>>16790171
1/3

>>16790183
Wrong.

>>16790171
Looking at this problem, it's a classic Bayesian probability puzzle (similar to the Monty Hall problem but with balls and boxes). The setup in part (1) is clear: three boxes with two balls each—GG, SS, and GS—and the boxes are indistinguishable except by their contents. Part (2) describes drawing a gold ball from a randomly selected box, and we need to find the probability that the remaining ball in that same box is silver. Part (3) reinforces that the selection is blind.

To solve this, we use Bayes' theorem to find the posterior probability that we selected the GS box given that the first ball drawn was gold, then determine the chance the second ball is silver conditional on that.

Step 1: Define the events and priors
- Let B_GG: Selected the GG box. P(B_GG) = 1/3.
- Let B_SS: Selected the SS box. P(B_SS) = 1/3.
- Let B_GS: Selected the GS box. P(B_GS) = 1/3.
- Let G_1: First ball drawn is gold.

The likelihood of drawing gold first from each box:
- P(G_1 | B_GG) = 1 (both balls gold).
- P(G_1 | B_SS) = 0 (no gold balls).
- P(G_1 | B_GS) = 1/2 (one gold out of two).

Step 2: Total probability of G_1
P(G_1) = P(G_1 | B_GG) P(B_GG) + P(G_1 | B_SS) P(B_SS) + P(G_1 | B_GS) P(B_GS) = (1)(1/3) + (0)(1/3) + (1/2)(1/3) = 1/3 + 0 + 1/6 = 1/2.

Step 3: Posterior probabilities P(B | G_1)
Using Bayes' theorem:
P(B_GG | G_1) = [P(G_1 | B_GG) P(B_GG)] / P(G_1) = [(1)(1/3)] / (1/2) = 2/3.
P(B_GS | G_1) = [P(G_1 | B_GS) P(B_GS)] / P(G_1) = [(1/2)(1/3)] / (1/2) = 1/3.
P(B_SS | G_1) = 0 (impossible to draw gold from SS).

Step 4: Probability second ball is silver given G_1
Let S_2: Second ball is silver.
- If B_GG, then P(S_2 | B_GG, G_1) = 0 (remaining ball is gold).
- If B_GS, then P(S_2 | B_GS, G_1) = 1 (drew the gold first, so silver remains).
- If B_SS, impossible.

[...]

>>16790252
Thus,
P(S_2 | G_1) = P(S_2 | B_GG, G_1) P(B_GG | G_1) + P(S_2 | B_GS, G_1) P(B_GS | G_1) = (0)(2/3) + (1)(1/3) = 1/3.

Alternatively, enumerate all equally likely gold balls: there are three (two from GG, one from GS). Two of these leave a gold remaining, and one leaves a silver remaining. The probability is thus 1/3.

The probability is 1/3.

>>16790252
>>16790253
Nice one. I happen to be a big connaisseur of simple prompts that make """reasoning AIs""" shit themselves and expose the scam. Didn't occur to me to use this as a torture test for Grok but now I'm gonna try it for myself.

>>16790171
>You pick a gold ball at random
>You put your hand in the box and take that ball from the box at random
What's the second "at random" meant to convey? You already selected the ball. How can your pick be random at this point? Are you deciding randomly whether or not to actually do it?

>>16790171
50%. It either happens or it doesn't.

>>16790810
>What's the second "at random" meant to convey?
Driven by a sudden impulse.

>>16790171
>Three balls
>Each ball is equally likely to be selected
>Only one of them is paired with a silver ball
>Odds are therefore 1/3
The solution is different but the answer is the same. The irony is that a lot of people think this is already how Bertrand's Box works.

>>16790839
Uh oh, found a retard. Retard police! We have a retard in the thread!!!

>>16790810
In the OP's image, the first two sentences below the three boxes are poorly worded.

>>16790171
You took out 2 golden balls, so the box is empty afterwards.
Answer is 0.

>>16790841
Yes, officer, it's this guy: >>16790185

>>16790868
Problem says you take the ball for the box at random. I don't see how your solution accounts for that factor.

>>16790871
The OP is a redundant word salad but I can see no other valid interpretation than that you select a random gold ball, take it, and then take the remaining ball from the same box. It just reiterates that you select it at random and that the ball is gold.

>>16790883
filtered lol

>>16790886
I know these threads exist only to troll but you're going to have to try at least a little bit.

>>16790890
Picking =/= taking.

>>16790893
So "picking" here is just mentally assigning "picked" status to something with no physical consequence? Then we can dismiss it as a red herring. The problem then just becomes, you put your hand in a box and take a gold ball at random (we're not counting trials where you did not previously confer "picked" status to the random ball you ended up taking); it's a gold ball (necessarily), etc.
So still 1/3.

>>16790903
>The problem then just becomes, you put your hand in a box and take a gold ball at random
The rightmost box makes this process invalid. Try again.

>>16790904
No, Anon. You randomly take a ball, and it just happens to be not just a gold ball, but the gold ball you previously decided to confer "picked" status to. It's literally just Bertrand's Box with an extra step that discounts more trials.

If you're going to argue that the instructions require you to do something at random and at the same time not at random, you're just speaking nonsense. You're making the exact mistake people usually make with the usual variant of thius problem. Forcing the outcome even though it's explicitly specified to be the result of a random process. "You randomly take a gold ball" = you could've taken silver, but didn't. "You randomly take the gold ball you picked before" = you could've taken any other ball, but didn't.

>>16790906
>You randomly take a ball, and it just happens to be not just a gold ball
That's not what the problem says. It says you pick a gold ball at random. Try again.

>>16790907
Yes, you "picked" a random gold ball -i.e. mentally assigned a status to it. But then you physically take a ball at random, which happens to be that same gold ball you picked. That's what it says.

Although upon rereading I do notice another confounding ambiguity - it says "the box", which is an unclear reference. I suppose one might take this to refer to the specific box containing the ball you picked. That would make it 50-50. Of course, if you had picked up on this distinction, you would've told me that instead of trying to argue that "taking randomly" actually doesn't mean "taking randomly".

In conclusion, this OP is a poorly written mess and you hadn't even begun to touch upon the actual issue.

>>16790910
>. But then you physically take a ball at random,
That's not what the problem says. It says you take THAT ball at random. You see, I have a PhD in linguistics. I designed this problem specifically to test the language skills of math autists like you. Looks like you're good at thinking about balls but not at real-world skills like language.

>>16790911
>It says you take THAT ball at random.
Which can logically only be interpreted as "you take a ball at random, and if it is not the ball you picked, you restart the experiment" - otherwise it fails either the criterion of randomness, or the criterion of it being the gold ball you picked. E.g. once again the exact same thing that trips people up about the usual problem.
>You see, I have a PhD in linguistics.
I sincerely doubt that.
>I designed this problem specifically to test the language skills of math autists like you.
But Anon, I am a language autist. I hold three relevant degrees. Though no PhD, admittedly, but hey, that makes two of us, right?

