 gold 1 silver box.
If you picked the 2 gold box its certain that your next pull will also be gold.
If you picked the 1gold1silver box, your next pull will be silver.
No need to mentally confuse yourself with statistics, practical wisdom is superior here.

>>23317998
youre skipping a step.

>step1: pick a box
we know its either the 1st box of gold-A + gold-B, or the 2nd box, with gold-C, or silver-D
>step 2: pick a ball within
we know its either A, B, or C (not D)
out of A, B, or C, which leads to D being the paired ball?
2 of the 3 dont, and 1 of the 3 does.

>>23317929
This is how I thought initially, but read >>23317927

>>23317920 (OP)
SLIDE THREAD FOR FUCKS SAKE STOP TAKING THE BAIT

>>23317999
No there is no A or B
The gold balls have no identification

>>23317920 (OP)
50/50 obviously retard. What kinda dumbass question is this?

>>23317998
You are ignoring the fact that one gold ball was already chosen.

>>23317920 (OP)
THEY GOT MY BALLS, MONTY. THEY TOOK MY BALLS.

>>23318002
I understand they dont, I gave them identification, because the question specifically states you pick AGAIN, within the possibility of 2 gold balls. which means each is a distinct ball from eachother, despite also sharing a color.
so i personally labeled them A and B, for the purpose of explaining the situation.

just because they are gold, doesnt mean they are the same ball, just as the 2 silver balls in the 3rd box are silver, doesnt mean they are the same ball thats in the middle box.

>>23318004
No I'm not.
Since we already picked one gold ball from the box we chose, and we have to pick another ball from the same box, we know we are either dealing with the 2 gold box, or 1 gold 1 silver box.
That's why I said stop bothering with statistical calculations. Its mental masturbation to trick you.

>>23317958
No, there's either 2 gold or one of each. You put the ball back in before grabbing again.

>>23317920 (OP)
I would think it's 1/3 but then taking the previous event into account sorta feels like gambler's fallacy with the way it's worded.

>>23318008
Where does the problem state this?

>>23318004
actually 2 gold balls were chosen the second you found out the first ball was gold leaving you with either a gold or silver

>>23317998
This the same way I was thinking initially. But it's faulty thinking. It's thinking in terms of drawing the second ball from either of two boxes. But you have only one box, not two. Read >>23317927

>>23318007
>stop bothering with statistical calculations
lol
the state of brainlets

>>23318003
The people not saying 50/50 fall into three categories
>talmud enthusiasts that read WAY too much into the problem things that weren’t actually said
>ESLs and other 45IQ vantablack gorillaniggers that don’t know how to read a problem and understand hypotheticals
>ragebait trolls who know it gets a fuckton of guaranteed replies (OP is one of them)

>>23318012
Your text wall is too long, but I'm assuming ur answer is 1/3?
That's incorrect according to the actual paradox, where the answer is 2/3: https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
Anyhow, its bullshit.
>>23318013
Keep clutching your pencils, nerd. I will pick a ball and it will either be gold or silver.

>>23317920 (OP)
>>23317921

faggoty groupier spins the wheel without you looking, you're told the number that came up was between 1-18, but not which one.

what do you think is more likely, "box 1" or "box 2"?

>>23318015
Wikipedia says chance of drawing GOLD, OP says SILVER, they're not the same problem.

Also, if that text is too long you're a coombrain and don't want to learn.

>>23317920 (OP)
But what are the chances Belle Delphine will suck my cock? Are they any greater if I produce 2 yellow balls?

>>23318015
The classic version of the problem asks the likelihood of pulling a second gold ball.

>>23318029
Women dislike asian boys.

>>23318014
It's a variation of a well known probability problem. Don't act like the 2/3 interpretation is some obscure interpretation for attention. Your only tenable position is that they have a misreading of the problem.

>>23318032
KEK yes. I was thinking that too. Lucky I'm not asian then.

>>23318034
>Everything before doesn't matter
I have 3 questions for you that no one with this interpretation ever seems to answer:
1) What part of the problem's wording led you to that conclusion?
2) It never explicitly states that, so why are you so certain?
3) What wording would you use to pose this problem in a way that doesn't disregard your earlier random choices?

>>23318034
tard

>>23317994
>The question doesn't assume that we pull a gold every time.
It literally does. If you don't pull out a gold ball, then there is no question to ask.

>>23318043
>1) What part of the problem's wording led you to that conclusion?
It only asks you what is the probability that the next ball you take from that same box is silver
It doesn't ask for anything else other than that
>2) It never explicitly states that, so why are you so certain?
Same as first answer essentially, it explicitly states about a very specific thing
>3) What wording would you use to pose this problem in a way that doesn't disregard your earlier random choices?
Something like
'You picked the silver balls !
What was the probability of it happening?'

>>23318064
>It only asks you what is the probability that the next ball you take from that same box is silver
>It doesn't ask for anything else other than that
See
>>23317957

>>23318076
It's not my fault that the question pinpoints a specific scenario, the question maker should chose their words better if they want to include a certain premise

In the original image the entire premise established before, was thrown out the window when it said : "It's a gold ball. What is the probability that the next ball you take from the same box will be silver."
It creates just a new premise and thats what I focus on as that is the main question

>>23317997
>We don't pick a gold ball "every time". That isn't written or implied in the question.
Yes there is, otherwise the condition for the question doesn't exist. Pay attention to where the question actually is.
>that every option we had in front of us was equally as likely as any other
It WAS, but now we're down a path where the third box doesn't exist.
>We were not guaranteed to have a gold ball in our hand first on any given hypothetical attempt. We just have one now.
Correct, but we find ourselves in one scenario, and only then does the probability question present itself.
You want to ignore the initial 1/3 box probability but include the "was a gold or silver ball grabbed first" probability, so you're not even following your own logic. The question is worded like shit. It's either 1/2, or the probability of the entire branch of outcomes.

