Gold Ball Problem

[Anonymous No.15827561]

Since this gets posted quite a lot here, I've decided to document the actual answer to this question and the reasoning behind it on this video:

https://streamable.com/mc9f1r

Now please stop arguing about it.

[Anonymous No.15827593]

high effort but low intelligence bait. 300 replies is guaranteed

[Anonymous No.15827746]

>>15827561
Bad bait, even worse because my thread (which actually is getting replies) is still up. What a stupid fuck.

Die.

[Anonymous No.15827775]

>>15827561
Which gold ball matters you moron. Only in QM there are scenarios where is impossible to tell what is what and crazy things happen, like cold welding and shit.

[Anonymous No.15827778]

>>15827775
How is cold welding crazy and insane? It's part of the basic electromagnetic nature of atomic forces.

[Anonymous No.15827782]

>>15827561
This poor fucker has brain damage.

[Anonymous No.15827786]

>>15827778
It took humans thousands of years to reach that level of knowledge. If you didn't have access to such knowledge it would be very hard for you to accept such a thing can happen.

[Anonymous No.15827789]

>>15827786
Oh yeah that's fair. I thought you meant something else by saying that.

[Anonymous No.15828003]

>>15827775
Please explain why "which gold ball matters". Keep in mind that we're only testing one scenario, not 100000 samples of it.

[Anonymous No.15828007]

>>15827561
>>15819104
Old thread's still up retard

Anyway I ain't watching a video if I already know you're going to be wrong by the end of it

[Anonymous No.15828008]

>>15827775
>>15828003
Let's add ten million silver balls to the middle box. You reach into a random box, take out a random ball. It happens to be gold.

Probably not that one among ten million is it

[Anonymous No.15828047]

>>15828008
Lmao ESL-kun, the question STATES that you DID pick the gold ball, you don't incorporate any of the silver balls into account.

[Anonymous No.15828051]

>>15828047
All right, consider the following:

You flip a fair coin. It lands heads. What were the odds of that? Can you tell me that?

[Anonymous No.15828054]

>>15828047
>you don't incorporate any of the silver balls into account.
Who are you calling ESL

[Anonymous No.15828075]

>>15828051
50/50? Don't know what you're reaching at here.

>inb4 uhm actually schweaty, it';s 49% because it can land on the side!

[Anonymous No.15828079]

>>15828075
>50/50?
Oh, really? That is most curious. Because I already stated that it DID land heads. Why did you take tails into account? Shouldn't it be 100%?

If you understand that it works this way for a coin, why do you assume it works any different for reaching into a box and randomly taking one of two balls?

>Don't know what you're reaching at here.
Foregoing the obvious jab, I'll just point out that this is once again unidiomatic English.

[Anonymous No.15828088]

1/2fags are just trolling at this point.

[Anonymous No.15828095]

>>15828079
You're either retarded or trolling:

What "were" the chances of that differ greatly from
"What WILL be the chances of an event given these parameters"

[Anonymous No.15828096]

>>15828095
He's retarded, not trolling. That's not the kind of mistake someone makes as a troll.

[Anonymous No.15828099]

>>15828095
Right, so what WERE the chances that you got gold from a box with one gold ball and ten million silver, when you had equal odds of selecting a box that has only gold balls in it?
>>15828096
Dear God, there's two of them, both equally oblivious to the blatant mistake they're making.
>>15828088
Actual footage of 1/2fags fucking up statistics 101 problem again and again

[Anonymous No.15828101]

>>15828099
the question does not ask about the chances of picking a gold ball first, it asks this:
- You've ALREADY PICKED A BOX AND A BALL - IT'S GOLD FFS. THAT MEANS YOU'RE LOCKED INTO THAT BOX AND YOU HAVE A 1/2 CHANCE IT'S EITHER G-G OR G-S BOX. FUCKING HELL 2/3 FAGS GET A GRIP ON REALITY

[Anonymous No.15828106]

>>15828099
>He doesn't know about sequential propability thought exercises.

Chance to pick a gold ball from 1 gold & 999 silvers = 1/1000

BUT this event DID happen - so the next question is: FROM that state, what are the chances that the next ball will be silver?

From this state you are locked into a 1/2 scenario no matter how hard you try to cope with "muh statistical probability" - It's not statistics if you only have 1 scenario. The question does not include 10000's of attempts, it only has one. And in that one, you are locked in the moment you see a gold ball.

Yes, statistically, you would pick the only gold box more, because you have a higher likelyhood of accepting that scenario (you've picked a gold ball)

But, since our sample size is [1], and the question already determined that we DID pick the gold ball, it becomes 1/2.

[Anonymous No.15828110]

>>15828101
>the question does not ask about the chances of picking a gold ball first
No, I'm asking you. What are the chances that the gold ball that you DID get came from one box, or the other?
Or, in other words, let's do it like this: same set-up, except once you select a box, you open it, look inside, and flip a coin to select a ball. Then, this process happens to produce a gold ball.