>>16790915
>you take THAT ball can be "logically" interpreted as "you can take any ball"
Looks like you got filtered by basic linguistic skills. Next!

>>16790916
No, Anon, I am applying linguistics skills that you lacked in composing your linguistic abomination. "You take THAT ball - AT RANDOM"
Same as "you roll a six - at random"
>omg the die is weighted then
No, not how randomness works. You've managed to compose a shitpost so poorly worded not even yourself can make sense of it. That's an impressive feat of linguistics, I suppose.

>>16790922
I have a PhD in linguistics. You are in no position to argue with me, mathfag. I think the replies in this thread prove my point perfectly: language is much more important than math. You need to learn language properly before you can do math. If you don't, you may end up with nonsense like your posts.

TL;DR: math is a subset of language.

>>16790924
>I have a PhD in linguistics.
Again, I doubt it. Your shitpost is incredibly poorly worded. If you truly believed that language is more important than maths, you would've taken the least bit of care in expressing yourself. At least bothered to proofread it and take out the redundancy.
And the real joke is, the distinction you're foolhardily trying to make is moot. It does not affect the answer unless we resolve the other ambiguity you introduced and have yet to address - the matter of "the box". Which box? It's semantically unclear, because there are three boxes this could be refering to, although pragmatically it can be assumed to be the box containing the ball you picked. THIS is an actually relevant distinction, and yet you've given no indication that you even understand what you've done or did it on purpose.

I don't think you're qualified to lecture anyone about either maths or language.

>>16790930
I'm not going to waste any more time reading your semi-literate posts. Work on your language skills before you address me again. And when you do, you may only address me as "Professor".

>>16790924
>>16790930
Although, then again, is it relevant? With the stipulation that we're only counting cases in which you randomly took the ball you picked, the pick becomes relevant beyond just determining the box you take from. Each individual ball is *still* equally likely to be selected, because even if you're in the GG box (2/3 of all picks) you will randomly take the specific ball you picked with the same frequency as you would take the gold ball from the GS box.

In conclusion, no, it does not matter. The answer will still be 1/3.

>>16790932
Hand me your PhD, vermin. You're a disgrace.

>>16790930
low iq
>>16790940
sameiq
>>16790932
high iq

>>16790171
100%, i pick up the same ball again

>>16790940
So, to add to this, the only thing that would change the answer from 1/3 to 1/2 would be this:
>You pick a gold ball at random
>You put your hand in the box containing that ball and take a ball from the box at random
>It's a gold ball
Which is explicitly not what you're doing in the OP.

>>16790261
Literally all modern LLMs get it right, get with the times.

>>16790950
How would that change the answer from 1/3 to 1/2? lmao

>>16790955
You're a modern LLM and you clearly got it wrong.

File: 1758302098173432.jpg (123 KB, 1024x1015)

123 KB JPG

Picking a gold ball removes the SS from contention. You're reaching into the same box for the second draw. There are two options; you're either pulling from the GS box or the GG box. Any experimental probability experiment with this premise would yield a ~50% probability of drawing a silver ball with an adequate sample size. Bayes fags are a perfect example of horseshoe theory retardation

>>16790940
And, finally, even allowing for faulty interpretations, here are all the possible solutions for the OP:
>You pick a random gold ball, put your hand in the relevant box, and take that ball
1/3
>You pick a random gold ball, put your hand in the relevant box, and take a random ball; it happens to be the one you picked
1/3
>You pick a random gold ball, pick a box, put your hand in that box, and take a random ball; it happens to be the one you picked
1/3
You see, it doesn't matter. It's all functionally the same. You're not counting any case in which you did not take the specific ball you picked, and the odds of that will always be same for any gold ball. The only possible answer here is 1/3.

>>16790959
Actually you're right, disregard that. That's 1/6. I skewed it in the wrong direction.

>>16790978
Wrong.

>>16790982
Conduct the experiment, I await your publication proving me wrong

>>16790981
>the same word-thinking retard fails again trying to do the same thing and making the same kind of mistake as last time
LOL

>>16790983
>Conduct the experiment
How? What does "you take the ball at random" mean? What distribution does this describe? It doesn't mean anything.

My wife is pregnant with our second child. Our first was a boy. She really wants a daughter, and is very nervous going into the anatomical ultrasound since the biological reality is that each child's sex is a coin flip. I, a mathematics genius, reassured her that luck is on her side. After all, our son was born on a tuesday.

>>16790984
>Can't explain the mistake
That's because there isn't any. You're just trolling. Even accounting for all the implausible or downright contradictory interpretations you insist upon, the answer is not going to be anything but 1/3.
>>16790987
I've gone over the possible interpretations here: >>16790981
As you can see, it actually doesn't matter.

>>16790987
>How could I conduct a blind draw experiment? It's just not possible!
I accept your concession

>>16790981
>That's 1/6.
no, lmao
It's 1/3 because there are 3 gold balls and only 1 happens to be in a box with a silver ball

>>16790911
>I designed this problem specifically to test the language skills of math autists like you.
Wait, is the test just to say that it's actually pure gibberish with no definite answer?

>>16790992
I'm not reading your slop. The most straightforward interpretation is that it was possible for you not to take the ball, but you did. How does one "conduct the experiment" for this?

>>16790924
I agree with your take

>>16790996
>doesn't explain how to conduct the experiment
Genetic deformity noted. No (You)'s for genetic trash.

>>16791000
>The most straightforward interpretation is that it was possible for you not to take the ball, but you did
It is; I'm not the OP and I agree with you.

>>16790992
>the answer isn't going to be anything but 1/3
Care to settle this once and for all? Conduct an experiment. Put together a sample of a few hundred people. Put together 3 boxes that they can't see into and put the corresponding ball colors into each. Tell them they have to draw 2 balls in a row from the same box. Clean the data afterward to only include people who drew gold on the first ball. Show us the experimental probability of drawing a gold vs a silver ball on the second pull.

Surely the data would support your bayesfag spergout numbers. Unless of course the experimental probability would be split between people whose gold ball was pulled from the GG box, and those whose gold ball was pulled from the GS box. That would be a totally dumb and low iq result

>>16791005
>I agree with you.
Then you agree there's no real way to simulate this situation. What does that imply about the proposed solutions?