>>23318016
Best explanation I've seen.

>>23317997
>We don't pick a gold ball "every time". That isn't written or implied in the question.
Yes you do. The s/s box is pointless to the problem. Has nothing to do with the odds as the problem is written.
The answer is 1/3 that you will draw a silver ball next.
If you can understand why, check this:>>23318016

>>23318096
>It creates just a new premise
It never says explicitly that it is a new premise, you're just pulling this from subtle wording choices so I don't know how you can be so certain. There is no convention in any kind of problem where you would disregard the previously outlined premise. That's not a good way to pose problems and it's a strange thing to assume, unless if you're expecting a trick question.
The way to read if you don't assume that this is a new premise is:
>It's a gold ball (because it happened to be gold, it was randomly selected using the process we just described). What is the probability that the next ball you take from the same box will be silver.
Can you at least admit that this is one possible interpretation and the question is at the very least ambiguous?

>>23318104
>It WAS, but now we're down a path where the third box doesn't exist.
And also down a path where half of the second box, the "pick the half/half box and draw Silver first" - as laid out in >>23318016 - is similarly excluded.

This logic does not exclude the "initial 1/3" arbitrarily. It excludes the parts of it that can be ruled out - 1.5 boxes of it - logically and systematically. The information given is that you have a gold ball in your hand and that it got there via a series of 2 random choices. There are three possible explanations (Box A, draw ball 1 - Box A, draw ball 2 - Box B, draw ball 1) for this event, and two of them happen in the first box.


>>23318122
Nigga what the fuck you're replying to an explanation that is trying to lay out the same point as >>23318016

>>23318130
Sure I can admit it
It's clearly a tricky question, I just focus more on a practical viewpoint rather than an objective total probability viewpoint

From my practical viewpoint you are already holding the gold ball and you're about to dip in your hand into the same box again
What is the chance its gonna be silver? 50%

>>23318122
You're accepting one premise but ignoring the other. Either you have to include the box choice and the ball choice, or you have to ignore all of that and accept the entire scenario of only one ball being left. (And that ball probability is 1/2.)

>>23318256
>From my practical viewpoint you are already holding the gold ball and you're about to dip in your hand into the same box again
>What is the chance its gonna be silver? 50%
1/3. If you were literally, physically doing this in real life, 2/3 of the scenarios in which you're holding gold first happen in the first box.

The wording of the question is not ambiguous. It uses very specific language to describe the hypothetical exactly as it would play out in physical reality.

>>23318256
If you look at it from a practical viewpoint... still 1/3.
I'm not going around wondering if people are dropping new premises on me in the middle of a story.
There is also no way to recreate this as an experiment or simulation as described without coming to the 1/3 answer.
That to me is not practical. It goes against common sense and reality.
Here's common sense - one box has two gold balls. The other box has two gold balls. THAT'S 5050. This question is clearly not the same.
More common sense, why would you even pose the problem this way if most of it is irrelevant?

>>23318144
I understand, but the probability question should be at the beginning, not asking when there are only two possible outcomes. It should ask "what is the probability of pulling out a gold ball and then a silver ball from the same box?"

>>23318390
>I understand, but the probability question should be at the beginning, not asking when there are only two possible outcomes.
There is not a difference. There are not, "only two possible outcomes." You are holding one of three balls, and in two of those cases the other ball is gold too.

>>23318384
>why would you even pose the problem this way if most of it is irrelevant?
To confuse
>This question is clearly not the same.
Different questions can have the same outcome

>If you look at it from a practical viewpoint... still 1/3.
I don't buy it, I would want to see the experiment performed the same way its described
Here's my thought process which only leaves a 1/2 solution
>>23318034

>>23318399
>You are holding one of three balls, and in two of those cases the other ball is gold too.
One of those cases.
You're assuming we're not holding a ball from the third box while also assuming that we're holding a gold ball. Either you factor in all of the possibilities or follow this strict path. Either way, the answer can't be 1/3, it's either 1/2 or every possible path down the probability branch.

>>23318402
>>23318034
If you performed the experiment in real life, making each choice randomly, it would boil down to the fact that there are six "paths" through the process.

There are three paths through that involve drawing a gold ball first. At the end of two of these paths is another gold ball, while at the end of only one of them is a silver ball.

If both choices are Random as the question states, then all six paths are equally likely, and all three gold-first paths equally likely to each other. That is why it's thirds.

>>23318399
I don't like the explanation that there's 3 balls because it's right for the wrong reasons. There can be 6 gorillion balls in the first box and it doesn't matter, it's still 2/3.
What matters is the concentration of balls. One box has 100% gold balls, the other has 50%. 100% is double 50% so there's a 2/3 chance that you drew the gold from that box.

people who post in this thread should be called ball fondlers

>>23318411
>You're assuming we're not holding a ball from the third box while also assuming that we're holding a gold ball. Either you factor in all of the possibilities or follow this strict path.
The fact that a ball is not held from the third box is not assumed. It is deduced, based on the fact that the ball held is gold.

