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

>>23317920
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.

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.

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>>23317920
They added more balls.

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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
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.

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

>>23317921
fpbp

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>>23317920
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
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
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
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
>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
>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
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
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
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
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
SLIDE THREAD FOR FUCKS SAKE STOP TAKING THE BAIT

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

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

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

>>23317920
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
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.

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>>23317920
>>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
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.

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>>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
?

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>>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.