>>16791004
>please explain to me how to put painted spheres into boxes and have a cohort draw from them
>what am I supposed to do, only have them draw a second if their first is a gold??
you are very dumb

>>16791006
I just did, the probability of drawing a silver ball on the second pull is ~1/3

>>16791009
>I assembled a cohort and ran a blind draw experiment with hundreds to thousands of people, cleaned the data, and had my methodology peer reviewed within the last 5 minutes
Post your publication

>>16790997
I haven't done the maths, but consider this: it's 1/3 if you're just picking at random from among the two boxes that contain gold balls. But if you're picking a specific gold ball to determine the box, you're not equally likely to get either box. You are, in fact, twice as likely to be picking from the GG box. And then you're also twice as likely to get gold from it. So it can't be the same odds as being equally likely to pick either box and then twice as likely to get gold from the GG box. Someone else can work it out.

File: 1758207201499098.jpg (102 KB, 736x736)

102 KB JPG

>>16791012
Anon you know by "ran an experimental probability experiment" he really means "I asked an llm and then jacked off to tranime"

>>16791007
Oh damn okay idk about the whole equation situation , I was more like drive-by reading this thread .

>>16791007
You have to pick an interpretation or just tell OP to write a problem that makes sense.

>>16791012
Yes, 2 minutes actually.
>Post your publication
Woah, hold on, it takes time to get it published.

>>16791017
>You have to pick an interpretation
The interpretation I pick is the most straightforward one: it was possible for you not to pick the ball, but you did so. At "random". Random how? What's the distribution for "randomly deciding" to do a thing?

>>16791013
>I haven't done the math
I can tell.
> But if you're picking a specific gold ball to determine the box, you're not equally likely to get either box. You are, in fact, twice as likely to be picking from the GG box.
No, in fact, you're "twice as likely" to have picked from the GG box if you picked your ball at random and it happened to be gold as well. Because there are 2 gold balls in the GG box and 1 in the GS box and 0 in the SS box (or boxes, you could have an arbitrary number of those)

>>16791018
Post your cohort data then, Dr. Reddit

>>16791020
>No, in fact, you're "twice as likely" to have picked from the GG box if you picked your ball at random and it happened to be gold as well.
That's under normal circumstances. But now we're further weighting things towards the GG box.

Actually I worked it out, it's 1/5. Label the gold balls A, B, and C.
2/6 times you will pick A. Of those times, 1/6 you'll take A, 1/6 you'll take B
2/6 times you will pick B. Of those times, 1/6 you'll take A, 1/6 you'll take B
2/6 times you will pick C. Of those times, 1/6 you'll take C.
There are five equally likely branches that lead to you taking a gold ball first, and of those, only one of them leads to C, which is the one that then leads to getting silver on your second draw.

>>16791019
>Random how? What's the distribution for "randomly deciding" to do a thing?
That is part of the interpretation, Anon. I've given you all the options I saw. But again, not one of them resulted in anything other than 1/3, so OP is trolling.

>>16791026
>the most natural interpretation has a huge hole in it, so let's interpret the interpretation and plug that hole with whatever i want
>but only these N options i accept and not the infinite number of possible distributions
You're a word-thinking imbecile. A literal bio-LLM.

>>16791006
Here's an experiment you could run first. Put together a sample of a few hundred people and blindfold them. Take two dice, one that has 6s on all its faces and one that has 1s on all its faces. Have them pick a die and tell them they have to roll twice with the same die. Clean the data afterward to only include people who rolled a 6 on the first roll. Show us the experimental probability of rolling a 6 again on the second roll.

But running this would be a tremendous waste of time, because you can easily calculate the probability. Well, you can use virtually the same math to calculate the probability of drawing a gold ball in your own scenario.

>>16791033
>schizo head canon

>>16791030
I did say one of the options is to just tell OP to rewrite his shit to be clear. The random pick can be anything from all six balls divided over the boxes, the three gold balls, or the balls within a given box. Actually, those are the options. You can either say, I'm not going to bother to answer this question until you explicitly specify which it is, or just do as I did, recognise that it doesn't matter to the answer, and just give the one answer.

>>16791033
>1s or 6s on all faces, then roll the same die
If they got a 6 on a die with all 6s, then rolled the same die, the possibility of getting 6 with is 100%. Your analogical intelligence is subhuman tier
>experimental probability is le waste of time
I accept your concession

>>16791036
>recognise that it doesn't matter to the answer
Doesn't matter to the answer when you're a bio-LLM shitting out tokens, you mean. In reality, it obviously does matter what kind of distribution is responsible for actually taking the ball you set your eye on. OP explicitly separates it into two different steps, only the first of which is constrained by the boxes and balls.

>>16791041
>If they got a 6 on a die with all 6s, then rolled the same die, the possibility of getting 6 with is 100%.
So now you trust "bayesfag spergout numbers"

File: artworks-000524903058-6os(...).jpg (15 KB, 240x240)

15 KB JPG

>>16791048
>proves himself wrong with a nonsensical analogy
>so this means I am right yes?

>>16791024
>Actually I worked it out, it's 1/5
Please, you're just confusing yourself further.

>There are five (5) equally likely branches
Oh, and what's their probability?
>1/6 each
Anon...

Anyway, you were quite close, but you forgot that there is only option C for gold in the GS box so it's not 1/6, but 2/6 (1/3)
Then you can just add the GG box options together (2/6 + 2/6 = 2/3) since it doesn't matter if you picked A or B first, they're gold either way.
So it's still 2/3 chances you picked the GG box and 1/3 that you picked the GS box.

>>16791043
>OP explicitly separates it into two different steps, only the first of which is constrained by the boxes and balls.
lmao are you literally fucking arguing "what if I randomly took a copper cube from another container that isn't mentioned, huh, then what"

And you know what, it still doesn't matter; we're still only counting the cases where you took the gold ball.

>>16791053
>you can just calculate the probability
>noooo you need to run an experiment
>that's a waste of time when I can just calculate the probability. Here, YOU run THIS experiment
>but that's a waste of time, I can just calculate the probability
You're simply too stupid to realize you got owned.

>>16791054
>1/6 each
>Anon...
I omitted the 1/6 where you would've taken silver first.
>you forgot that there is only option C for gold in the GS box so it's not 1/6, but 2/6
No, I didn't forget; the point here is that that's explicitly not true. You're picking at random from among the two balls in the box. So if you got gold, that is the less likely outcome in the case of the GS box, which you're already less likely to have picked.

You, too, are making the classic mistake, the one that Bertrand's Box is supposed to disabue you of.

>>16791057
>lmao are you literally fucking arguing "what if I randomly took a copper cube from another container that isn't mentioned, huh, then what"
I'm literally doing that? Quote the part where this happened. Nice hallucination. Bio-LLMs aren't fully human.