>>23318402
>I don't buy it, I would want to see the experiment performed the same way its described
Here it is in a simulation, prints close to 33% every time. Let me know if you disagree with any part.
https://pastebin.com/ZSrZJc2D

>>23318430
I disagree with it because it doesn't take into account that you're already holding the gold ball

It should be

Boxes = [silver,gold][gold,empty] or [silver,empty][gold,gold]

>>23318422
Factual, but the meta-puzzle I'm trying to solve every time I see this thread is to come up with an explanation that will make it actually stick on someone, so really leaning into the concrete reality of the puzzle as-written feels more prudent than spinning up new hypotheticals.

If a person can grasp it for the "wrong" reason the path to the right one might be easier.

>>23318429
Then we can also deduce that the next ball is either gold or silver.

>>23318566
Yes. And additionally, based solely on the information provided, deduce that it is twice as likely that we got a gold-first choice by picking the all-gold box than it is that we got it by picking the gold/silver box.

>>23318575
>it is twice as likely that we got a gold-first choice by picking the all-gold box than it is that we got it by picking the gold/silver box.
It is, but the question isn't asking that. It only cares about the sequence of gold ball -> silver ball.

>>23318586
>It is, but the question isn't asking that.
Yes it is. The color of the next ball drawn depends on the box chosen. The box where the next ball will be gold is twice as likely an explanation for the ball in our hand than the box where the next ball is silver. Ergo, a 2/3 gold and 1/3 silver probability.

>>23318449
Functionally the same, I didn't want to do it because it's a bit more verbose, but here it is:
https://pastebin.com/EGpiQZDU

we need more of the troll science/math threads. I miss them.

do the two-coin flip one next. reminder: it doesn't matter what order you flip the coins.

>>23318422
No. You're not drawing from either of two boxes. You're drawing from one box.

>>23318621
And you don't know which box it is. "What is the probability that the next ball will be X" and "What is the probability that this box I have picked is box X" are functionally the same question.

>>23318621
Yes, and you don't know which box it is. The concentration of balls in the boxes is therefore relevant.
If there was 100% gold balls in both boxes it would be 50/50 that it was either box.
If there was 99.9999% silver balls in one box and 100% gold balls in the other, it would be incredibly likely that you selected the box with 100% gold balls.
And in the case in OP, it's 1/3 that you selected the box with one silver ball.

>>23318598
Why does the problem present a third box if it's never supposed to be considered in the probability? Why are you including the probability of pulling out a gold ball (out of four) when it tells you that you pulled out a gold ball?
Do you see how you're not being consistent?
Shouldn't it be 2/3 * 1/4 ?

>>23318450
When someone is deeply invested in the 50/50 answer - really deep - they're protecting their large ego and getting them to change their mind in the same thread is unlikely. The best you can do is illustrate how it's not rooted in reality or common sense, but unlikely semantics.
It will never stick with someone unless if they're new to the problem and just misunderstood it, the best you can do is hope that observers don't go down the same rabbit hole.

A: Bye.

>>23318673
>Why does the problem present a third box if it's never supposed to be considered in the probability?
Who said it wasn't supposed to be considered? It is considered, just excluded by the fact that we randomly drew a gold ball.
It ends up being irrelevant but if this was a question, for example, on an test on probability, it would be a possibility that would have to be eliminated, not adding much of an obstacle to the question but still helps establish that the student knows how to eliminate options.

>>23318641
No. Literally nobody ITT read my post: >>23317927

>>23318654
You didn't read >>23317927

>>23318686
I'm trying to leave my ego at the door but I can't get over the fact that you are holding the goldball already, that means when you are going to use the same box again this box can only have one of the following outcomes, you pick a silver ball or you pick a gold ball.

IT doesn't make practical sense to me that you either pick a silver ball or a gold ball or a gold ball (durr)

>>23318686
It's not a semantics problem.

>>23318733
I urge you to consider these three cases and question yourself how the case where all balls are gold and the case where one ball is silver could possibly be the same:
>>23318654
>1: If there was 100% gold balls in both boxes it would be 50/50 that you randomly selected either box.
>2: If there was 99.9999% silver balls in one box and 100% gold balls in the other, it would be incredibly likely that you randomly selected the box with 100% gold balls.
>3: In the case in OP, it's 1/3 that you selected the box with one silver ball.

>>23318673
>Why are you including the probability of pulling out a gold ball (out of four) when it tells you that you pulled out a gold ball?
Because we know the color of the ball, and we know that we drew it first on a random pull, but we do not where it came from.

We can deduce that it is *more likely* that it came from the all-gold box, exactly twice as likely as the same thing happening with the half-gold box. Because if we'd picked the all-gold box this was a sure thing from that point on, while if we'd picked the half-gold box this event was 50/50.

Because it is twice as likely that this happened because we picked all-gold, we can deduce that it's twice as likely that the next ball will be gold too. We divy up the likelihood of all possible events from here on out (1) between the two colors, knowing one is twice as likely as the other, and that gives is the 2/3 & 1/3.

>>23318741
I appreciate that you are trying to clear up the problem and that in your specific case the problem was not a semantics problem, but my arguments are mostly aimed at people who are very deep into the problem, understand it exactly, and still think it's 50/50. That IS a semantics issue.
Look at the people in this thread arguing that the ball would be gold no matter what. This happens a lot, a subset of /pol/ is convinced that the question is saying the ball is fated to be gold and saying it doesn't is Jewish thinking (I denounce the talmud by the way). This is idiocy.

>>23318733
Because you don't pick either of two boxes the second time around. You only have the one box you already chose. Your fault is thinking in terms of two boxes, drawing from either of two boxes, you don't, you draw from one box, literally fucking read my post that nobody fucking read >>23317927. But that's too much text for you fucking coombrains.

