well? it's clearly 50 % right?

2/3

33%

>>7983991
>>7984053
WRONG

>>7983996
CORRECT

to everyone who reply after me
2/3 is objectively correct and if you arrive at another number, double check it because it's wrong

>>7983996
>>7984066
yep.

If anyone wants an intuitive description,
You're picking 1 ball at random, equal probability for all. So if it is gold, its probability is split evenly between those three.
2 have gold neighbour, and 1 has grey => 2/3

>>7984066
BUT

do you put the first ball back?

If you don't then it's 50%

Otherwise yes I agree it's 2/3

>>7984133
If you put it back it's 5/6

Let's name the balls A B and C, A and B are in the same box, C is with a gray ball
You pick a golden ball and it's...
A => 100% chance of golden ball next
B => 100% chance of golden ball next
C => 0% chance of golden ball next
so we have 1/3*1 + 1/3*1 + 1/3*0 = 2/3

If you put it back we get
1/3*1 + 1/3*1 + 1/3*0.5 = 5/6

It doesn't say put it back. Its 50%

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>>7984151
I came here to laugh at you

Its 50/50 you dont get to choose which box you pick So you pick from one box which is 50/50
If you get to choose a box its 2/3

You start with a box that already had a gold ball removed so it's 1/2 since it's either the box with the gold or the box with silver.
If you were trying to get 2 gold balls after you picked 1, it would be 2/3 since there is a box with 2 gold balls.
I hope that makes sense. The problem worded differently from the drawer exercise to confuse people.

oh my ever loving sweet lord baby jesus in space. Is this all happening again?

the energy spent here at 4 chan, is now significantly less that the energy needed to run an experiment and put it on you tube.

.... I thought 1/2, then realized its 2/3. There is a 2/3 chance your in the double gold box to begin with, and thats all that matters here

>>7983991
... and I hope, OP, you are somewhere cackling about your probably successful bait thread. that would be the healthiest motivation for breathing new life into this madness

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I'll post this again. For anyone who has trouble visualizing why it's 2/3, consider the same question but with more balls. Here it is more easy to realize that if the first ball you pick out of a box is gold, it increases the odds that the box you're picking from is the one with more gold balls in the first place

--------------------

Also, to anyone who refuses to believe it's 2/3 and genuinely isn't shitposting, you should know that this is a very well-known thought experiment called Bertrand's Box and the answer is already known. See https://en.wikipedia.org/wiki/Bertrand's_box_paradox

>>7984947
>>7984813

>>7984947
Why is this complicated? Assuming you dont put the ball back, there are 3 possible scenarios for what the next ball you pick is, 2 of them are a gold ball, one of them is a grey. Why would anyone genuinely struggle with this?

>>7985015
The thing is, that's what you assume it is.
The problem is actually asking a scenario where you are presented with a box that is missing a gold ball already, so there are only two options.
The original drawers question was what the probability of finding a gold ball in a box and then a gold ball again, which in that case it would be 2/3.

>>7983991
Forget the boxes

It's the same as putting 4 balls in a sack (3 gold, 1 silver) and taking 2 balls out.
The first one is gold
>what are the odss that the second one is also gold?

>>7985025
The question is literally about a box that's missing a gold ball though.

>>7983991

The key part of this question is "YOU PICK A BOX AT RANDOM"

That's what makes it 2/3 and not 50%

If it said "You pick a box with a gold ball in it.." then it would be 50%

>>7985028
>>7985025
Set up the scenario yourself and test it, tell us the results

>>7985025
This is the most enlightening thing I've ever seen regarding probability. Thank you.