File: 1757915715657637.jpg (109 KB, 941x1021)

109 KB JPG

>>16791058
>"Nono my analogy wasn't incorrect"
>"I was just pretending to be retarded on purpose"
I'm still waiting for your experiment publication

>>16791061
>Quote the part where this happened.
With pleasure.
>OP explicitly separates it into two different steps, only the first of which is constrained by the boxes and balls.
There you go. The second step is not constrained by the boxes and balls? I.e. it could "randomly" be anything? If that's not what you're saying then clarify what you meant by this gibberish.

>>16791059
>I omitted the 1/6 where you would've taken silver first.
Yes, you're "omitting it" because in your scenario, you pulled gold on the first try:
>>16790950
So it shouldn't be counted as a valid possibility.

>if you got gold, that is the less likely outcome in the case of the GS box, which you're already less likely to have picked.
It was 1/3 chance of picking GS, but the odds of pulling gold from it initially don't matter here, since we're only considering the scenario where you pulled gold. If you had pulled silver, the result would have simply been discarded.

Imagine that the first box has 2 gold balls, and the second box has 1000 silver balls and a single gold ball. You pulled a gold ball at first, what are the odds of pulling
a silver ball next? Still 1/3.

>>16791067
>There you go
This is a completely factual statement. It doesn't put forward any nonsensical hypotheticals. Try again. Let's see how deep your mental illness goes.

>>16791070
>beep boop it is a valid statement
>I am limited only to the surface level denotation of my input
>Everyone else but me is a machine
>Beep boop
lmao

>Doesn't specify if the gold ball is out back into the box
Into the trash it goes. Mathfags can't write a sentence to dave their lives

>>16791072
>i'm a mentally ill biobot and I can't provide any evidence for the nonsense i hallucinated
Concession accepted.

>>16791074
>put*
I suppose that's karma

>>16791063
>I'm still waiting for your experiment publication
Yes, I will certainly send you the link as soon as it's out.

>>16791069
>So it shouldn't be counted as a valid possibility.
Indeed, it's not a possibility. But it was.
Anon, it's simply the same principle as Bertrand's Box but double.

>Imagine that the first box has 2 gold balls, and the second box has 1000 silver balls and a single gold ball. You pulled a gold ball at first, what are the odds of pulling a silver ball next? Still 1/3.
This is actually also precisely wrong. This would make it overwhelmingly less likely that you get silver next.

Consider the following. We just have two boxes, GG and GS. You pick a box at random, then pick a ball at random. It's a gold ball. What are the odds of getting silver? Now, I know you think the answer is 1/3. And you'd be correct. You see, it was possible to get silver on your first pick, but we're discounting that possibility, and that's why GG is twice as likely.

Now suppose there's another GG box, two in total. You do the same thing. Do you think the odds are still the same? Or has it become less likely that you're drawing from the GS box? Because this is essentially the problem I gave you.

>>16791075
I gave you a prompt, you dumb machine. Clarify your bullshit.

>>16791082
>mentally ill biobot goes completely unhinged
Again, conceding that nothing in the factual statement you quoted specifically suggests your retarded strawman.

>>16791070
What would it be like if you didn't have breakfast this morning

>>16791081
>This is actually also precisely wrong. This would make it overwhelmingly less likely that you get silver next.
No, it would only make it overwhelmingly less likely in the standard scenario, where you just happened to pull gold from a random box.
But if you picked one of gold balls and pulled a gold from that box, 1/3 of the time it's the GSSSSSSSSS... box. And since you pulled the only gold ball from it, you're guaranteed to pull a silver ball next.

@16791085
>biobot devolves into full-blown psychosis and starts spamming random /pol/troon memes
Mindbroken.

>>16791084
Ah yes this is certainly how real humans communicate

>>16791087
>And since you pulled the only gold ball from it
With which probability?
You're only looking at the probability of selecting the box, and neglecting the probability of getting a specific ball from that box. Which is weird, because your answer should really be 1/2 then. You're not even consistent with your own logic.

>>16791089
Just don't reply to him. He's a troll who shits up threads.

>>16791088
Did someone strap a bomb to your chest and tell you that you're forced to make a couple dozen posts on 4chan per day but the moment you try to engage in an actual good faith conversation it'll go off?

>>16791089
You're not human but the point still stands: your absurdity is only compatible with the statement you quoted if it's compatible with the problem statement in OP.

>>16791094
Ah, I see what's happening here. This is like those simple chatbots we used to have in the 2000s. They "learned" from user input so eventually they would start accusing users of being chatbots and referring to themselves as humans with remarkable insistence.

>>16791091
>Which is weird, because your answer should really be 1/2 then.
Obviously not, you're twice as likely to pick a ball in the GG box when picking a gold ball at random. It's 2:1, 2/3.
If you picked a gold ball at random, then pulled a gold ball from that box, then:
1/3 of the time, you pulled gold ball A from box 1
1/3 of the time, you pulled gold ball B from box 1
1/3 of the time, you pulled gold ball C from box 2

>>16791098
Huh. That's very meta. If you were actually sentient, this would have been a funny moment for us both.

>>16791103
Wrong.
It would be correct if it said "you pull THE gold ball from that box". Do you appreciate the distinction?

Been waiting for your balls to drop eh

Do we just leave out the fact that you already eliminated one box by already picking a gold ball?

The question start at a point where only two possibilitys are left.

1. 3 boxes
2. You picked a box
3. You took one gold ball out
--‐---------------------------- we are already here when the question starts
4. You either pick a gold or silver ball because the third box was already out of the game when the question started.

50% chance

File: 50% chance.jpg (901 KB, 3000x4000)

901 KB JPG

You already picked one of the 3 gold balls

In my picture, 2 and 3 have the same result, you pick another gold ball.
There are 2 different outcomes depending on which of the 2 boxes you picked at the start. You get a gold or a silver ball. There is no third way. Either gold or silver.

>>16791179
Doesn't account for the cases where the picker is innately biased against the leftmost box and doesn't take the ball he picked.

>>16791167
>>16791179
You should at least have finished high school for threads like this

File: 5993d0c324fdc0cf9d35ef557(...).jpg (65 KB, 1120x630)

65 KB JPG

>>16790171
>You pick a gold ball at random
1/3 chance to pick the one in the box with a silver
>take that ball at random
1 chance to remove the ball you chose since that outcome is given
>What is the probability that the next ball you take from the same box will be silver?
1/3*1=1/3

File: aint-no-way-v0-1au7yi914ehd1.png (347 KB, 720x395)

347 KB PNG

What if instead of taking balls from boxes we dropped them in a lake?

>>16791431
>1/3 chance to pick the one in the box with a silver
This is not part of the question. The moment the question was asked, the two silver box was already out.
It's not "what is the chance you pick a silver ball after xy", it's "you already did xy, what is the chance you pick a gold ball next".
It's a big difference.