>>23318770
If they think it's 50/50 they don't understand it, simple as. It's not a matter of semantics. You also don't understand it because you think if you have 1k gold balls in box 1 it's the same probability, it's not.

>>23318733
Try coming at it from the other angle then, and assume you're right. Suppose we don't care what order the gold balls are drawn in, and that it really only represents one outcome - a gold ball.

Now take that assumption back to the start of the experiment. Only one thing can happen in that box, while two things could happen in the other box. Can you figure out the way you'd be artificially shrinking the probability of outcomes from the double-gold box, and arbitrarily declaring that choosing the half/half box is twice as likely as it naturally is?

>>23318808
Yeah, I'm getting the gist of it at this point
From my point of view if you were to use the reverse of this 'paradox', which is the original paradox,
I would say the chance of pulling another gold would be 2/3, makes sense because there's 2 golds there and you're looking for the gold outcome

But I would still intuitively think that the chance of pulling a silver is 1/2 because we're looking for the silver outcome
It's really hard to overcome that part for me, I might be retarded and engaging with this retardation is a waste of everyones time

>>23318780
I'm not gonna read all that you're right

>>23318801
It is the same probability because we randomly select the box first. If we randomly choose the box with all gold balls, we will always draw gold, the probability doesn't change when we add more balls. The concentration of gold balls is always 100%.
Here is the problem simulated exactly as written again, but with 1000 balls in one box instead of 2. Again it gets close to 33% every time.
https://pastebin.com/raw/F9gbWDtL

If you actually want to see the probability change, change the actual ratio of silver to gold in any box.

>>23318801
Also they do understand it in the sense that they know that if they accept all random choices are taken into account, the chances are 1/3. However they do not interpret the question in this way. Saying they "don't understand it" is probably fair but I don't know how else to frame this argument charitably.

bye coombrains, rot in hell

>>23318939
?

>>23318909
Each ball is black and labelled as in the picture.
You take a ball at random from any of the boxes, you only peek and see it is labelled "G" but you still haven't seen the right side with the number. What is the probability that you are holding the ball labelled "G 3"?

You can't see into the boxes. For all you know you could pull out a red ball or a glass ball.

>>23318703
This is the part that isn't ambiguous "what is the probability of choosing a gold ball and then a silver ball from the same box". What's ambiguous is at what stage it's being asked:
1. Within all 3 boxes.
2. Within the first 2 boxes.
3. After you're already holding a gold ball.
Going by where the question is posed, it's the third scenario, but I'm just trying to dissect this poorly-worded question.

>>23318749
But the question is posed after you're holding a gold ball. If the question was "what the probability of choosing a gold then silver ball from the same box" you would definitely be correct. As it's written it's ambiguous at best.

>>23319288
The ambiguity is around what the premise is. Is the ball randomly selected, in which case it's 1/3, or was it fated to be gold, in which case it's 50/50? In both these interpretations you're already holding a gold ball, that's not the issue.
Interpreting that the ball was fated to be gold is just a very specific and strange thing to assume and it flies in the face of convention.

>>23319299
The 1/3 answer is the probability that is deduced based on the fact that you're already holding the gold ball.

At the start of the process, it was a 50/50 shot. Now that you're holding a gold ball which you drew first, you know your odds of getting silver next just went down, because there is a 2/3 chance you got that gold ball in your hand by picking the double-gold box.

>If the question was "what the probability of choosing a gold then silver ball from the same box" you would definitely be correct.
If that was the question, meaning you're not holding the gold ball yet, the answer would be 1/6. There are 6 equally likely permutations of box and ball selection, and that is one of them. Already having the gold-first part out of the way doubles your odds to 1/3, because one of the three remaining possible permutations is the silver one.

If, in the alternative, the question asked what the odds of drawing gold then gold or silver then silver, that chance would climb to 1/3 - but only because there are two permutations in both cases that are of equal value based on that criteria.

None of this is ambiguous.

>>23319338
>The ambiguity is around what the premise is. Is the ball randomly selected, in which case it's 1/3, or was it fated to be gold, in which case it's 50/50?
This is mostly correct, but the premise isn't ambiguous. The question clearly states that the ball choice was random.

If you have a magic hand that will always pick a box with gold in it and then always draw a gold ball out of it, your odds are 50/50. If, as the question states, you are holding a gold ball and you got to that point with two random choices, your odds are 1/3.

>>23319370
I would agree that the question basically isn't ambiguous for the same reason you said, but some people nonetheless choose to interpret the gold ball as a fated choice simply because it says "it's a gold ball" so I'm not sure how else to put it. It's "ambiguous" in the same way anything can be ambiguous if you choose to accept extremely improbable interpretations.

>>23319338
>>23319370
>in which case it's 1/3
You're not factoring in that you had to first pick a box at random.

>>23319400
>but some people nonetheless choose to interpret the gold ball as a fated choice simply because it says "it's a gold ball" so I'm not sure how else to put it.
Right, and that speaks to the fundamental misunderstanding of Probability that drives the wrong answers to the question.

The problem twists people's heads because it's counterintuitive to apply Probability backwards in time. But it makes perfect sense when you grasp the fact that, "How likely is it that X explains the present?" is every bit as appropriate a question to apply Probability to as "What will happen next?"

>>23319440
I very much am, or maybe you can find a flaw in my logic: https://pastebin.com/raw/D3NkeQu5

>>23319440
Yes we are. How do you think the box choice is being left out, and what do you think the probabilities change to when you add it back in?