>>7985019
I'll put it another way. If the first ball you drew was gold, then are are three possible things that have happened.
1.You picked the box with a gold and a grey ball and drew the gold
2.You picked the box with 2 gold balls and picked ball A
3.You picked the box with 2 gold balls and drew ball B

You are in one of these three scenarios, and its equally likely to be any of them. Scenario one always results in drawing a grey ball second, scenario's 2 and 3 both result in drawin a gold ball. 2 scenarios draw a gold, 1 draws a grey, its equally likely to be any of the 3, so your odds of a gold ball are 2/3

>>7985047
Sexy explanation i fell retarded now

>>7985034
Actually the box with 2 silver balls has no effect on the outcome. If the scenario was worded without that box being mentioned it would be exactly the same

>>7985057
Dont worry, I think I only got this so quickly because ive argued over the monty hall problem so many times, and this is a sort of similar thing. Probability is unintuitive sometimes

Isn't this board supposed to be the smartest?, its 50, the jpg clearly says from the same box, and never says you return the ball. Cant belive this is a thread

>>7985063

>>7985047

>>7985066
No, see
>>7984813

>>7985035
Let's say A is gold and B is silver.
If you were looking for finding a gold ball in a box after you already drew a gold ball, then it would be 2/3 since you can draw two instances of AA.
However, if you start with a box that already has A removed, it can only be an AA or AB box so it is 1/2. The question is asking for the probability of said box after the gold ball has already been removed so it is 1/2, rather than choosing a gold ball and then another one.

>>7985071
Except thats not how reality works, and that guy admitted as much after he read the explanation

>>7985082
That's how the retarded problem is worded.

>>7985079
Say box 1 has 2 gold balls and box 2 has a gold and a silver. If you pick a box and draw a gold ball, the probabilites are not equal that the box you are holding is box 1 or box 2. It is more likely to be box 1. See >>7984947 for a more obvious example of the same thing

>>7985086
Not it isnt actually, the wording is very clear

>>7985091
And I'm not talking about removing the ball. The box is presented having a gold ball removed. I know it is 2/3 if you go through the process of removing a gold ball and then a gold ball since there are two gold balls.
But if you are given a box that has already had 1 gold ball removed, there are only two possibilities to what box it is: The gold/gold or the gold/silver. The question starts with the gold ball already have been removed.

I've got a question about taking samples from a population:
If I have a population of 1105, and I need to create 50 random samples of 7, is it okay to randomize the population once collect a sample of 350 and break that into 50 samples without re-shuffling? Does that still meet the criteria of at least random?

I'm don't need simple random samples.

>>7985099
No it doesnt, the question starts with you picking a box and removing a ball, which is gold.

Il rephrase the question, but keep the scenario identicle. You have 2 boxes. In box 1 there are 2 gold balls, in box 2 there is a gold ball and a silver ball. You pick a box, and remove a gold ball. What is the probability the box you are holding is box 1?

>>7985109
The question starts after the ball has been removed since there is a period between ball and What.

>>7985109
Do you pick the box by random?

>>7985111
Yes

>>7985110
Whatever, the point is that you start with a box from which a gold ball has been removed, and a box with at least 1 gold ball in it is more likely to be a box with 2 gold balls than a box with 1

>>7985114
It's 50%

>>7985110
Look at this way. There is box 1 with 1 million gold balls in it, and box 2 with 1 gold ball and 999999 silver ones. You are given a box, and pull a gold ball out of it. Are you more likely to be holding box 1 or box 2?

>>7985117
>https://en.wikipedia.org/wiki/Bertrand's_box_paradox

It really, genuinely isnt

>>7985114
If you just pick a box by random, it's 50%

>>7985114
It would be 2/3ds
>>7985118
Look at it this way. You know that of the three boxes, you know that there is gold balls in two of them.
If you see a gold ball in one of them, what is the precentage that that particular box is the one with two gold balls?

>>7985130
Yes, but you know something about the box you picked, making it more likely to be one box than the other

>>7985136
I know, im trying to convince this >>7985130 guy of that

2/5

>>7985141
Oh, then it would be two thirds since there are two ways to get gold and gold. I think I'm just arguing about what exactly the question is asking since I think it's about whether said box that already had the gold ball removed is the correct box rather than the chance of getting a gold ball and then a gold ball.