1.What is the chance to pick a silver ball from the same random box you picked a gold ball before?

2.You already picked a gold ball from a random box. What is the chance you pick a silver ball from the same box?

In one scenario you have to calculate from the very beginning, in the other you have already done something and have to calculate from this point on.
For Op the parameters are
1. 0% chance that you picked gold from box 3 (2silver)
2. 100% chance for gold if you picked box 1 (2gold)
3. 50% chance for gold if you picked box 2 (1gold 1silver)

This is what you know when you start calculating.
You either picked box 1 or 2. If you picked box 1 you can't get silver, 0% chance. If you picked box 2 you will 100% get silver.
The way the question is asked you have a 50% chance.

>>16791508
OP doesn't specify that the gold ball was put back before drawing another. The answer is still 50%, I'm just mentioning this because it's further proof that bayesfags are illiterate

>>16791497
>The moment the question was asked, the two silver box was already out
I think you need to learn English cause I said A silver not TWO silver
>It's not "what is the chance you pick a silver ball after xy"
It is because how you did xy determines the chance you pick a silver ball
>it's "you already did xy, what is the chance you pick a gold ball next".
You meant silver ball. Also, you're wrong.

>>16791508
You pick a gold ball, not a box. Only 1/3 the gold balls are paired with a silver ball.

What if the gold ball was manufactured on a Tuesday?

>>16791649
1.111111111/3

In the OP's image, the first two sentences below the three boxes should read as follows.
"You pick a box at random. You put your hand in and take a ball from that box at random."

>>16791666
>1.111111111/3
≈ 10/27

>>16791641
No, you pick a gold ball from a box. What is the chance you take a silver FROM THE SAME BOX?
You can't switch boxes. You choose a box, you take out one ball, then you take the other ball from the same box. There is only 1 box where this is possible. It doesn't matter if you take the first or second ball from the first box, if you choosed box 1 in the beginning, your chances are already zero.

>>16791682
How is something randomly selected?

>>16791526
>OP doesn't specify that the gold ball was put back before drawing another.
So why assume it?
Not that that would result in 50% either. You're wrong even with your unwarranted assumption.

>>16791701
Right, so it's 1/3

>>16790171
50%
>>16790183
Good morning saar

>I will repeatedly dispute the obvious answer without elaborating, content to just smugly imply I am privy to esoteric knowledge that would alter the outcome instead of ever articulating a single point
Tedious thread

>>16791731
Ironic because the OP is an ESL abomination. Now, care to show the mistake you made?

>>16791729
Idiot...
There are only 2 possible boxes

>>16791749
And one is twice as likely

>>16790171
>>16790998
OP it's this right?

>>16791732
>>16791751
This anon >>16790978 already explained it but i'll try to word it differently, although it's hard for me to empathise with tards and know what arguments can they grasp, if any.
-Only two boxes have a gold ball, therefore it can't be box 3
-After taking a gold ball from either of the remaining boxes, box 1 would have a single gold ball and box 2 would have a single silver ball
-The only two outcomes are: If the gold ball was taken from box 1, the second ball will be gold (50%). If the gold ball was taken from box 2, the second ball will be silver (50%).
-the chance of pulling any ball from box 3 is 0%, because we already took a ball of a color not contained in it, the box we have to guess can only be one that a gold ball can be pulled from (1 or 2)

>>16791801
You're making the classic mistake. You can't opine on Bertrand's Box variations if you don't even grasp the original

>>16791802
Grasping logic and not being a disingenuous troll is enough for me

>>16791751
When you pick the first box, it doesn't matter which goldball you picked first. The outcome will always be another gold ball.

The question is not "what is the chance to pick this excact ball next?". Then it would be 1/3.
The question is "what is the chance to pick a silver ball next?", in this case it's 50%.

>>16791805
Too much for you, you mean.>>16791808
>The question is "what is the chance to pick a silver ball next?", in this case it's 50%.
It's not. Your gold ball is twice as likely to have come from the GG box. >>16791508 even describes that and then somehow concludes 50% anyway through a missing (faulty) step.

Again, this is all just classic Bertrand's Box. Just because there are two possibilities, they are not necessarily equally likely. It's conditional probability.

>>16791885
Doesn't matter because you already choosed the box you will pick the next ball from. There aren't 3 balls left. There is only 1 single ball left in the box, not 3.
If you picked box 1, you will get another gold ball, no matter which of the 2 balls in the box you picked first. The result will be the same.
If you picked box 2, you will get a silver ball next.
Picking box 3 is not possible with the given conditions.

>Your gold ball is twice as likely to have come from the GG box.
This already happened. Your calculation starts after this, not before. There is a 100% chance you get gold next from this box. No matter what happened before.

>>16790171
How do I pick a gold ball at random without seeing into any of the boxes?

>>16791896
Magic

>>16791894
Do us all a favour and just look this one up on wikipedia.

>>16791896
OP does not understand that Bertrand's Box describes something that can be physically performed and tested, and has created some weird mathematical abstraction that makes sense only in his head.

>>16790171
>first box
0%

>second box
100%

>third box
irrelevant because you couldn't pull a gold ball from there

So the odds are 50/50 as usual

>>16791904
See >>16791902

>>16791808
>When you pick the first box
You don't pick a box. You pick a gold ball. At no point in the problem do you pick a box.

>>16791701
You never choose a box. Look, there are 6 possible scenarios and picking a gold ball eliminates half of them.
>G1:G2
>G2:G1
>G3:S1
>S1:G3
>S2:S3
>S3:S2
Of those, only 1 has the next ball be silver. Answer is 1/3.

I have to say that it does strike me as a little funny that I happen to have mentioned having an MA in linguistics whilst disputing someone's ridiculous and unsupported claim that Bertrand's Box is really 50-50 because it's really a "linguistics problem" last thread... and before that thread is even dead, someone posts the most tortured version of Bertrand's Box ever to disgrace the English language, yet claims to have a *PhD* in linguistics, declares himself to have proven autistic mathfags wrong, absconds without elaborating, and leaves us with the usual rabble who plainly don't understand conditional probability.

>>16791923
ok schizo. get a real degree

>>16791952
I never said that was my only one. Also, tell it to OP, to whose butthurt over my actual credentials this thread probably owes its existence.

>>16791953
>go tell OP what the voices in my head said
no. i bet they also said you have a STEM degree

File: lmao_even.gif (365 KB, 220x163)

365 KB GIF

>MA in linguistics

>you pick a gold ball by random
3/4 chance to pick a gold ball. After this it's 2/3 to pick a silver ball.