>>23319452
Box1
Gold Gold
Gold Gold
Box2
Gold Silver *
Silver Gold
Box3
Silver Silver
Silver Silver

* Isn't just 1 out of the 6 paths the correct one?

>>23319478
1/3 because only 3 of those paths have a gold ball first.

you are all retarded trolls.

once you pull one ball out, you have eliminated one box. that leaves two: one with both balls the same, and one with one of each ball. there is no third option, after you have pulled out one ball. so the answer is a 1 in 2 chance. every time, and for every color ball.

but please, continue to collect (You)s and responses.

>>23317920 (OP)
It's 50/50 and every other answer is thinking about the wrong things when trying to figure it out

>>23319482
Only 1 of those paths have a gold ball first and a silver ball second.

It says you pick a box at random and it happens to be on the correct path. It says you pick a ball at random and it happens to be on the correct path.

I don't understand how you're ignoring the first 2/3 probability while factoring in the 3/4 probability of pulling out a gold ball. But it isn't just pulling out a gold ball, it's gold then silver. Shouldn't it be

Boxes * Gold->Silver
2/3 * 1/4 = 0.165

>>23319558
No one's ignoring anything and again you're free to find errors in my code that simulates this and prints close to 33% every time.
You can't take the selection of box and ball separately, they're deeply tied together, or you could say you only have one relevant random choice in this scenario. Factoring in probabilities actually goes something more like this:
You pick a random box with at least one gold ball. This could be only one of two boxes, since they are the only ones with gold balls.
If they had even concentrations of gold balls to silver balls, it would be 50/50 which box you had just selected. However, one had a 50% concentration of gold balls and the other had a 100% concentration.
It is twice as likely you drew a gold ball from the box with 100% gold balls, so that's a 1/3 chance you selected the box with one silver and one gold, meaning the next ball will be silver, and a 2/3 chance you selected the box with only gold balls, meaning the next ball will be gold.

>>23319551
It's a well known problem and has been proven countless times to be 1/3 (or 2/3 depending on the variation of the problem).
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
It's the people who are saying 50/50 who are wrong, their only tenable position is that the question is somehow different from Bertrand's Box which relies on ridiculous interpretations.

>>23319627
>You pick a random box with at least one gold ball. This could be only one of two boxes, since they are the only ones with gold balls.
I don't accept that premise. It says that there are 3 boxes and you pick one at random.
Going by the same logic, you could start at "one gold ball is removed" and then determining the probability of the next ball being silver is 1/2.

>>23319680
>I don't accept that premise
Then you're rejecting the question. You're free to live in your own world if you want to but the premise of the question is we selected a gold ball, which only could have come from one of two boxes.
We have incomplete information, so we can eliminate one box, but not all of them. It's not a problem of mindlessly multiplying probabilities adjacent to random choices we made and hoping we get the right answer, it's a problem of figuring out what the probability is that we're in a certain state given incomplete information.

>>23319708
>but the premise of the question is we selected a gold ball, which only could have come from one of two boxes.
Then the premise is that you've removed a gold ball. This sets the order of things. "Gold or Silver first" doesn't factor into this probability, but that's where you're getting tripped up. You can't say "Box 1 offers gold then gold AND gold then gold." It's only gold then gold or gold then silver for both boxes.

>>23319655
This paradox is bullshit and Bertrand is clearly not a gambler

>>23319558
>>23319680
>>23319722
This rationale is sufficiently fucked up in different directions that I'm finding it hard to believe it isn't an artful bait.

>>23319722
>You can't say "Box 1 offers gold then gold AND gold then gold."
I absolutely can say that because it has two different gold balls. You can view this as part of the incompleteness of the information in the question. I can draw ball 1 then ball 2, or ball 2 then ball 1. You just presumably have no way to distinguish between them. Your random choices don't actually care about the color of the ball, it says you drew a random ball, not drew a random color then drew a ball of that color.
But even this doesn't actually matter, it's the ratio of gold to silver between the boxes that determines the probability, not the exact number of balls. 2 balls is the minimum number you could have though.

>>23319829
Yes it's not really a paradox, just a probability problem some people get wrong.

>>23319892
>I absolutely can say that because it has two different gold balls.
Yeah, but it told you you've removed a gold ball, just as it told you that you're dealing with a box that has some gold in it. Do you not understand how accepting one part of the premise but not the other is inconsistent?

>>23319851
Factoring the entire problem: 1/6
Working with only 2 boxes: 2/3
Accepting that a gold ball has already been removed: 1/2

It just depends on the state of the problem when you ask for the probability.

>>23319558
>>23318673
Ok I think I'm kinda cracking the code on this fever dream.

If you're measuring from the start of the experiment, I can see how you'd deduce that you have 2/3 * 1/4 as a probability to land on that exact permutation. Probability of picking a box that will make a gold-first pull possible, multiplied by the probability, once you've picked a box, that the first ball will be the gold ball from the half/half box.

It is a fucked up way to break it down but does in fact correctly land you at the 1/6 probability that the gold -> silver permutation has at the start of the experiment. You are schizo but this is accurate.

Your error is not integrating this into your probability calculation: The information that we've gained once we do the box choice, then do the first ball choice, and observe the gold ball in our hand.

