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File: 1459888119410 (2).jpg (129 KB, 701x576)
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If you spend your days grabbing balls from boxen, does you a faget be?

inb4 fuck the 2/3 gayops
>>
>>109341137
40%
>>
>same box
4/9
>>
>>109341137
Your brain is worthless.
>>
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>>109341197
Bump for 50/50 CHADS

WINNING !!!
>>
>>109341137
If I've already reached into the box and got a gold ball, that means I've either picked a gold box or a mixed box. So 50%.
>>
2/3 FAGETS ARE THE MINDKILLER

I WILL NOT FEAR THE 2/3 FAGET
>>
>>109341218
Nope. If you picked the gold box there are two different gold balls you could pick out. Which means there are three possible scenarios, even though there are only two valid boxes. Care to admit you're wrong or are you going to double down?
>>
>>109341237
I double downed your mom last night
>>
>>109341137
It's a semantic problem.
The "it's a gold ball" sentence is not compatible with the two previous statements.
>>
>>109341137
100% unless it's a silver ball.
>>
>>109341137
50/50
either the next ball is gold or it isn't
>>
6 potential paths to choose
gg gg; gs sg; ss ss
ab ba; cd dc; ef fe
--------
3 paths remain after excluding all non viable paths
gg gg; gs
ab ba; cd

the answer seems trivial
>>
>>109341137
depends, is your other child born on a tuesday?
>>
>>109341269
Probability Math is a mossad psyop
>>
>>109341272
Only my wifes son as we double team her with 4 balls in her box
>>
File: u499mvuafmy31.png (56 KB, 200x200)
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What if there is no silver ball.
>>
>>109341269
Exactly.
>>
>>109341269
Wat about bbc?
>>
File: output (7).jpg (30 KB, 640x640)
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50/50 MASTERRACE REPORTING IN
>>
>>109341137
First thing first: If you pick the left box the probability for gold ball next is 100% on the left box and 0% on the middle box, so it's the combination of how often you pick which box.

The trick is in the assumption. It says you pick a box and a ball at random, but it also says you picked a box with a gold ball and within that box you picked the gold ball specifically. That's a limited set of the random outcomes. Within that limited selection, the scenario of picking the middle box happens half as often, since half of the scenarios lead to you picking the silver ball, which are not included in the set of outcomes. Whereas, every picking of the left box is included.

Basically you keep doing the random pick, and whenever you land on a silver ball, it didn't count because that's not what the scenario was about, it was about the situations where you picked the gold ball. Out of all of the outcomes that "count", you picked the left box twice as often.
>>
>>109341260
You are halfway into the solution
>>
Should 2/3 degenerates be rounded up for th>>109341355
e gulag?
>>
>>109341343
What if i pick my left ball then my right ball?
>>
>>109341382
you're gonna cum
>>
Your probabilities are siloed to the 2 options of box 1 or box 2. 50/50
>>
>>109341408
I siloed my balls in you moms backpussy last night
>>
>>109341237
Double down of course. This fucking "paradox" is a semantic, not a logic problem and the problem is that the question here might be ambiguous, but the way I read it, Omega is not a set of {gold, mixed, silver}, it's a set of {second gold, second silver}.
In other words, if you were to do it experimentally a 1000 times and count it, your answer would be correct if you wrote down each two draws and counted the all golds to first gold ratio. But the way the question is phrased, you only started counting after having taken out a golden ball. If there were no silver boxes, it'd be 50%. If there were 99 silver boxes, it'd still be 50%, you'd just take longer time before each new item.
>>
>>109341439
This.

FOR RETARDS IN THE BACK ROWS
ITS 50% 50%
ITS NOT MONTY HALL PROBLEM
READ THE FUCKING SHIT
50% 50%
>>
It's actually 33%

In the beginning there are three golden and three silver balls.
You take a golden ball out so now three silver balls are left and two golden. Which means 2/3 chance that next ball is silver and 1/3 the next one is golden.
>>
>>109341479
Yeah, the 2/3 faggots dont consider the 0% practical outcome when they claim GO TEST IT URSELF MY NUMBERS IS RIGHT A JEW TOLD ME

They are functionally bred to be slaves to KIKES

If you see 50% YOU ARE ARYAN
>>
>mathematics
clearly a portal to demons. They aren't physically here.. yet
>>
what sort of experiment would you devise in real life to simulate the problem and get the answer
>>
>>109341519
I'd silo my balls in your moms backpussy
>>
>>109341519
Simply make a game
Every round pay the retards $20 of a $10 bet if the next ball drawn is not gold. If it is gold you keep the bet. Once the retards lose all their money they will realize it's only 1/3 probability of the next ball not being gold
>>
>>109341519
Consider anothef version of the scenario.
>A neighborhood has 3 houses: one with a lesbo couple, one with a gay couple, and one with a heterosexual couple
>You don't know which is which, because they all have pride libtard flags on their lawn
>You knock on one of the doors and hope to call the gays or lesbos a homophobic slur
>A man opens the door
What is the probability that this guy is a faggot?
>>
>>109341560
Probability of 1, liberal suburbia is entirely gay
>>
>>109341547
YOU CANT SWITCH BOXES YOU FUCKING RETARDED PIECE OF SHIT
>>
>>109341582
Nobody switched anything.
Play this game yourself with 3 boxes. Whatever ball you pick make a bet the next ball you choose out of the same box is a different color.
Your probability of winning is only 33%
>>
THERE ARE NO 3 POSSIBLE OUTCOMES ONLY 2
THERE IS NO G1 G2 G3
ITS ONLY NEXT BALL FROM THE 1 OUT OF 2 BOXES YOU PICKED GOLD BALL FROM
AND ITS EITHER GOLD OR SILVER
AND THAT ONLY DEPENDS ON WHICH 1/2 BOXES YOU PICKED GOLD BALL FROM.
>>
File: 1784725828625842.jpg (1.08 MB, 1000x4000)
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GOOD EXPLANATIONS DONT REQUIRE A FUCKING BOOK YOU 2/3 NIGGER CATTLE
50% 50% DECIDED ON BOX PICK
GTFO
>>
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>>109341613
FUCK THIS FAGET
>>
>>109341620
Another way of wording this question is, what are the chances that you picked 1 if the first ball you pull is gold?
>>
>>109341631
Which ball do you pull?
>>
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/g/ - Technology
the board that hates coding
>>
>>109341647
Yet it loves pribability and logic
>>
>>109341639
the ball in the box. The question is whether the box has one or two gold
>>
>>109341656
Yes but which do you pull?
>>
>>109341663
the one in the box i picked. Did i pick gg box or gs box?
>>
>>109341674
You picked the bb cox
>>
>>109341682
>immediately starts posting about nigger dicks
par for the course
>>
>>109341691
You're the one reaching into the mystery box with two balls.
>>
2/3 SUBVERSIVES ARE ENEMY OF THE STATE
>>
I only need 2 boxes and 4 balls because box 3 is not relevant to the question, so it'll be 50/50 disrobing distribution
>>
>>109341702
>>
>>109341674
You are failing to comprehend the prompt and are just focusing on the boxes lmao. You’re an idiot with low IQ and now this whole thread knows you’re dumb
>>
The Pool of gold balls is finite, at 3
The Pool of boxes that COULD contain a gold ball is finite, at 2.
The Pool of balls left between those 2 boxes is finite, at 3
The Pool of gold balls left between those 2 boxes is 2.