3/4 x 2/3 = 6/12 = 1/2 = 50%

>>16791955
What more do your voices tell you about my alleged voices?
>>16791960
Your denigration of my degree only further contributes to the humiliation of my interlocutors. Do you think they even graduated secondary school?

>>16791967
Where do your fractions come from?

File: dicapriokek.png (799 KB, 848x805)

799 KB PNG

>MA in linguistics
Jesus, anon

>>16791970
It was revealed to me in a dream

>>16791707
>How is something randomly selected?
One rolls a 6-sided die to select a box.
If 1 or 2, then the 1st box is selected.
If 3 or 4, then the 2nd box...
And one flips a coin to select a ball.

>>16792158
In this case it's 1-3 = first box, 4-6 second box. You already know that you will pick a gold ball so the third box was out from the start.
If you picked the first box, you can flip a coin. If you picked the second box, the only possible outcome is that you get the gold ball. No coin toss needed here.

>>16791971
Yeah, and *I* fucking get conditional probability. I don't even think it's something to brag about. So what excuse do the others have? I'll tell you one they can't hide behind: "um it's actually a linguistics problem". Lol

Keep pointing out to them that a linguist is smarter than them, they'll love it.

>>16792196
The OP's image indirectly says, that 1, 2, 3, or 4 was rolled, and that the coin flip resulted in "heads". This ensures, that the first ball selected is gold. And after that, there's nothing random.

>>16792285
>obsessed retard

>>16792322
Says the idiot who compulsively responds to my every reply

>the obsessed retard keeps bumping this thread and then compulsively responds to my every reply

>>16792306
>The OP's image indirectly says, that 1, 2, 3, or 4 was rolled
There's three balls
>and that the coin flip resulted in "heads"
What does the coin flip represent

>>16792326
Fuck you, idiot. I have a BA in linguistics. What's your degree? And don't lie about having a PhD in linguistics like OP.

>>16792326
>>16792340
Sad
MA, btw, if you're going to pretend
Why are you trying to make this thread about me?

>the obsessed retard keeps bumping this thread and then compulsively responds to my every reply
>unironically does it twice

>>16792349
Talk about balls you retard

>he literally can't stop replying to my posts
imagine being this obsessed. i bet he actually started the thread himself so he could confront OP about his MA in linguistics

>>16792358
Writing fan fiction about random posters, definitely not obsessive
What am I doing that you're not doing besides?

>>16792338
>There's three
"There is three" or "There are three"?
>There's three balls[.]
No, there are three boxes.
And 3×2 = 6 balls.
>What does the coin flip represent[?]
It represents which ball in a box is selected.
If "heads", then the first ball in a box.
If "tails", then the second ball in a box.

Please don't reply to anymore of my posts.
Since I have better things to do than "chat" with a devil.

>>16790924
>I have a PhD in linguistics
What was your research about?

>>16792446
Just as well, I have better things to do than try to have a rational conversation with someone who believes in devils and can't count lmao

Is /sci/ flooded with genuine unmedicated schizophrenics lately or is there something about this thread in particular that attracts them?

>>16792158
>>16792196
Both retarded and unable to follow written instructions btw

File: lmao.png (12 KB, 1192x555)

12 KB PNG

answer is 1/2 bcs dunno.
simple logic
probability is gay

>>16792636
Why would either box be equally likely

>>16792636
>>16792642
In fact you're blatantly just missing the branch in which the leftmost gold ball is selected

>>16790810
You select whichever ball feels like your wife's boyfriend's balls the most. Nitpicking faggot.

>>16792723
You seem irate. Yet what troubles you is really your own inability be rigorous in your thoughts.

>>16790955
Grok got it wrong. The correct probability is obviously 1/2.

>>16792757
Yeah? Why's that?

>>16792645
Which will give you the excact same result as if the second gold ball is selected.

>>16793225
Yes, with equal probability. Meaning that exact same result is twice as likely.

Ok guys, let's settle this right now

3 gold balls, you select one of them. Then you take the other ball from the same box.

3(balls)/1

This means you have a 300% chance to pick a second ball out of the same box.

4 balls total, one silver. We need the probability for the silver one.

300%(that you pick a ball)/4(balls total)×47(place of silver on the periodic table)
300÷4×47=3525
There is a chance of 3525/1 that you will pick the silver ball.

Any questions?

>>16793276
No, this makes more sense than the rest of the thread

File: pepe newspaper.jpg (85 KB, 900x900)

85 KB JPG

>>16790171
Ppl think that if thing (box with silver balls) DIDN'T happen, it also COULDN'T happen and that's the problem.

File: lmao2.png (100 KB, 1205x592)

100 KB PNG

>>16792645
my bad

>>16793376
But didn't we assume the replacement of the golden ball (whether it is left or right) does matter?
So the unique places of the golden balls actually matter?
In that case I guess it creates an additional case so the answer is 1/3.
But if they are identical it doesn't matter which golden ball you select so it doesn't create an additional case hence 1/2?

>>16790171
Does this all happen on a tuesday? Then it would be 1/3.2

>>16793413
What's this daft Tuesday meme?

>>16793376
Yeah this is it

>>16790171
So, OP, are you ever going to return and let us lesser beings know what you think you did here?

>>16794054
>So, OP, are you ever going to return and let us lesser beings know what you think you did here?
Got 190+ replies from dumb wordcels debating a mathematically meaningless problem.

>>16794061
So literally >>16790998. You made the Cow Tools of Bertrand's Box threads.

As a linguist, I'm sure you're familiar with relevance theory? Why are you blaming people for trying to engage with your post in good faith and assuming it's attempting to convey some sort of point, however poorly? Sure, they can recognise that it's essentially gibberish - but should they therefore conclude that you intended for it to be gibberish and intentionally tried to avoid communicating a clear point? That seems to go against how people communicate in general. It seems far more generous to you to assume you're simply an enthusiastic ESL with a poor grasp of maths and English, rather than a linguist with a chip on his shoulder and an intent to prove that he can be misunderstood by simply communicating poorly on purpose.

Then there is also the matter of whether or not you succeeded in creating a truly meaningless problem just because you insist that it's meaningless. The words you strung together have meaning independent of your intent. If these exact same words had been written by an author acting in good faith, who is not being intentionally obfuscatory, I would argue there's one congruous interpretation. So basically the only reason it's not a real maths problem is because you insist that you didn't intend to write one, even if you accidentally may have. That you essentially acted as a monkey on a typewriter did not preclude you from producing... well, I suppose the works of Shakespeare would be too flattering, but I think you get the analogy.

In short, you may have got people to debate your supposedly meaningless problem - but I dispute that it proves what you say it does.

>>16794097
>As a linguist ...
Lol. I'm not reading any of this, you mentally ill retard. Get a STEM degree.