At that point we know definitively that we are in one of only three of the four permutations possible with the two boxes that have at least one gold ball in them. With this hindsight, the box probabilities shift and the box choice accounted for here - as there are twice as many equally-likely permutations involving the gold-gold box that explain the status quo, we can now deduce that it is twice as likely that we've selected the gold-gold box than it is that we've selected the gold-silver box. Three permutations, one of which is the "correct" outcome, and two of which have equal value to us as gold-last, or "incorrect". Hence, 1/3.

>>23319937
I'm absolutely taking everything the question says into account, again you can show me in my simulation where I'm not. I even went and made it a little more readable: https://pastebin.com/raw/Td4YtcfV

>>23319955
>Factoring the entire problem: 1/6
Correct. Taking it from the start, your odds of landing gold-first silver-second are 1/6.
>Working with only 2 boxes: 2/3
Incorrect. If you take the silver-silver box off the table upfront, you're left with 4 remaining permutations all equally likely. 1/4
>Accepting that a gold ball has already been removed: 1/2
Incorrect. Once you've pulled a gold ball, you've eliminated the possibility not only of the two permutations that involve the silver-silver box, but also of the permutation where the gold-silver box is picked and you draw silver first. Three permutations remain, of which you're looking for one. 1/3.

>>23317920 (OP)

gold odds: 1/3
silver odds: 2/3

theres no trick

>>23320090

whatever color you draw you know that box isnt the one that has 2 of the opposite color in it

>>23320090
There's no trick but you still got it wrong
Because you took a gold ball you know you didn't get the silver only box, which you now can remove from your consideration. Now you know you picked either the half and half box, or the all gold box. And since you already took a gold ball, them if you did pick the half and half box you're certain to get a silver one next, and if you picked the all gold box you're certain to get gold next. This reduces the whole question to "what are the odds I picked one of these two boxes" and since it's completely random and we've already narrowed it down as far as we can it's 50/50

>>23320125
yeah thatwas a typo

the odds of drawing a silver next are 50%

>>23320007
>Incorrect. If you take the silver-silver box off the table upfront, you're left with 4 remaining permutations all equally likely. 1/4
Typo. I mean to say 1/3 like a lot of people in this thread. But you're right there's another 1/4 stage where you're presented with two boxes and you're not assuming you've picked a gold ball.
>Incorrect. Once you've pulled a gold ball, you've eliminated the possibility not only of the two permutations that involve the silver-silver box, but also of the permutation where the gold-silver box is picked and you draw silver first. Three permutations remain, of which you're looking for one. 1/3.
You have to think about it at the box level after a gold ball is removed. At that point, it's 1/2.

>>23319985
>It is a fucked up way to break it down
It's literally the narrative of what someone would be doing as instructed in the question.

>as there are twice as many equally-likely permutations involving the gold-gold box that explain the status quo, we can now deduce that it is twice as likely that we've selected the gold-gold box than it is that we've selected the gold-silver box
Yes, but here's a different reading of this: We don't choose a ball out of a box, we remove a gold ball every single time. We don't get lucky anymore than if we got lucky choosing one of the first two boxes (that we do every single time).

You're saying "we can assume we chose one of the first two boxes" but not "we can assume we have removed a gold ball and only a gold and silver ball remains." See how that's inconsistent?

This question is worded like shit. If the intent was to be ambiguous and throw people for a loop with different interpretations, then the author is a genius.

>>23320289
>You have to think about it at the box level after a gold ball is removed. At that point, it's 1/2.
Fine, think about it "at the box level". Still 1/3, because the likelihood that we picked the gold-gold box is twice as probable an explanation for how a gold ball got into our hands on the first draw. Same answer.

>>23320326
>Yes, but here's a different reading of this: We don't choose a ball out of a box, we remove a gold ball every single time.
That isn't a different reading of it. That is a different scenario. Yes, probabilities shift if you change a random choice into a non-random choice.

>>23320326
>You're saying "we can assume we chose one of the first two boxes" but not "we can assume we have removed a gold ball and only a gold and silver ball remains." See how that's inconsistent?
It's not inconsistent. "we can assume we have removed a gold ball and only a gold and silver ball remains" is just a false statement. We've removed a gold ball, and either a gold ball or a silver ball remains in the box we've selected. And it is twice as likely than not that the box we selected contains another gold ball, because it's twice as probable an explanation for how the gold ball we're holding got into our hands.

The question is perfectly clear and unambiguous.

>>23320601
I'm impressed by how much effort you guys are putting into being wrong
It's literally just this >>23320125

>>23320601
>Still 1/3, because the likelihood that we picked the gold-gold box is twice as probable
Not if it's understood that a gold ball is removed every time. You can run this 100 times and every time a gold ball is removed first. There is no likelihood at this stage. (if one is interpreting it this way)

>Yes, probabilities shift if you change a random choice into a non-random choice.
Just like if we're assuming box 3 is never chosen.

>We've removed a gold ball, and either a gold ball or a silver ball remains in the box we've selected.
Ok but there wasn't a scenario where a silver ball could be chosen first. (in this interpretation)

>The question is perfectly clear and unambiguous.
Obviously not. No one would care about this problem if it were unambiguous.

>>23320631
>>23320125
>This reduces the whole question to "what are the odds I picked one of these two boxes" and since it's completely random and we've already narrowed it down as far as we can it's 50/50
The whole question reduces to "what are the odds I picked this gold ball from the gold/silver box, meaning the next ball is silver" and the answer is 1/3, because you'd have to be luckier to draw gold first if it was that box versus the other one.