Thus 2/3 =
66%
>>
>>109341737
POOL OF BALLZ !!!!!!!
>>
>>109341613
What percentage of gold balls have another gold ball neighbor in the same box?
>>
1/10th
>>
>>109341717
no, it'll still be 66% because there are 3 gold balls and only two of them are in a box with another gold ball
>>
File: 1765853880959522.jpg (58 KB, 683x449)
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>>
>>109341755
400% because my wifes son and I are double teaming my wifes box
>>
>>109341762
Nice try CIA glowIE.

The truth will not be suppressed by your propaganda mind control. Your 5G towers wont rewrite our minds with 2/3 bullsit
>>
>>109341777
wtf
>>
>>109341647
/lit/ hates reading
/sci/ hates science
/a/ hates your favourite anime
>>
>>109341836
can i post my favorite anime girl on /g/?
>>
>>109341830
4 balls gives 400%
>>
>>109341844
Only if she has six balls and three boxes
>>
>>109341853
i think she technically has three boxes but i prefer them ball-less
>>
>>109341137
why can't someone that isn't me code this up? you (not me) can even use AI to do it
>>
If the 50/50 fags are so sure, you should go setup this game in public, where people line up to pick a ball from a box. If they pick a gold ball, they get shown a flyer with this question and then they can bet for either gold or silver. You can set the bet multiplier to 1.6x (shitty 80% return to player). A few desperate idiots might bet silver ball, but for most people, the return rate would look like a complete rip-off.

However, then my 2/3 gang shows up, bet gold every time and backrupt you in an hour because the actual RTP is 106.67% when betting gold ball only.
>>
>>109341897
> you should go setup this game in public, where people line up to pick a ball from a box.
This sounds like some genre of german porn
>>
>>109341932
Porn where I become rich and you go bankrupt
>>
>>109341942
Is tgere much money in gdrman ball-box probability porn?
>>
>>109341897
2/3 GANGBANG FTW
>>
i'm siding with the anon who is talking about human balls
>>
>>109341137
>put the ball back in the box
>lift every box and pick the one which feels the heaviest
>?
>profit!

checkmate atheists
>>
>>109341137
didnt read
its 50%
>>
>>109341584
You don't need 3 boxes. The word problem eliminated the box with 2 silver. And it asked the probability of the ball [from the same] box.
There's only 1 ball left, you're not choosing it. It's going to be either Gold or Silver. 50-50
>>
>>109341584
No. The problem being asked is you take out the golden ball once out of one of two boxes, one of which has a silver ball, the other has no silver balls and start betting which is which. So you end up with 50% because you don't redraw the first golden ball ever, because it and the box with two silvers is a herring.
>>
>>109342124
however there are 3 golden balls, all three are equally likely
>>
>>109341137
For the statlets: you need to calculate the probability of each selected box being both chosen and drawing a golden ball. And then normalize the probabilities.
>>
File: 1452656797390.jpg (55 KB, 625x305)
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>>109342140
The setup of the question removed one of them, and now there are two golden balls. You end up with two possibilities:
{(S, GG); (G, GS)
, either of which has 50% of possibility. The draw being asked happens later than you think it is.
>>
but I don't have a box
>>
>>109342205
you do have two boxes, anon
>>
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>>109342196
so is this also 50%?
>>
>>109342210
I have two balls
>>
>>109342219
and two boxes right
>>
>>109342140
You're not picking a box. You're not picking a ball.
There's only 1 ball in this final state. It asked which color is it. The color.
>Not which box
>Not which ball
>What color?
>>
>>109342231
AI post
>>
>>109342216
yes
it's either one of the 259 gold or one of the 259 silver balls
exactly 50%

dumb thread tbqh
>>
File: none of this matters.jpg (693 KB, 701x958)
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>>109342216
Yep. Was considering removing one golden ball from the modified pic, but left it in to drive home it doesn't matter either.
>>
>>109341647
based monte carlo enjoyer. i know nothing about probability or statistics yet can always get a ballpark figure with this method
>>
>>109341620
If the selection was random, but you always get a gold ball, that means you have the Midas touch, and the actual answer is 1/3
>>
It doesn't make a bit of difference, guys. The balls are inert.
>>
>>109342361
"you have a golden ball in your hand" is not equivalent at all, because the full scenario contains crucial information about how the golden ball was picked, which determines the answer, because you have to pick from the same box as the first ball.

So, when you pick a ball at random in a way that allows asking the question (getting a gold ball), it likely came from the left box.

50/50fags fail to understand the probabilistic mechanics of the hypotheticals, which creates all sorts of weird issues. They think along the lines that after picking the box, the question magically forces them to pick the one gold ball from the 259 silver balls. It doesn't do that. The ball is picked at RANDOM.

In similar manner, they probably magically think that picking the full silver box is impossible, which is wrong. Picking any of the boxes and balls is equally likely, though picking the full silver box doesn't change the probability of the limited set of situations being asked about. The question only comes to effect, if/when after the prescribed random pick landed your hand upon a gold ball.

The language "It's a gold ball" is a little tricky, it's blunt and almost sounds like the choice was forced, which it wasn't, and makes you easily forget that getting the gold ball was a result of a random pick Other ways to word it without changing the meaning is "You picked a random ball, and got gold ball" or "assuming that the random pick gave you a gold ball, what is the probability of..."

The way of picking the balls is definite, but the question then concerns a limited hypothetical scenario within the full range of possibilities. Within that limited hypothetical scenario of the random pick landing on a gold ball, it's more likely from the left box than center which informs the probable result of the second pick.