You understand coin flips. What you do not understand is that this part of the process is functionally equivalent to a coin flip. The gold ball was not guaranteed. It was the result of a random process. Which fucking means that, if you ALREADY have gold at this point, it was for more likely that you got to this point by selecting the box where the outcome of the coin flip didn't matter.

Your two mistakes are: thinking that something that is stated to have happened as part of the problem statement was 100% likely to happen (or forced to happen), and thinking that if there are two possible outcomes that both are equally likely. Both are obviously false if you think about it for even ten seconds.

[Anonymous No.15828112]

>>15828110
Nigger we are discussing the question in the imagine, not your scenario you've made up.


>No, I'm asking you. What are the chances that the gold ball that you DID get came from one box, or the other?

Irrelevant, since we know we did pick gold. It's already happened. You don't give a shit about the chances of that happening, because you only have this one try. No matter how fucking unlikely it was - IT MIGHT HAVE HIT THE SILVER BOX ONE - therefore, from that point onwards, you know it could be any of those 2 boxes. 1/2 again. 2/3fags are on suicidewatch

[Anonymous No.15828113]

>>15828106
>Yes, statistically, you would pick the only gold box more, because you have a higher likelyhood of accepting that scenario (you've picked a gold ball)
>But, since our sample size is [1], and the question already determined that we DID pick the gold ball, it becomes 1/2.
That is literally not how this works lmao

Again, what you're saying is equivalent to saying "the coin landed heads so it's 100% since I only flipped it this once"

[Anonymous No.15828114]

>>15828113
Which is exactly the case. It was 50/50, but the moment it landed on heads, the probability of heads became 100%. It's literally quantum mechanics simplified.

The wave function of a particle is a range of probabilty - that collapses to a set 100% chance by detection.

[Anonymous No.15828116]

>>15828112
>It's already happened. You don't give a shit about the chances of that happening
And that is why you are unable to accurately assess the situation. You blatantly ignore some of the information available to you.

>>15828114
You are beyond helping lol

[Anonymous No.15828117]

>>15828116
>name calling as a last resort
>no explanation given

2/3 fags just cannot win anything, can they?

[Anonymous No.15828120]

>>15828117
I cannot reason with someone who fundamentally rejects reason, no. If you conclude that anything that happened retroactively becomes 100% likely to happen, you are simply unfit for statistical analysis. Only if I can disabuse you of this pigheaded notion can we begin to make progress, but it doesn't seem to be a rationally held position, which means my options are rather limited through text alone.

[Anonymous No.15828124]

>>15828120
Well, the past is a 100% guaranteed to have happened. You're just not educated enough to discuss sequential probability scenarios. You've probably read the wikipedia page on the bertrand's box paradox and you think it applies the same logic here, therefore you defend it because muh basedence said so!

[Anonymous No.15828129]

>>15828124
>You've probably read the wikipedia page on the bertrand's box paradox and you think it applies the same logic here
It is LITERALLY BERTRAND'S BOX holy shit lmao how does a person end up like you?

[Anonymous No.15828140]

>>15828124
>Well, the past is a 100% guaranteed to have happened.
When the probability of a future event is contingent upon the probability of a past event, then obviously just filling in 100% everywhere will lead to wrong conclusions. You need to know how likely it was for something to have happened in order to accurately deduce what the current state of affairs probably is.

[Anonymous No.15828169]

If you have a d6 and a d100, and you grab a die at random and roll it, and you get 6, is it equally likely that you got either die?

[Anonymous No.15828172]

>>15828169
What if the d100 actually had 99 sides that said 6 on them, and only one that didn't? Does it change the odds?

[Anonymous No.15828177]

>>15827561
Another great brainlet filter like the goat problem. People just can't get it into their heads that information determines likelihood.

[Anonymous No.15828178]

>>15828177
Like with the goat problem, they fail to even recognise that they have been given information.
>All I know is, it's not the open door
>All I know is, it's not the silver box

[Anonymous No.15828245]

The issue lies with the semantics:
Original bertrand's box question: "If the gold is gold" vs this question: "The ball was gold".

This slight difference takes it from a 2/3 statistical probability to a 1/2.

[sage No.15828303]

>>15828245
>You put your hand in and take a ball from that box at random.
>It's a gold ball.
Your program assumes i already knew the first ball would be gold and which one to pick.

[Anonymous No.15828325]

>>15828047
I would love to know how you can randomly, non-randomly pick an object. You seem to be interpreting its gold to mean a supernatural force makes the player always choose gold, rather than simply being told the outcome of a random event.

[Anonymous No.15828338]

>>15828245
Its logically impossible to randomly select a specific object. The only logically valid interpretation is 2/3.