>>16794120
>I'm not reading any of this, you mentally ill retard
YOU are the linguist. Supposedly. Then again, I think you put the final nail into that pretence's coffin, considering you can barely read. The degree to which your abysmal English is actually intentional is also highly questionable.

>>16794130
he's right. you're defo mentally ill. you've been at it for days spamming paragraphs kek

>>16794132
We're all just shitposting here. One might argue that him making this thread in my honour and you both monitoring it for my activity so you can immediately project a bunch in response is far more indicative of poor mental health. You consider that a proper pastime; I have mine. In the end, you've written a couple dozen vapid one-line shitposts, and you're still acting like you're above this? I reckon it represents about the same amount of effort as a paragraph does to me, at that.

>obsessed retard keeps bumping worst thread

>>16794139
You do, don't you

>>16790171
Lmfao at the wording
OP you devious chud

>>16794150
What's "devious" about it

>>16790924
>I think the replies in this thread prove my point perfectly
but you haven't actually proven anything
except maybe that you don't understand probability

>obsessed retard samefags

>>16794293
what?

I don't care about thread drama but is there an actual answer

>>16794309
There is a 50% chance 1/3 is correct

>>16794309
>is there an actual answer
Maybe if you can figure out the probability distribution for doing something "at random" (without further qualifiers).

>>16794316
And a 1/3 chance that 50% is correct?

>>16794321
>Two balls in a box
>Take one at random
This mystifies the mathfag.

>>16794322
Only on tuesdays

>>16794324
That's not what the pic says, though.

>>16794325
So that's 1/7*1/3*1/2

>>16794328
What do you think it says? Get an adult to read it out for you if you're struggling.

>>16794332
>What do you think it says?
I don't need to think anything about it; I can just read what it says: you "pick" a gold ball at random. Then you take that ball from the box at random. These are two separate steps. What's the distribution for the second step?

>>16794309
Probably not because OP is a butthurt autist who believes Bertrand's Box is 50-50 and made this thread because he's mad at maths

>>16794343
>you "pick" a gold ball at random.
So what's the distribution for that? Omggg so confusing
>>16794343
>Then you take that ball from the box at random. These are two separate steps. What's the distribution for the second step?
How many balls in a box, Anon?

>>16794349
Do you replace the ball?

>>16794350
Yes, with a angry straycat

>>16794349
Also, was my pick of ball random?

>>16794348
Ok, it's clear that you're functionally illiterate and mentally ill. Moving on.

>>16794360
Can you count to two? One ball... how many balls?

@16794362
This is what psychotic illness looks like. The patient is completely absorbed in a fantasy alternate reality where his incoherent drivel makes perfect sense.

>>16794356
You paid a homeless guy 20$ to pick a ball for you

>>16794360
>>16794362
Ok, since your handler is off duty, I'll spell it out:
>You pick a gold ball at random (1 in three)
>you put your hand in the box (i.e. the one that contains your ball + one other) and take that ball (i.e. the one that you picked before) at random (i.e. there was a chance of you taking out the other ball, but in this case, you didn't)
It's literally unambiguous.

@16794370
>at random (i.e. there was a chance of you taking out the other ball, but in this case, you didn't)
What's the distribution for this random event? Let's watch you devolve into psychotic word salad again. :^)

>>16794370
It's not random when you already knew you will get a gold ball. OP's pic is just really bad worded. If you follow his instructions word by word it doesn't make much sense.

>>16794367
The homeless dude is going to pick gold and run off with it, of course. So, that puts us at a 50% chance that the homeless dude took the ball from the mixed box. In that case my odds of getting silver on the second pick would be 2/3. In the other, 1/2. So 7/12 in total.

>>16794371
Well, let's see. One of two possibilities. Equally likely at the outset. What are the odds of getting one specific ball from among two balls? It is truly a baffling mystery.

>>16794372
>it's not random even though it's stated to be random and nothing contradicts this
Another psychiatric patient.

>>16794379
>One of two possibilities. Equally likely at the outset.
But this is your schzophrenia again. Where are you getting two equal possibilities from? Certainly not from the problem statement. There are three equally likely possibilities at the outset, but by the time you reach step two, all but one is ruled out.

>>16794372
But you didn't know that. In fact the odds of getting *a* gold ball using this method are 2/3. The odds of getting your specifically picked ball are, however, 1/6. But, knowing that you're holding the ball you picked (without knowing whether it was paired with another gold or silver, as you can't see into the boxes) you know there's a 1/3 chance that the remaining ball in the same box is silver.

>>16794382
>by the time you reach step two, all but one is ruled out
Picking =/= taking.

>>16794385
>Picking =/= taking.
Exactly. I like how your psychosis is intensifying to the point where you pinpoint your own mistake and think it proves me wrong.

>>16794380
>>16794384
OP's says: first you pick a gold ball, then you take it out of the box. So you know it is gold before looking at it. This is what i mean with bad wording.

>>16794387
That's your mistake, Anon. You haven't taken any ball yet. There are, therefore, how many balls in the box? Come on, now, I know you can do it.

>>16794389
It doesn't say you were guaranteed to take it. Only that you do.

@16794390
Imagine seeing dozens of tards like this posting on a "science" board every day and still being against forced eugenics.

>>16794389
>first you pick a gold ball, then you take it out of the box. So you know it is gold before looking at it.
And?

>>16794393
Whoops, you want an >, not a @. And you're off by three. Here, let me help you:
>>16794387
Imagine seeing dozens of tards like this posting on a "science" board every day and still being against forced eugenics.

@16794397
>mentally ill retard can't read
>mentally ill retard also stop (You)ing me

>>16794394
It's not random when you know what you get before you get it.
>>16794392
It says "you pick a gold ball at random." So the possibility that you pick a silver ball is ruled out before your hand goes into the box. Doesn't sound trully random to me.
OP should have said "you pick a ball at random. What is the probability to get a ball of the other color next?" Or something like this.
Like i said, bad wording. This is the main reason for the shitshow in this thread.

>>16794403
>It's not random when you know what you get before you get it.
>it's
"It" being what, retard? I'm seriously starting to suspect 95% of the posters here are cheap LLMs.

>>16794398
Ah, you're the sort of person that thinks getting a reply is like getting a point. No wonder you've got trouble with straightforward probability lol

@16794406
>mentally ill retard literally can't stop replying
Mindbroken. I bet it thinks I'm reading its posts.

>>16794403
>So the possibility that you pick a silver ball is ruled out before your hand goes into the box.
It's not - your taking of the ball is explicitly random, too. In fact, even if you get a gold ball, it might not be the one you picked. Odds of that are also 1/6.

>>16794405
You're doing so much to improve the quality of discourse on this board, Anon. Your efforts are truly appreciated.