Hope this helps.
>>
>>109341137
Number the balls left to right from 1 to 6. If the first ball is gold, it's either 1, 2, or 3. If it's 1, the other ball is gold. If it's 2, the other ball is still gold. If it's 3, the other ball is silver. So the answer is 2/3.
>>
>>109341647
nice one, gg bro
>>
the 50/50fags just completely ignore half of the question, which is a required section, just because it's stated as a past action.
>You choose a box and take a random ball, what is the probability that the ball still in the box is gold if the one you picked is also gold?
>>
>>109343012
>The language "It's a gold ball" is a little tricky, it's blunt and almost sounds like the choice was forced
It sounds live the choice was froced because it was. You can write extra paragraphs of cope about how the question doesn't mean what it means but in essence the question tells you have a golden ball and now start guessing if the box is one of the two configurations. If >>109341647 was done accordingly with text of the problem, it would start an inner
while(true):
loop in
if second_ball == 'gold':
clause and perform random draws there (and end up with 50%). Which doesn't make sense, but that's my point - that the question is wrong. The proper question the answer to which would be 2/3 would be something like "What would be the probability of you having chosen a box with two golden balls if you chose a box and drew a golden ball from it?" But with this clear wording nobody would be fooled. Instead you are told to consider the random chance after the conditional part is removed from the equation. I can't explain it in more simple terms.
>>
File: 1772764725484964.jpg (38 KB, 636x424)
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The underlying issue is similar to the portal question. When the question is a slightly vague, you have to fill in a coherent reality around it, at which 2/3fags and and Bfags succeed, whereas 50/50fags and Afags require weird new physics or magic that contradicts the question.
>>
>>109341137
There are 6 balls. The first 3 are gold, the rest silver.
You roll 1d6 and pick up the appropriate ball. You get a gold ball, so you must have rolled 1, 2, or 3.
Also, the balls or in boxes or smth, and you're in one of these boxxy scenarios:
> 1: Ball A1. Other ball is A2, also gold.
> 2: Ball A2. Other ball is A1, also gold.
> 3: Ball B1. Other ball is B2, silver.
>>
>>109343395
That's a good comparison. When a question is incoherent 2/3fags and and Bfags create a new reality to accomodate the problem, while 50/50fags and Afags run the bitch to ground where it belongs.
>>
File: output.webm (1.05 MB, 1920x1080)
1.05 MB
1.05 MB WEBM
>>109343395
that's different because Afags are correct in the case where the top beam is slow enough
both cases can happen, it just depends on the speed of the portal
>>
>>109341463
>ITS NOT MONTY HALL PROBLEM
Why do 50/50 dumbasses always say this, as though it has any relevance?
>>
File: 1742497960078858.png (57 KB, 236x254)
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>>109341137
50/50 brainlets seething at 2/3 chads. How long did it take you to solve the captcha to make this thread?
>>
100%, because I can apparently transmute silver to gold just by touching.
>>
33%
>>
>>109341137
2/3

The trap is thinking there are now two possible boxes, so it must be 1/2. But the gold–gold box had two different ways to give you the first gold ball, while the mixed box had only one.
>>
50/50 brainlets also don't understand that even if we dismiss the silver box entirely it's still 2/3. It's even more intuitive in fact.

If there are two boxes, one has two gold balls, one has a silver ball your odds of picking a gold ball are 3/4. Now there are two gold balls left and one silver ball so the odds are 2/3.
>But you can't switch boxes!
Makes zero difference. The fact you got a gold ball on the first pull makes it statistically more likely you have the box with two gold balls.
>>
>>109343334
>It sounds live the choice was froced because it was.
No, it wasn't forced, it explicitly defined as being random. Being forced or magical is your interpretation, but it contradicts the stated fact so you can't just add that.

>You pick a box at random. You put your hand in and take a ball from that box at random.
This describes the methodology of your action
>It[the ball, which you picked up at random, from the randomly chosen box]'s a gold ball.
This is a description of the outcome. It doesn't contradict the facts of the methodology. You are incorrectly interpreting it as "It must be a gold ball" "You were forced to pick a gold ball", which contradicts the methodology. This interpretation is not required, but seems psychologically attractive to automatic thinking or easy to overlook.

>"What would be the probability of you having chosen a box with two golden balls if you chose a box and drew a golden ball from it?"
Yes, this is essentially the original question (yours is missing the randomness) but with only the addition of "if"
>"You pick box at random. You put your hand in and take a ball from that box at random. IF it's a gold ball, what is the probability that the next ball you take from the same box will also be gold?"
which is assumed when dealing with a hypothetical question like this, and which makes the intent easier to understand. The addition of "if" also doesn't change the logic of answering the question: in both cases, the methodology of how the ball was picked is fundamental to calculating the probability in the answer. You can also say "assuming it's a gold ball" or "in the case you picked a gold ball".
>>
>>109343334
the simulation you quoted does exactly what the text says, it only counts situations where it has already picked a gold ball
the probability is only counted after it gets a gold ball
>>
>>109343458
>50/50fags and Afags run the bitch to ground where it belongs.
reality is a bitch
therefore 50/50fags and Afags run the reality to the ground.
>>
>>109343601
Cool simulation, though the slow descent doesn't really represent A because the point of A argues that the cube stops with the piston. The slow example is just so slow that the cube tumbles down by gravity while still working by the same correct B physics.
>>
>>109343012
> you have a golden ball in your hand
Looks like youve got the balls in your hand
>>
>The number of 50/50 posters
This is sad. I expect that kind of embarrassing shit on /pol/ or /tv/ but not /g/
>>
>>109342368
If you have the Midas touch there is a 0.5 probability the next ball is gold and a 1 probability it will be gold.
>>
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>>109341137
i still think it's 1/3 and i refuse to listen to "reason" from the so called "qualified experts".
>>
>>109343890
Try reading the posts you respond to first next time. My point is that due to how the problem is worded, golden ball in hand is an axiom. It just is. The scenario doesn't start existing until the golden ball is drawn. In other words, you don't return the ball to the boxes between the draws. Hence the inner loop.
>>
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>>109344234
you're making no sense
but what about this
if you picked the mixed box then the ball will be silver, but if you pick the gold box the next ball can either be the gold 1 or the gold 3, that makes 3 situations and only 2 are gold therefore it's 2/3
>>
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>>109341137
This is a technology thread, so you can easily get the answer by simulating it.
>>
>>109344399
>you're making no sense
Good because this question is nonsensical. In this scenario, it's finally 2/3rds. Three possibilities:
{(S, G1G3);(G1, SG3);(G3, SG1)}
, 2 of 3 are the one we're looking for. The problem with the original question is that it has accidentally logically severed the first draw conditional from the problem by stating it as an a priori assumption. So you couldn't differentiate between the both golden ball states
{(G1, SG3);(G3, SG1)}
, like you could if the first draw was made a part of the problem.
>>
>>109344604
>So you couldn't differentiate between the both golden ball states
expect you can, you're just collapsing the states because the balls are the same, it's the exact same scenario
just because the balls are the same doesn't make the states the same
>>
>>109341137
The ball you grabbed was gold. There are 3 total gold balls you could've grabbed.
Box 1 gold ball A - your next ball will be gold ball B
Box 1 gold ball B - your next ball will be gold ball A
Box 2 gold ball - your next ball will be the silver ball

3 total cases, 2 of them you get a gold ball next. So it's 2/3.
>>
>>109344542
>nano
>lua
>i3
oh no no no
>>
>>109341137
I can think of 2 balls you could grab, wonder if you can guess their color
>>
>>109344669
skin color
>>
you need special vocabulary to see where the layman language falls short
>>
>>109344655
What's wrong with i3?
>>
>>109344669
negro colored
>>
#include <iostream>
#include <random>
#include <tuple>
#include <vector>

enum class Ball : unsigned char
{
GOLD,
SILVER,
};

int main()
{
const std::vector<std::tuple<Ball, Ball>> boxes = {
{ Ball::GOLD, Ball::GOLD },
{ Ball::GOLD, Ball::SILVER },
{ Ball::SILVER, Ball::SILVER },
};
const long inters = 100'000'000;
long both = 0;
long attempt = 0;
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<int> dist(0,
static_cast<int>(boxes.size()) - 1);
std::uniform_int_distribution<int> dist2(0, 1);
for (long i = 0; i < inters; i++)
{
const auto r = dist(gen);
const auto [b1, b2] = boxes[r];
const auto first = dist2(gen);
const auto u1 = first ? b1 : b2;
const auto u2 = !first ? b1 : b2;
if (u1 == Ball::GOLD)
{
attempt++;
if (u2 == Ball::GOLD)
both++;
}
}
std::cout << ((static_cast<double>(both) / attempt) * 100) << "%\n";
return 0;
}
>>
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why yes I rendered these shitass balls in common lisp too
and the caption is even more vaguely worded
>>109326302
>>
>>109344763
CGOD is in the thread
>>
>>109344786
Whoops it's C++
>>
>>109341137
0%, because I value silver more than gold and will not pick up a gold ball.
>>
>>109341137
Suppose you roll a fair three-sided die 30 times and, conveniently, each face comes up exactly 10 times. Whenever face 1 appears, you choose the box containing two gold balls, so all 10 first draws are gold. Whenever face 2 appears (the mixed box), 5 of the first draws are gold and the other 5 are silver. Whenever face 3 appears (the box with two silver balls), all 10 first draws are silver.