[Anonymous No.15828434]

>>15827561
Say the first box has 100 gold balls, the second 99 silver and 1 gold, the third 100 silver.
You randomly pick one box and get gold. It's way more likely you *have* picked the first box. In fact you know with 99% certainty you picked the first box. Which is also the likelihood you'll get another gold ball.

People seem confused by there being two random events, pciking the box and picking the ball. They're random but connected, since you know the initial situation of how the balls are distributed. Getting one result (first gold ball) recontextualizes the situation. You know now:
That you haven't picked the all silver box.
That there's a small chance you picked the mixed box.
That there's a bigger chance you picked the all gold box.
So there's a bigger chance to get another gold.
It's really the same logic as monty hall.

[Anonymous No.15828495]

>>15828245
"The ball was gold. Then..." is semantically and logically equivalent to "If the ball is gold, then..."
You are making a distinction that does not exist out of a desire to outsmart the riddle. Suggests an inferiority complex.

[Anonymous No.15828497]

>>15828434
>That you haven't picked the all silver box.
>That there's a small chance you picked the mixed box.
>That there's a bigger chance you picked the all gold box.
Yes, this! People make the mistake of thinking all it does is exclude the all-silver box. They don't know it tell you something about the relative probability of ALL boxes.

[Anonymous No.15828522]

>>15828047
>but I did have breakfast this morning

[Anonymous No.15828558]

Look you 1/2 spastics, imagine it works like this:
>you pick a box
>you put on a blindfold
>you pick a ball from your box
>you are then asked "what is the probability that the other ball in your box is the same colour as the one you are holding?"
The problem setup is symmetrical, so it doesn't matter if you are holding a silver or gold ball, because the answer is the same for either. There are 3 boxes, and 2 of them have balls of the same colour in: 2/3. There are 6 balls, and 4 of them are in boxes with another ball of the same colour: 4/6, or 2/3. At this point, even you tards must agree that its undeniably 2/3, regardless of which ball you have.
>you remove the blindfold to reveal you are holding a gold ball
>you are asked "what is the probability that the other ball in your box is gold?"
Does the probability now change to 1/2?

[Anonymous No.15828597]

I fucked up both this and the Monty hall problem in my first attempts.
It's over...

[Anonymous No.15829173]

>>15828597
If you can admit you're wrong and learn from it, you're still miles ahead of half this thread

[Anonymous No.15829209]

>>15828597
>I fucked up both this and the Monty hall problem in my first attempts.
Was the Monty Hall problem given properly? It often isn't.

I wouldn't feel bad if you solved the wrong problem right.

[Anonymous No.15829771]

>>15828106
>The question does not include 10000's of attempts, it only has one.
>Yes, statistically, you would pick the only gold box more, because you have a higher likelyhood of accepting that scenario (you've picked a gold ball)
>But, since our sample size is [1], and the question already determined that we DID pick the gold ball, it becomes 1/2.

Okay, consider the following:
Supoose I'm literally just going to perform this experiment, let's say, 3000 times with 1/1000 odds. I can be expected to get around 1000 gold balls by picking the all-gold box 1/3 of the time, and at the same time, I can expect one (1) gold ball from the mixed box in all those 3000 tries. You agree with me so far, right? So of the 1001 gold balls I would get, there is only one (1) time where it doesn't lead to me getting another gold ball next.

Now suppose you come in around trial 2453 and say "hey, can I have a go just once?" and I say "sure". You pick a box at random, take a random ball from that box, and it happens to be gold. Do you really think your odds now are 50-50 because you're only drawing once? I have been "drawing once" 2453 times up to that point, got 817 gold balls, and they all led to me picking a gold ball a second time. What do you think the reason is that the distribution works out that way over 3000 tries? It is because each individual try has those odds.

So plainly, "it's 50-50 because we're only doing it once" is absolute nonsense.

[Anonymous No.15829796]

>>15829771
>I picked gold. 50-50 at another gold. And... I did it again.
>Picked gold. 50-50 at another gold. And... again!
>Picked gold. 50-50. Wow, another gold!
>I'm really lucky today!

[Anonymous No.15829827]

Threads like this must surely be cause for introspection in the average person. The fact that people can be entirely demonstrably mathematically wrong about something and still cling to their convictions completely makes me wonder, were I wrong, would I be equally oblivious to it? And if that is the case, am I? How can we truly know anything if we cannot know ourselves?

[Anonymous No.15829902]

>>15827561
You 1/2 faggots: Put your money where your mouth is. Open a casino and offer 4/5 that whatever colour ball is picked, the other one will be the same and a (sucker) bet at the same odds that it will be different. With your advantage, it should be a profitable game.

[Anonymous No.15830065]

>>15827561
Correct answer, thank you OP.

[Anonymous No.15830072]

>>15830065
(OP's answer was incorrect)