>>23320675
What
No
You've already drawn the gold ball, you don't need to think about how lucky you are to have drawn it, you just need to think about the consequences of the fact that you already have drawn it
Now knowing that you have a gold ball, you are in a situation that means drawing from the same box, which only has one ball left in it, will give you a silver one or a gold one. And there is only one box that could have been the one you drew from that would result in you drawing gold a second time, and only one box you could have drawn from that leads to you drawing silver. Since we do not yet know which of those two boxes you actually drew from, and the way it was chosen is completely random, you're now in a 50/50 situation.

>>23320735
>you don't need to think about how lucky you are to have drawn it
>you just need to think about the consequences of the fact that you already have drawn it
The next event follows mechanically from the ones before. The next ball has already been selected by the random choices already made - the next step in the procedure is merely to reveal it. Thinking about the luck, or probabilities, involved in the prior steps is where all of the action is in this probabilities question.

>Since we do not yet know which of those two boxes you actually drew from
But notice how you've figured out that it's two? That's because we don't know, but we have a clue, a gold ball drawn first. All I'm saying is that this clue gives us more information than you've realized yet.

>>23320790
You forget
There's no such thing as true randomness, only actions taken without complete knowledge of the outcomes
Which ball you drew first was also a mechanical result of which box you chose
Revealing a gold ball just told us which of the three boxes WASN'T chosen. We're now asking which one WAS chosen.

Okay fucknuts I will try again.

You have drawn a silver ball, correct?
At that point, what chance is there that you have the box with two gold balls? Hopefully, your answer is "zero". There is zero chance that you have two gold balls, because you already drew a silver one.

If that is not your answer, then review your work.

So you either have the box with two silver balls, or the box with one silver and one gold ball. Hopefully, you have arrived at this conclusion.

So what are the chance that you have the box with two silver balls, out of your two possibile options? Your chance is 0.5, or one in two. The next ball you draw will confirm which of the two boxes you chose.

>>23320858
That's what I've been saying but these guys keep trying to make it more complicated and getting lost along the way
They would not make good gamblers

Goddamn I fucking hate you all you fucking coombrains

I was thinking that because I'm holding a gold ball in my hand, therefore I know that my next draw cannot be from the box which has two silver balls, but rather is going to be from either of the other two boxes.

My thinking is that the fault is in thinking in terms of having two boxes, and thinking you're going to be drawing from either the first or the second of these two. You don't have two boxes. You only have the one box you picked up. Therefore you can't think in terms of two boxes at all, you have to think only in terms of the balls that are in the two boxes which you know your box is one of. So you originally had 3 gold balls and 3 silver balls, and you were equally likely to draw any of these 6 balls. But what you know given the draw of a gold ball, and given that you have to draw the next ball from the same box, is that you drew your ball from a total of 4 balls, out of which 3 were gold and 1 silver, and that your next draw is going to be from a total of 3 balls out of which 2 are gold and 1 is silver.

>>23320976
There, I shortened my post. Is it short enough for you fucking goldfish attention-span coombrains now?

>>23318909
Kys fucking retard

>>23320985
It's not a problem of it being too long or complicated
It's just fucking stupid

>>23320858
>>23320886
It's extremely simple. You're holding one of three balls in your hand, you don't know which, but you do know that two of them come with a twin. Two times out of three you're getting the twin.

>>23321037
Arguably kinda sorta technically true maybe... but I'd argue against it. Inarguably though, 100% of the time completely useless for understanding the issue.
You'd not make a good gambler.

>>23321055
People who understand probabilities don't gamble much, specifically because they understand it.

But you'd be signing me the deed to your house by the end of poker night.

>>23321036
Nah you're just a fucking coombrain

>>23321078
You have a lot of confidence for someone who doesn't understand that you need to evaluate things from the consequences of what you already know rather than treating your givens as being subject to randomness

>>23321115
Sounds like the conversation is over then

>>23321159
None of you have any counterarguments to what I wrote because it flies over your tiny fucking coombrain heads.

>>23320976
>>23320985
>>23321037
Why would you think in terms of individual balls, when it's about gold and silver and 2 boxes? You people are retarded.

>>23321225
Midwit behavior

>>23321225
>>23321253
Did you read this? >>23318016

>>23321288
Different kind of question entirely

>>23321225
Because when you draw a gold ball you know your box is box 1 or box 2. But the balls aren't glued in place. You have to view them as fluid, meaning all you know is you drew from the pot of 3 gold 1 silver, these 4 balls could be in either of box 1 and box 2 in any order. After drawing 1 gold from this pot of 3 gold 1 silver, you know your next draw will be from the pot of 2 gold 1 silver, but these balls will be in any order randomly mixed in box 1 and 2. You can't split this pot into two sets, it's 1 set.

>>23321336
It's not one set
It's two sets, and you don't know which set you're in

>>23321346
Yeah and because you don't know which set you're in you have to treat it as one set.

>>23321381
Why do you have to treat it as one
The question is which one is it
You drew gold
Now if you are in set one you'll draw gold again, and if you're in set you'll draw silver
Both of those are 100% certain
The uncertainty comes from the fact that you don't know which set you're in
So it's 50/50

>>23321403
Because you don't know which of the 3 gold balls you drew. Neither of the 3 gold balls, nor the 1 silver ball, is tied to any particular of the two boxes. It's all fluid.

>>23321422
They are tied to the boxes though
Just not in a way that gives you knowledge of which box you drew it from

>>23321441
>They are tied to the boxes though
Not for our purposes. Irrelevant that physically they are where they are.