Since the problem tells us that the first ball drawn is gold, we only need to consider the cases where that actually happened. There are 15 such cases in total: the 10 from face 1 and the 5 from face 2.

Of those 15 cases, only the 10 from face 1 can possibly have a second gold ball, since the mixed box contains only one gold ball. Therefore, the probability that the second ball is also gold is 10/15 = 2/3.
>>
>>109341137
50/50
you grabbed a gold ball, so that eliminates teh silver box.
since you grab from the same box, only 2 possibilities:
you are either in the gold box and get the second gold ball
or you are in the mixed box and get the silver ball that's left, since you already took the gold ball.

any other answer is poor trolling.
>>
>>109344763
This is grotesque.
>>
>>109344833
Why do you ignore the instruction which tells you to randomly select a ball. How exactly do you randomly select a specific object? There are cases in which you could randomly select a silver ball from the second box. 1/2 requires one to outright ignore the instructions.
>>
>>109344628
balls 1A and 1B are the same case, zero difference. so it's 1/2
>>
>>109344878
Nta but are you trolling? That's the whole point. There's 2 potential gold outcomes and only 1 silver outcome, so it's 2/3.

Supposing there was a box with 99 gold balls and 1 silver ball, is the chance of picking gold 50/50 because the 99gold outcomes are the same? That's the argument you're making.
>>
>>109344878
Take a marker and write "A" and "B" on them. Now it's not the same case. Has the marker changed the odds?
>>
>>109344862
The random selection is not the probability that's being asked here. The random selection already happened and gave the initial gold ball. that's done.
the probability you are being asked to calculate is the next ball. which can only come from 2 boxes, so /2. and only the first box will give you a gold ball, so 1/2. simple as.
>>
>>109344833
>since you grab from the same box, only 2 possibilities:
No there are three possibilities but two of them appear identical. See:>>109344915
>>
>>109344915
>Supposing there was a box with 99 gold balls and 1 silver ball, is the chance of picking gold 50/50 because the 99gold outcomes are the same?

No, you are changing the parameters of the mixed box.

But if you were to put 100 gold balls in the gold box (and leaving the mixed as is), it's still 50/50, either you're in the mixed box and you will grab the silver ball, or you're in the 99 gold box and you will grab a gold ball.

You are reasoning at balls level while the choice is at a box level, which there are only 2.
>>
>>109344959
It's not 50/50 though. The fact you picked a gold ball informs us of the likelihood you picked the box with multiple gold balls. This is more intuitive if you expand the numbers. Imagine there's two boxes, box A has 1 gold ball and 99 silver balls, box 2 has 1 silver ball and 99 gold balls. You pick a box and random and get a gold ball, now which box would you honestly think you have picked? You instinctively know that the odds are higher that you picked the ball with 99 gold balls. However when it's only the 2 gold balls vs 1 gold ball you are less likely to recognise this, even though it's still statistically more likely you picked the box with 2 gold balls.
>>
>>109344923
You have no issue with the third boxes probability being reduced to zero, but that exact same mechanism reduces the probability of the second box by half.

Also, If you applied the 1/2 logic properly the answer would actually be 1/3 because the third box can give a gold ball through quantum tunneling.
>>
>>109344959
Another way to think of this is too look at how many potential outcomes there are. People that say 50/50, assume there are only two outcomes but there are three. Imagine you have Box 1 that contains Gold A and Gold B, Box 2 contains Gold C and Silver. You pick a gold ball, you obviously have no way to know which gold it was, so you either:
>Picked Gold A, next ball is Gold B
>Picked Gold B, next ball is Gold A
>Picked Gold C, next ball is silver
So 2/3 of the outcomes result in a Gold ball, 1/3 result in a silver ball
>>
>>109344919
>Take a marker and write "A" and "B" on them. Now it's not the same case.

It's still the same case. You are being asked "the probability that the next ball is also gold".
If you're in the first box :
If you grabbed A, the probability that the next ball is also gold is 100%.
If you grabbed B, the probability that the next ball is also gold is 100%.
It doesn't matter in this riddle, both balls give the same exact result.

So if you're in the first box, you get 100% a gold ball next. If you're in the mixed box, you get 0% a gold ball next. Hence 50%.
>>
>>109345037
Nta but I hope you're trolling
>>
If you pick a golden ball you have to exclude 2 silver balls from a box. You have 2 golden balls and only one silver.

66% for a golden ball and 33% for a silver.
>>
>>109345001
>You pick a box and random and get a gold ball, now which box would you honestly think you have picked?

That's not what is being asked here. You are being asked the probability for the next pick only. Not the overall probability of 2 gold picks back to back. That probability is not 50/50 for the reason you gave and I agree. But it's not what is being asked here.
>>
>>109345059
Lets try again. There are two boxes, Box A has 100 gold balls, Box B has 1 gold ball and 99 silver balls. You pick a box at random, it's gold. What are the odds that the next ball you pick from this same box is gold? Do you think it's 50/50?
>>
>>109345084
Yes.
There are 2 possibilities: I picked box A or box B.

If I picked box A earlier, I will get a gold ball next 100%.
If I picked box B earlier, I will get a silver ball next 100%.

So in one case I get a gold ball, over 2 choices. That 1 over 2. 1/2.


It's still the same probability even if you put 99999 silver balls in box B, since you already picked the one gold ball, you will still get the same 100% probability to grab a silver ball next in box B.
And it will still be 100% chance to grab a gold ball from box A if there are 999999999999 gold balls there.
>>
>>109345124
You are incorrect but that's ok. I do admire that you stuck to your position rather than tried to argue that my example somehow didn't apply to the scenario. Most people seem to intuitively get it when you exaggerate the number of balls but then don't like admitting to themselves they were wrong.
>>
>>109345124
>And it will still be 100% chance to grab a gold ball from box A if there are 999999999999 gold balls there
but there are 999999999999 gold balls and you only picked one, so there are 999999999999 different scenarios because each ball is a different scenario
if you pick a random ball in a random box and it's gold then you have 999999999999 / (999999999999 + 1) odds of choosing the box with 999999999999 gold balls
>>
>>109345200
>each ball is a different scenario
I disagree. What is asked here is "the next pick will be gold". The box was already chosen.

