Thread 16790171

New balls dropped.

>>16790171 (OP)
1/3

>>16790183
Wrong.

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

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

>>16790171 (OP)
>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 (OP)
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 (OP)
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.

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.

>>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"

>>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.

>>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

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

>>16790171 (OP)
>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

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.