>>23321403
Okay answer this.
You have two boxes. One has 1000 gold balls. One has 999 silver balls and 1 gold ball. You pick a box at random. You draw a ball from the box at random. What is the chance that if you draw another random ball from the same box that it will be gold? Still 50/50?

>>23321554
Forgot to mention the first ball is gold

>>23321441
Do you have 3 identical decks of cards? If not, buy it. Pull out 3 kings of the same suit and 3 queens of the same suit. Arrange them in 3 stacks:
stack 1: king + king
stack 2: king + queen
stack 3: queen + queen
Put them facing down on the table. Close your eyes and shuffle them around. Then open your eyes and pull one stack to right in front of you away from the other two stacks. Lift the top card. If it's king, what are the odds the other card is queen? If its queen, what are the odds the other card is king? Do this physically, it might aid understanding.

>>23321555
I think I've finally been confronted with an argument that actually challenges my conclusion in an intelligent way rather than making absurd claims about how I should be thinking about things without providing an explanation for why.
Good job. I'll have to think on this for a while.

>>23321580
Even if I'm wrong I don't see why thinking of it in terms of a fluid mass is going to be useful
It's genuinely not the reality of the situation that they're all in the same box

>>23321582
We all tried our best. In Swedish the word "dum" in children's speak means both "asshole" and "stupid", people like you make that seem sensible.

>>23321622
I'm just following the old classic, when in Rome do as the Romans

>>23321625
Then fuck off back to where you came from and the average iq of this board will go up.

>>23321636
Unlikely, I just need to make a better effort to keep my brain sharp.
This place makes me dumber as I get used to it, not the other way around.

>>23321582
Look up videos about The Monty Hall Problem on youtube.

>>23321646
I'm not sure how that relates to this one but alright

>>23321643
Kys faggot

>>23321670
Yeah that's about the expected response.
Have a nice day.

>>23321686
I hope you have a miserable day

>>23321580
I made a simulator for this which you run in your browser.
>open this link:

https://pastebin.com/ANBM3Vg4

>click "download"
>change ".txt" in the filename to ".html"
>click to open the html file
>it will open up in a web browser

>>23322147
Kek, pastebin butchered the text, but other than that it's working. Black cards are king, red cards are queen.
>press button to shuffle
>press any stack once to reveal the top card, twice to reveal both cards, three times to hide both cards
I made it with chatgpt.

>>23321609
Try this simulator. Hope it helps.
>>23322147

Man, no matter how rough this board could get, we had us a community. There wasn't no poster who didn't matter. Now all we got is trolls nad predatory motherfuckers like OP. Makes me sick how far we done fell.

>>23321554
>>23321555
that has nothing to do with the question in the OP.

>>23322210
Retarded or troll?

>>23322208
Shut the fuck up faggot and be grateful for the shitton of work I put into this >>23322147.

>>23322147
>>23322168

I fixed the corrupted code, now it's showing king of spades and queen of hearts.

https://pastebin.com/SF0MDzgV

>>23323455

I tried two hosting websites so all you have to do is click to download and then click the file to run it. I was hoping for an html link but this is the best I could do. Let me know what you think about this game. I might try github later. Anyone know a good site?

https://limewire.com/d/1cWQ3#k8PD6k0Vpl

https://we.tl/t-IjHyXLc5JK

>>23322208
Also fuck you asshole. I tried my best to help that faggot and all he gave back was saying it was absurd, not trying to explain, unintelligent etc etc and he said my original post was dumb too, fuck both of you homos. Kys

>>23320858
Just because there's 2 answers doesn't automatically mean 50/50.
Chances are not always evenly distributed. It doesn't have to be 50/50, it could be 25/75, 10/90, etc. as long as all possibilities add to 100%.
In this case, it's weighted towards the box with two gold balls because it has twice as many gold balls. So it's 2/3 that you drew the ball from the box with two gold balls versus 1/3.
Yes, you made a fair random choice between two boxes. And if all we did was eliminate one box somehow and choose between two boxes, it would be 50/50. But we have more information than that, we also have the gold ball.

>>23324377
Other thread on /pol/ died lol.
Someone there asked how you can get to 33% with 2:1 odds.

It's simple really, odds have to add to 100% right? So with 2:1 odds it adds to 2 + 1 = 3. 2/3 = 66.666...% and 1/3 = 33.333...%.

It's easy to prove because 2/3 and 1/3 are the only two values where one is twice the other and they add to 100% total.

>>23317920 (OP)
It’s 1/3 you have to factor in all gold balls so you eliminate the right silvers, then you could either pick box A/B as they have gold

GG
GS

Seeing as 1 gold is removed from the pool - that leaves G/G/S in the pool = 1/3 = 33%

I made another game with actual boxes and balls.

https://limewire.com/d/B8mAD#b0he0jg4pg

>>23325634

Link that opens up the game directly in the browser:

https://litter.catbox.moe/jljwe6lnmcbwxtmx.html

>>23326364
Nice, but you should display running stats for the probability.
Also don't show the "shuffle" button until someone has clicked a box twice.

>>23326375
>Nice, but you should display running stats for the probability.
What is that?
>Also don't show the "shuffle" button until someone has clicked a box twice.
Why?

Also, if you download the html file from this link and copy-paste the code into chatgpt you can ask it to tweak it any way you want. I tried to have a sound for shuffling but it doesn't work. At least I don't hear a sound, but it has in its code to make a sound.

https://limewire.com/d/B8mAD#b0he0jg4pg

>>23326396
Oh wait, I guess the stats wouldn't matter because you're not forcing the first ball chosen to be gold every time. In other words, we know it's 1/6.