"the next pick will be gold" will always be 100% in the gold box.
And "the next pick will be gold" will always be 0% in the mixed box.

In the gold box, it doesn't matter if you pick ball A or B or C or 999999, the probability to grab a gold ball next if you're in the gold box is 100%.
>>
>>109344786
outta the way sepples fags
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define GOLD 0
#define SILVER 1

#define TRIALS 10000000

// Counters for probability calculation
int gold_counter = 0;
int silver_counter = 0;

void experiment(int** boxes) {
// Pick a random box
int box_pick = rand() % 3;
// Then pick a random ball
int ball_pick = rand() % 2;
if (boxes[box_pick][ball_pick] == GOLD) {
// If the other ball is gold, increment the gold counter
int other_ball = (ball_pick + 1) % 2;
if (boxes[box_pick][other_ball] == GOLD) {
gold_counter++;
}
// Else increment the silver counter
else {
silver_counter++;
}
}
}

int main() {
// Seed the random number generator using unix time
srand(time(NULL));

// Construct the boxes
int box1[] = {GOLD, GOLD};
int box2[] = {GOLD, SILVER};
int box3[] = {SILVER, SILVER};
int* boxes[] = {box1, box2, box3};

// Repeat the experiment for however many TRIALS
for (int i = 0; i < TRIALS; i++) {
experiment(boxes);
}

// Calculate the probability
float probability = (float)gold_counter / (float)(gold_counter + silver_counter);

printf("Gold ball counter = %d\nSilver ball counter = %d\nProbability of picking a gold ball = %f\n", gold_counter, silver_counter, probability);

return 0;
}
>>
>>109345257
but you don't know which box you're in, you only know that you got a gold ball
to figure out the odds that the next is gonna be gold you need to figure out the odds that you chose the correct box while only knowing that you got a gold ball from it
>>
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>>109344763
Oh my god this guy wasn't lying, C++ niggers really need to do all this weird shit to just generate a random number.
>>
>>109345321
No that would be the overall probability.
Sinc you picked a gold ball, you know you are either in box A or box B and not box C. That's already done.
This is the situation you"re in, now you're asked "will the next one be gold". If you're in box A that's yes, if you're in box B that's no. It's true or false, no other choice.
>>
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2.69 MB
2.69 MB WEBM
>>109343395
>>
>>109345349
It's a bit more boilerplatey for simple cases, but at least it generates high quality randomness unlike C's retarded rand() function where every tutorial worth anything tells you not to use it because of its countless shortcomings and it can produce different distributions of randomness easily.
>>
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>>109345417
I just use my trusty PCG, copy-paste with some changes once and it's done
>>
>>109345463
That spaghetti sure is a lot easier to remember than the equivalent C++.
>>
>ITT: brainlets who can't into probability
>>
>>109345475
this is the best I have seen
here I was thinking of using Lisp cons cells but I was too much of a brainlet to do the cons cell diagram version of this because you have to map diagrams like this to understand the REDUCE function.

This stuff is implicit in nested lists (((parentheses)))
>>
>>109345475
Yeah, I don't understand why people have so much problem with just testing every scenario and then calculating the probability for the asked outcome. I thought that was the gold standard highschool method you should use when available. Something about the first gold pick assumption is tripping them up hard. Suddenly the "testing every outcome" gets thrown out of the window and now both balls from box 1 is somehow reduced into one possibility, even though it has clearly 2 possibilities.
>>
>>109341137
50%
>>
im convinced this thread is for training ai and of course so college statistics homos feel like their debt slavery is worth somethi g
>>
>>109345553
the ais are already trained bud, there's a gemini response screencap in this very thread.

That you think this...dude what would LLMs be without conditional probability? How would an LLM even be possible then, noob-boobs?
>>
>>109341137
It's 2/3. It either is, or it is, or it isn't.
>>
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>>
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>>109345475
Cute but you didn't answer the question. I circled it in red for you.
Hint: the left half of your image is outside the scope of the question.
>>
>>109341218
how do you know which golden ball you grabbed from the gold box
>>
>>109345616
elegant!
>>
>>109345677
it doesnt matter, the result is the same. You'll get a gold ball on second draw either way -> probability = 1
>>
>>109341137
2/3 obviously.
There are 3 boxes in total.
2 of them contains gold.
So 2/3.
>>
>>109341137
ugh, this again... take *this*
>>
>>109345553
this thread > your college's explanations
>>
>>109345747
anything is possible if you cover yourself in oil and believe in yourself
>>
>>109345801
oil the fuck up anon i'm going inside
>>
Understanding Probability and Sample Space
Definition of Probability

Probability is a numerical measure of how likely an event is to occur.
It is expressed as a number between 0 and 1, where:
0 indicates impossibility (the event will not occur).
1 indicates certainty (the event will definitely occur).

Definition of Sample Space

A sample space is the set of all possible outcomes of a random experiment.
It provides the framework for assigning probabilities to specific events.
>>
>>109345747
>The opposite end of the rod responds to movement immediately
this is the lie, it propagates at the speed of sound
>>
>>109345640
Correct.
ITT: people have worse attention mechanisms than AI.
>>
>>109345640
preach, sister!
stupid snailcats flooding this board makes me sick
>>
>>109345640
but that makes it 1/3 though, dummy anon
>>
>>109341137
>Same Box
Timeline 1: I select box 1 (GG), it is 100% probability
Timeline 2: I select box 2 (GS), it is 0% probability
>>
>>109346458
Fixed:
Timeline 1: I select box 1 gold ball 1, it is 100% probability
Timeline 2: I select box 1 gold ball 2, it is 100% probability
Timeline 3: I select box 2 gold ball, it is 0% probability
Total probability: ~66.7%
>>
>>109345037
Lets label the balls ABCDEF. You pick a box at random. It could be box 1, 2 or 3 with equal probability.

If you reached into 1, you got either ball A (gold) or ball B (gold) with equal probability.
If you reached into 2, you got either ball C (gold) or ball D (silver) with equal probability.
If you reached into 3, you got either ball E (silver) or ball F (silver) with equal probability.

However, the problem says that the first ball you picked was gold. So it can't have been a time that you got ball D, E, or F. There's 2 chances to get a gold ball in box 1, and only one chance to get a gold ball in box 2. So if the premise is you already picked one and it's gold, you're twice as likely to have gotten it from box 1.
>>
>>109346484
>probability of next ball taken from the same box.
The next ball choice happens in the same box after the first selection.
I.E once you grab a ball, you grab a ball from that box again.