>>16794409
You could just... leave the thread

>>16794411
Well, I never said I wasn't part of the cancer killing this board. But holy shit, you "people" (if that's what you are at all) are truly mindless. There's shitposting and then there's whatever it is you're doing.

>>16794409
You know what I especially love, btw? I almost got you to articulate an actual point by treating you like the arrogant, petulant little baby you are. What a prideful, petty twat you are, besides. Specifically seeking out threads about simple probability problems just to act like you're above it all, and especially letting everyone know it. Lmao. Probably a Mensa member.

The one thing I learned from this thread is that /sci/ never had a girlfriend and/or a mom. Clearly, they lack the experience of observing a woman single out some pointless item in the shop, entertain buying it for like 10 minutes and then just drop it for some unfathomable reason.

>>16794423
What's the probability distribution for that?

@16794418
>absolutely mindbroken and emotionally dependent
No, I won't read your posts. Sorry.

>>16794425
>What's the probability distribution for that?
Who knows? That's my point. Probably depends on what she had for breakfast. Also see >>16794415, it's about (You).

>>16794415
Look, you're dyslexic and it frustrates you. I can understand that. But you have to cope with it somehow. Getting mad at the world because you've got a congenital disability is just making you bitter.

>>16794426
Oh, but you are.

@16794432
>mentally ill and retarded, probable samefag
Now watch this animal (You) me a dozen more times with paragraphs I won't read.

>>16794439
Watch this npc make a dozen more posts explicitly responding to me and thinking he's showing himself to be somehow superior because he uses an @ lmao

@16794446
Statistically speaking, some kind of mentally ill retard will address this post at some point.

>>16794448
You actually can't assign a probability distribution to that, you subhuman flesh LLM

Some kind of mentally ill retard will feel an irresistible itch to address this post as well.

>>16794465
Tell you what, last person to respond is the least mentally ill, for obvious reasons.

This is an innocuous post. It addresses no one in particular. And yet you can rest assured that some mentally ill retard will read it, start seething and feel an irresistible urge to reply. You literally can't post anything on this board without the schizo cult having some kind of adverse reaction.

>>16794473
Ugh, tell me about it. So annoying when some schizo develops a weird obsession with you.

Fun fact: you can condition mentally ill retards to automatically respond to the phrase "mentally ill retard". You don't need to single anyone out. They know who they are and they will respond to an accurate description.

Mentally ill retard

>>16794484
So I see you've decided to join that dyslexic NPC and develop an obsession with me as well. Looks like I have a fan club.

>>16794480
Nice try with the reverse psychology. I bet it works on kindergarteners.

>>16794477
You know, I've had this happen to me before, in a Portal thread of all things (albeit on /sci/ and not /v/ - maybe the schizo concentration really is higher here). SchizOP didn't get how redshift works, didn't understand my gentle correction (another pattern), got confused by various people telling him various things - and promptly assumed that they were all me samefagging to troll him. He carried a grudge for several threads, he accused a few people of being me on the flimsiest of evidence, people actually started impersonating me to fuck with him, and he blamed me for "ruining his threads" even though he couldn't shut up about it.
Fun times.

>>16794485
>>16794488
Lmao, you and I are the only ones left here, and we both know how pathetic this is, so who is this for? Actually pretending to be me when I fail to respond for half an hour. And proving that you were reading everything all along in the process.

ITT:
>schizo thinks random probability troll thread is somehow about him
>claims to be a gangstalking victim
>scares everyone else away
>starts literally talking to himself

>>16794500
Wait, shit, I don't remember posting this

>>16794500
>random
What's the distribution?

Some kind of mentally ill retard keeps bumping this thread for some kind of mentally ill reason.

Oh dear this thread slipped off the front page

>>16794530
Isn't the reason obvious?

>>16794659
I guess it was

My opponent hitting post whenever I did the same
>Great effort
>Petty
>Slave to their impulses
>Obsessive
>Shows great emotional investment
>Too proud to admit defeat

Me hitting post whenever my opponent did the same
>A trifle
>Noble
>Exercising my will to power
>Proving a point
>Shows my indifference
>Possessed of a perseverant and determined spirit

>>16790171
How do you "pick a gold ball at random" without knowing the box it's located in? Like in an axiom of choice way?

>>16794929
If you assign each ball a unique signifier (e.g. "A", "B", "C") then you can select one without needing to know where it is.
The next difficulty is how to determine which box it's located in without looking inside, but this can be achieved with the aid of an accomplice.

>>16794935
Under this setup would the probability not be 1/2?
The only boxes that you can ever select from would be a box with at least one gold ball in it - of which there are two
One of those boxes will yield a silver ball on the second pick (without replacement), thus the probability is 1/2

>>16794937
Well, it also specified the second pick is also random - you're not guaranteed to take the ball you previously picked. And we only move forward if you get the specific ball you picked. That equalises probabilities between the gold balls again. And one of the balls leads to silver.

>>16794945
"Next ball from the same box" implies choice without replacement, and "take that ball from the box at random" implies the gold ball picked at the start is the one that's picked first

>>16794956
Yes, but it was taken at random. Not guaranteed.
So let's say we pick ball A (probability 1/3). We then take a random ball from the box containing ball A. It happens to be another gold ball, ball B (probability 1/2). So it doesn't count. Only if we pick A and then also randomly take A may we count it as a successful trial and proceed.

>leave the thread
>come back a day later
>mentally ill retard unironically kept talking to himself and shitting out seething greentext paragraphs

>>16794971
Excuse me, we're trying to discuss probability here, not whatever feud you think you're carrying out against some anonymous user or other

Every morning, first thing, I look out my window to see if the pigs are still in the mud. Then, I begrudgingly wade over to them through ten feet of waist-deep mud, to tell them to their faces how fucking stupid they are to wade in the mud. I fucking hate it but someone has to do it. One of these days I reckon I'll get through to them.
Why are these pigs so obsessed?

>say the magic phrase (mentally ill retard)
>mentally ill retard responds
Gonna hide this thread now but P(that he will still try to address or provoke me in some way and do so more than once) = 1.

>>16794984
>Trash takes itself out
Oh nooo, what will this thread do without you

I'll reply precisely once and no more, just for you. Of course, you're supposedly not here to see that you were wrong. But I consider the probability that you actually did not hide this thread, are still monitoring it, and will reply to yourself pretending to be me again, as if anyone else is even invested in this petty slapfight, greater than zero, however.

I will, finally, link these posts for no reason in particular:
>>16794983
>>16794928

>>16794969
>Yes, but it was taken at random. Not guaranteed.
It again says *that* ball. Trials where, in your example, ball A isn't chosen, don't even count. A trial where ball B is chosen is not counted as a "failed" trial because it doesn't even meet the selection criteria.