Yes, there are three timelines initially, of which 2/3 probability to select a gold ball, but it is stated you have already grabbed one.
>>
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>>109345620
Gayest post I've seen on /g/ was a guro board. Mind, I don't come here often anymore.
>>
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>>109343753
This post is AI. You should hire me for selecting the most obvious posts, AI man.
>>
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>>109344699
Checked, but you're ESL or autismo.
>>
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>>109344769
Heterochromia is pretty cool boku.
>>
>>109344807
>three-sided die
Why are they like this?
>>
>>109345052
Where'd the 0.01 go, you idiot?
>>
>>109345371
Ah yes, the Dalit Double Downer. Good luck with your English studies, bud.
>>
>>109341137
66%
>>
>>109344833
It's twice as likely that you drew the gold ball from the box with 2 gold balls though. So double the odds that you pulled from that box.
>>
>>109346484
Timeline 3 can't happen since you already grabbed a gold ball. It was already discarded before the question was asked.
Total probability: =50%
>>
>>109347975
>double the odds
No because >>109345640
>>
>>109343646
> I can apparently transmute silver to gold just by touching
touching your what?
>>
>>109344710
Kek
>>
>>109346817
Uh, why do you think my post was AI exactly?
>>
>>109348200
Read his post again, moron
>>
>>109345909
Mathematics is the tool of the devil
>>
>>109345620
Bertrand was a faggot. Literally. This discredits his 2/3 faggotry.

Therefore 50/50 is the correct.
>>
>>109345620
OPs ball problem is known as Paradox of Bertrand's Box. Literally the fagetist fag fag title of a problem in all of mathematics.

No wonder Chebyshev often called him a faget to his face at symposia fightclub
>>
>>109345677
You know becausd the black balls belong to a nigger who wilk buck break you when you sieze them
>>
>>109348469
>OPs ball problem is known as Paradox of Bertrand's Box.
Most people know this. We learned this in primary school and were put into groups where we had to come up with a physical way to test it and got close to 2/3 odds. The fact there are grown adults that not only can't understand why this is, but will vehemently argue it's 50/50 even after it's explained to them is shocking.
>>
>>109348695
What if the 50/50 know this and are baiting the 2/3 crew for the hilarity. Its why I post these threads.
>>
>50%ers are the people telling you uni is a waste of time/makes you stupider
kek
>>
>>109348695
Aaaactually the drawing of balls causes a split in the quantum universe into two new universes upon drawing the balls. You are literally bifurcating reality by pulling your balls.
>>
>>109341343
Holy shit this explains it so clearly for me. I was using the conditional probability equations I learned from quantum mechanics, which I never really completely understood, since I never had a full course on probability. I got the 2/3 answer which is the correct one, but it didn't make intuitive sense to me until I read this.
>>
>>109348931
I dunno, that explanation was kind of a word salad.
A simpler logical explanation:
Because you pulled a gold ball first, there is a higher chance that the box you selected was the one with 2 gold balls, since you can only pull gold balls from it.
>>
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>>109349094
Also, the core logic is the same as the Monty Hall problem, they both have to do with your initial pick.
Since your initial door has a higher chance of being wrong, you should always change your answer once one of the two incorrect doors is revealed/eliminated, since the remaining unchosen door will more likely be the winner.
>>
>>109349146
Theres a nigger behind the second door raping the ass of that goat hidden behindvthe door.
>>
>>109341137
100%. i'm not some faggot loser to grab a silver one. fucking pleb.
>>
the picking a box part is just there to confuse you. Pick a box at random and then a ball at random means you pick a ball at random. Now if you pick a golden ball, 2/3 it's from the box with another golden ball. Hence the odds are 2/3
>>
import random

boxes = ('GG', 'GS', 'SS')
wins = 0
valid_attempts = 0
attempts = 1000000

while valid_attempts < attempts:
box = random.choice(boxes)
chosen_index = random.choice((0, 1))
chosen_ball = box[chosen_index]
other_ball = box[chosen_index ^ 1]

if chosen_ball == 'G':
valid_attempts += 1

if other_ball == 'G':
wins += 1

print(f'GG pulled {wins:,}/{attempts:,} times ({wins / attempts * 100:.2f}%)')

>GG pulled 666,565/1,000,000 times (66.66%)
>>
>>109348742
Some of them are but not all of them
>>
>>109349094
>logical explanation
Yeah, more logical explanations I don't need. Just follow the math and you get the answer. That's all the logical explanation I need. What anon did there is explain it intuitively
>>
>>109341439
>>109341463
Your brains are worthless.
>>
>>109343334
Your brain is worthless.
>>
>>109351901
> print(f'GG pulled {wins:,}/{attempts:,} times ({wins / attempts * 100:.2f}%)')
I have never really got the appeal of the new formatting syntax, its grotesque and unreadable. The old c style formatting syntax is superior.
>>
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i might be retarded, but this is how i see it. you don't know which one you took it from, but since it's from the same box, it doesn't matter. you would be left with one ball regardless of which one you took it from.
>>
>>109342140
Doesn't change, the 3 balls aren't in the same box, you're either in GG or GS
>>
>>109345200
>999999999999 different scenarios because each ball is a different scenario
It's not
>>
>>109354620
the problem with that is that the two gold balls are not interchangeable in probabilities, so you also need to add the box with both gold balls and an X on the right ball, that's why it's 2/3 and not 1/2
>>
>>109354805
but you don't actually choose a box, you choose a ball and then you look at the other ball in the box
>>
>>109354870
Yep.
>>
>>109354805
Your brain is worthless.
>>
>>109354143
Sorry bro, but he's right :-)
>>
>>109354620
Since you chose gold, you're twice as likely to have chosen the left box than the right box.
>>
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>>109354620
It's more obvious if you remove the boxes. The scenario ends up the same (blindly fishing a ball out of a randomly-selected box will give you a random ball everytime, so the boxes themselves are an irrelevant detail, you might as well just have been picking balls out of a hat).
The only thing the box framing does is eliminate 2 silver balls from the probability question.
So in reality, picrel is what the scenario looks like. Here it's much clearer that the probability the next ball you pick up will be gold is 2/3 (66%).
>>
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With the boxes, this is the correct framing: you picked up 1 of the 3 gold balls marked with a question mark. But which one? You don't know, so that leaves 3 possible scenarios for what the other ball could be.
>>
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>>109354870
>>109355893
>>109356036
>>109356071
nah. in fact, a simpler way to put it is that there's one ball left from the box we drew from (the same box we have to draw from again), and it can only be gold or silver. so... 1 ball / 2 possibilities. the boxes and other balls are honestly irrelevant. i refuse to think anything else
>>
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>>109341137
I think I've got it, although my method will take a little explaining.
>>
>>109341137
I don't see how it could be anything other than 50%. The 2/3 fags are either
>trolling
>more intelligent than I can possibly comprehend
>more retarded than I can possibly comprehend
>>
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>>109341137
>>
>>109345475
why is there 2 balls left in the boxes when you have already taken one ball out?
>>
>>109341620
What if someone picked the right, rather than the left ball, from the leftmost box? You have failed to consider three distinct possibilities.

Left box, left ball
Left box, right ball
Middlle box, left ball
>>
if i pick a gold ball it means i either
>picked left ball of box 1
>picked right ball of box 1
>picked left ball of box 2
if i picked box 1, the next ball is gold
if i picked box 2, the next ball is silver
therefore it's 2/3
qed
>>
>>109356228
Fucking kek
>>
>>109356342
The tree is showing possible outcomes, not the current state. You don't know which of the 3 gold balls you took, so each of them is a distinct branch.
>>
The first half of the problem happens before we take control of the situation. It happens magically, before the Big Bang, and therefore free will and probability do not exist at that point. The real problem is that we are given 2 boxes, and the box that we pick at random is missing a gold ball, and we take the other ball that is in it. The contents of the box that we do not pick do not matter, and so saying that that box is also missing a gold ball makes the problem much easier. Two boxes: one with a silver ball and one with a gold ball. 50/50.
>>
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It's 66%
I made a version that even drooling retards can understand.
>>
>>109343395
Weird enough, I'm 50/50 on OP question but B on this question.
>>
>>109341343
>it didn't count because that's not what the scenario was about
Math is the art of ignoring variables until desired results are achieved
>>
>>109356119
but have you looked at any of the simulations that proved you wrong?
can you find the bug in them that makes it 1/2 instead of 2/3?
see:
>>109351901
>>109345316
>>109344763
>>109344542
>>109341647
>>
>>109341218
>If I've already reached into the box and got a gold ball, that means I've either picked a gold box or a mixed box. So 50%.
You are looking for the double-gold box, but the double-gold box is x2 more likely to be the one that caused you to be in the situation we test (that "first ball was gold"). So 2/3=66%

>>>>I run 10000 tests. Number of tests that match our situation (firt is gold) was 5052 and in these cases, the next ball was also gold 3376 times, which was around 66.825%

#include <iostream>
#include <cstdlib>
int main() {
srand(time(NULL));
int tests=0; // number of all tests (trials) you run
int firstWasGold=0; // how many time (out of all the tests), the first ball you pick was gold
int nextWasGold=0; // how many time (out of all the tests), the second ball you pick was gold (it is not that important)
int nextWasGoldTooAfterFirst=0; // how many time, out of cases where first was gold, the secold ball was gold too
for (int i=0; i<10000; i++) {
int box=rand()%3+1; // you pick box: box 1, 2, or int32_t
int right=rand()%2; // you pick ball: 0:left 1:right
++tests;
if (box==1) { ++firstWasGold; ++nextWasGold; nextWasGoldTooAfterFirst++; } // the two-gold ball box, first ball and next ball here are gold.
else if (box==2) { // the silver/gold mixed box
if (right==0) { ++firstWasGold; } // you take the left ball: it is gold; and the next ball here is NOT-gold
else { ++nextWasGold; } // you take the right ball: it is NOT-gold; and the next ball here IS gold
}
else if (box==3) { } // both balls are silver, none is gold in this box
}
std::cout<<"I run "<<tests<<" tests. Number of tests that match our situation (first is gold) was "<<firstWasGold
<<" and in these cases, the next ball was also gold " << nextWasGoldTooAfterFirst << " times, which was around "
<< (nextWasGoldTooAfterFirst*100. / firstWasGold) << "% \n";
return 0;
}
>>
>>109356401
>if i pick a gold ball it means i either
>>picked left ball of box 1
>>picked right ball of box 1
>>picked left ball of box 2
>if i picked box 1, the next ball is gold
>if i picked box 2, the next ball is silver
>therefore it's 2/3
>qed
based and literally qed
>>
>>109342216
haha based, the retarded 50% american is BTFO.
No wait he still fails to grasp it lol LAMAO! >>109342361
>>
>>109342272
>it's either one of the 259 gold or one of the 259 silver balls
>exactly 50%
you big dumb
>>
>>109356228
ok i get this one so it was formerly chucks but now belongs to sneed and eed and uck sounds thus get rhymed and repeated into feed and seed thus it's chuck's feed and sneed
>>
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>>109357583
i ain't readin' any that shit nigger
>proved you wrong
lmao
>>
>>109341137
I decided to try this with coins 5 cent (silver) and 10 cent (gold) and three cups
I pick a cup at random and then a coin it was silver (5 cents)
Now I don't know what to do
>>
>>109359643
you discard it and try again, you only count when you get a gold because that's the starting position
>>
>>109359621
>I can't read code
classic /g/
>>
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>>109359668
>that's the starting position
>>
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>>109359724
>implying i can read at all
you can't make me
>>
50/50 subgroids and 2/3 abbobrains kneel before the 100% white. It's 100% because if you cannot draw the correct ball next you simply do not have the Faustian spirit and are brown.
>>
you toss a coin twice. The first toss resulted in tails. What's the probability that the second toss will also be tails?

>noooo it's 1 over 4 because there is 50% chance that you tossed tails first time
>>
>>109360959
>you toss a coin twice. The first toss resulted in tails. What's the probability that the second toss will also be tails?
you are brown
>>
>>109360959
Each coin toss is a random event and not remotely comparable to Bertrand's box. Don't post in this thread again
>>
>>109342361
Do you not realise that even in your modified image, it you stuck your hand in one of the two boxes and got gold it would be overwhelming more likely that you picked the box on the left? What sort of retard would think it's equally likely they managed to pick the solitary gold ball from the right box?
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The answer is 1/2 because the box is chosen before you know that the ball chosen from the box is gold. Therefore it is not possible to suppose THREE scenarios where the gold ball is picked, because there are only TWO boxes that contain a gold ball at all.
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>>109362363
There are three scenarios left with the two boxes. Gold 1, Gold 2, or silver as you don't know which gold ball you picked.
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>>109356237
It's the second option, which is sad because it's really not that difficult and this is something a lot of kids learn about in elementary school when learning about probabilities.

https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
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>>109362413
You can't double count one of the boxes just because there are two gold balls in it. The balls are indistinguishable.
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>>109356237
it's a trick of probabilities, the only thing tripping up 50/50fags is the fact that 2 gold balls are counted as different even though the outcome is visually the same, see >>109362454
one way of thinking about it is that all objects have a hidden unique id, and therefore picking either of the gold balls produces different states because the id of the other ball is different
you can see this example, which makes it clearer >>109344399
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>>109362470
If you make each ball distinguishable then just tag them by color, then you're asking a different question. In that case you CAN distinguish picking ball #1 in a box from picking ball #2 in a box, which the OP question presumes you cannot.
So yes, in the case where you allow every ball to be distinguishable, the probability is 2/3. In the case where the balls are indistinguishable other than by color, the probability is 1/2. The *kind* of probability matters.
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>>109341246
High five.
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>>109362454
Do you want to attempt to articulate why that? Try a different scenario. Imagine you stuck your hand in a box with 999 gold balls and 1 silver ball, you intuitively understand that it's more likely you'll pick a gold ball, but if we follow your logic that probabilistic outcomes that appear similar don't count as separate probabilities then the odds are 50/50, silver or gold.

You do in fact count the two gold balls as indistinguishable because that's how probability works. Btw if you reply with something like
>But there's only one ball left in the box!
Then you have completely failed to understand what I've just explained to you.
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>>109362485
You still don't get it. The question is regarding the probability of getting a gold ball. There are two ways to get a gold ball because as you've identified they are indistinguishable. But for some reason in your head you've decided to count it as though there's only one way, because they're indistinguishable, which makes no sense and you can't even articulate why you're doing it.
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>>109362485
how about you write up a simulation to prove your point?
or maybe just point out the error in the simulations already posted
it's easier to understand your logic if you write it in a logical way
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>>109362509
>But for some reason in your head you've decided to count it as though there's only one way, because they're indistinguishable, which makes no sense and you can't even articulate why you're doing it.
that's because he is brown.
solution is 66%, everyone told that poo already why and pasted simulations and all...
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>>109362329
If you have a million dollars, it's equally likely you earned it working over several decades or won the lottery.
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>>109362492
>>109362509
>>109362527
I thought about it more. Even if the box is fixed to be a gold-coin-containing box, the coin draw from that box is still random, so the GG box has less rejections. So it is 2/3.
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>>109356237
>I don't see how it could be anything other than 50%
Imagine if you had to do this over and over to estimate the probability empirically. Half of the time you pick the middle box, you'll pick a silver ball first and have to discard that trial. Meanwhile every time you pick the leftmost box, you'll pick a gold ball. i.e. the leftmost box will be 2x over-represented in the valid trials.
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Why is everyone so retarded.
It doesn't matter what color you pick initially.
The question is technically asking you what are the chances that you picked a box that has two of the same color inside, which is 2/3rds.
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>>109363020
Genuine congratulations on being able to admit your mistake and understand the correct answer.
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>>109364164
It's because the answer would still be 2/3 even if the box containing the two silver balls didn't exist and you were only picking between two boxes.
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>>109365215
Thanks. One way I can think of to recover the 1/2 probability is to require that the coin drawn is gold (that is, no rejection sampling occurs, and the coin draw is in fact not random).
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>>109364164
No the question is what's the chance you picked the box with double gold.
Which is initially 1/3 but after grabbing one ball and noticing it's gold your confidence raises to 2/3
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How about a real test of mental fortitude?
>>109341216
50% indeed.
Silver box was eliminated.
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>>109365501
>your confidence raises to 2/3
nigger your confidence raises to 1 of 2 boxes containing at least 1 gold ball.
You confidence is literally cut in 1/2.
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>>109365522
What if there were 2 million balls in each box instead of 2?
One box has 2 million gold balls, one has 1 million gold plus 1 million silver balls, and the last has 2 million silver balls.

You pick 1 million balls and they all happen to be gold.
How confident are you now that you picked the box with only gold balls?
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>if balltake is gold
>remove silver box
>for each box
>goldballs-1
2 potential boxes remain. This is all that matters.
1 potential ball remains regardless of box chosen. It can be either gold or silver. Flip a coin.
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>>109365576
What weighs more: A ton of feathers or a ton of bricks?
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>>109341137
anon, why do you even keep your balls in a box?
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>>109365629
because I'm trans btw
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>>109341218
how likely is it that you grabbed from the gold box, and how likely is it that you grabbed from the 50/50 box?
you have to take that into account, nigger.
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>>109365602
a ton of feathers weighs more if they are tarred, less when untarred
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>>109362435
i learned about it in university where i studied meth and got a degree after 10 years
i pity kids these days who won't have a chance to slack off like i did
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>>109367002
I learned about in what we can primarily school in the UK, when I was about ten. In fairness I was in the advanced class (bad idea on the long run), so some of the stuff we learned was over the heads of other kids. Bertrand's box should be incredibly simple to understand for any functioning adult though.
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>>109362454
think about it differently. the actual question is: did you initially draw from the gold box or did you initially draw from the mixed box?
these are not equally likely.
and now you simply draw from the same box again. no choice about it and no random pick. there is only one ball left in that box.

in the first case (which is twice as likely), the next ball you draw will also be golden.
in the second case, the next ball will be silver.
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>>109341137
anyone saying other than 50% is fucking retarded.
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>>109367208
>anyone saying other than 50% is fucking retarded.
you sir are a dumb retard, you are proven wrong by experimental data, by logic, it's a well known paradox with simple solution
but yo uare the kind of idiot that can't get smart no matter what
please commit suicide
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>>109367481
if the box is already chosen and I already know the ball is gold. The second ball is either gold or silver. As such there exists only two choices.either the next ball is gold or it is not. It's 50%.
Fuck off
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>>109341236
You clearly are because we’re correct
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>>109341137
You can only pick up 2 gold balls or a silver ball after seeing the first one is gold so it’s 2/3

Simple as
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>>109365597
>2 potential boxes remain. This is all that matters.
wrong, it's not just the boxes but the balls within them
the GG box contains TWO gold coins, even though they are fungible, they are still unique entities
if you get left one, then right one is next, if you get right one, then left is next, if you get the one from GS box, then silver is next, that's 2 out of 3 possibilities for gold and 1 out of 3 for silver
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do you still think it's 50% now?
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What 50/50 retards fail to realize is the boxes are completely arbitrary and pointless, you picked a BALL at random. You don’t know if it’s G1 G2 or G3 when you get your first gold ball.
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>>109367689
Not entirely. When you put this into Bayes formula, P(A|B) = (P(B|A) * P(A)) / P(B) ... the P(A) is literally which box you have. You're asking what is the probability of getting GG given that you have g. P(A) = GG, which is 1/3, P(B) = g (any of the 3 gold coins), which is 1/2. In this case, P(B|A) is simply 1, because you will always get g from GG. so (1 * 1/3) / 1/2 = 2/3.
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>>109341137
You pick 1 ball at random from the 3 boxes, it's a gold. You're then carefully explained to in a manner that you are certain to understand, that statistically you are more likely to also get a gold ball next if you pick it from the same box. The person in charge of the event knows which box has which balls and seems extraordinarily invested in you understanding the statistical odds at play, and that you should absolutely definitely pick the next ball from the same box.
What are the odds they're an asshole, trying to trick you into picking poorly?
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>>109367521
>As such there exists only two choices.either the next ball is gold or it is not. It's 50%
Yeah, just like playing the lottery, you either win or lose, it's 50%
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>>109367966
Arguably the more tickets you buy, the less likely you are to win.
You probably know some people who constantly buy a dozen tickets at a time, have any of them won? But every time someone is on the news for winning it's some random jackass who bought their first ticket in a decade at some random gas station they ended up at by chance.
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>>109367832
Thanks for confirming exactly what I just said
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>>109368006
You're missing a subtle point. All I was saying is it's still part of the formula being the "prior" P(A) in Bayesian terminology. The sampling procedure is fundamental to the question which involves selecting a box. I probably should have clarified that the reason why the marginal, P(B), is 1/2, is not simply because there are 3 out of 6 coins, but rather is a result of the boxes themselves. P(B) = 1/3(1) + 1/3(1/2) + 1/3(0) = 1/2. Essentially, you have a 1/3 chance of getting any box, GG is 1/3 times 1, all coins are gold, GS is 1/3 times 1/2, half of the coins are gold, and SS is 1/3 times zero. This is why the image people post like this >>109367678 would actually still yield an answer of 2/3.
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>>109368115
i actually thought it changed the probability like the monty hall problem

i guess adding more gold balls to the first box doesn't do anything since you already have a 100% chance to get a gold ball from it no matter what?
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>>109368248
Exactly.
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>>109368248
Correct. If you added more silver balls to the gold/silver box then the odds of getting gold on the second draw would increase though.
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You nerds talk about your magical "probably" but in reality it's just a coin flip.
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>>109369786
It's the equivalent of a coin flip with a three sided coin, with two heads (gold) and one tails (silver).



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