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Visualization

If you don't believe the math behind it, here's a simulation to show it:
http://cpp.sh/2mbxk

>>7985146
Thats correct, and the question is clear, it just doesnt seem to be because of internal bias. Its like monty hall

>>7985142
2/3*

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>>7985155
The question does not seem clear since it's worded kind ambiguously whether to what is asking for: The percentage of the remaining boxes or of the entire sequence.

>>7985161
"What is the probability that the next ball you take from the same box will also be gold"

It is not ambiguous

It's 1/2 take this from an engineer, seriously I know math. I took a term in probability and we did this question.

>>7985167
>hurr engineers are sooo stoopid XD

>>7985164
That is the entire question. If the question was "what is the probability of the next ball being gold from the same box if you have already taken a golden box from it," it would be 2/3rd since there are two golden balls. But the question is "What is the probability that the next ball you take from the same box will also be gold", where you engage a box that is a missing a golden ball, it would become 1/2.

>>7985175
Its says you take a gold ball from a box, then asks the probability of getting another gold ball from the same box you took the first gold ball from. What do you think "the same box" is referring to?

File: 2000px-Monty_open_door.svg.png (76KB, 2000x1111px) Image search: [Google]

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Next Question!

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say
No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?"

What should you do?

>>7985184
Well you're supposed to pick door 2 to get 2/3rds since there is one less goat, but you're still kinda dicked into a 1/2 chance.

>>7985181
The question is only "What is the probability that the next ball you take from the same box will also be gold". Everything else before that simply modifies it as is not part of the question itself, which essentially ask: What is the chance of the box being the gold-gold box if it is missing a ball?

>>7984947
50%, either it happens or it doesn't.

>>7985187
Yes, but thats the same as just asking the odds of it being the gold-gold box. Its 2/3 either way. You have confused the question into thinking its asking "if there are 2 boxes in front of you, one with a gold ball in it, and one with a silver ball, what are the odds of picking the box with the gold ball". When in fact you have already picked a box

>>7985173
Fuck off, we're not stupid

>>7985025
No. It's just coincidence that those problems get the same answer. See >>7984947.

>>7985193
Look man, if the question was "asking if you pulled a gold ball out, what is the chance of pulling out another gold ball?" it would be 2/3rd. But the question only asks "what is the chance of pulling a gold ball out of a box if it is already missing a gold ball?" which is 1/2.

>>7985195
This is probably the least clever bait I've ever seen. Fuck off

>>7985200
Those two questions are literally identical

>>7985207
They are not, read closely.

>>7985207
The first question gives you a box that has two balls in it. The second gives you a box that has only one ball in it.

>>7985210
I did, they are asking exactly the same thing, the only difference is whether you pull the gold ball out yourself or the gold ball is already removed, as long as its a gold ball it doesnt change anything.

Remember that you are not being asked the odds of picking one box over another, you are being asked about the odds of a box you are already holding

>>7985151
>http://cpp.sh/2mbxk
Shitty random, changed to N=100
--> every time the answer was
m:34 M:47 prob:0.723404

>>7985212
Both questions give you a box with 1 ball in it. n both cases you are being asked the odds of the second ball being gold, and its 2/3 in both cases

>>7985184
This is the exact opposite of Bertrand's box,
here you are selecting a 'box'
boxA has two doors in it (P=2/3)
boxB has one door in it, the door you picked. (P=1/3)

by opening one door from boxA, monty
has changed the P distribution within boxA
from 1/3+1/3 to 2/3+0
You should understand that you are actually selecting between boxA and boxB

>>7985226
So what do you do?

>>7985215
>>7985219
The question does not exist before the ball is removed. You only know that the box is missing a gold ball, it is about the boxes; not the ball. The subject is about the content of the box being gold-gold, not of whether you can get gold and then gold.

>>7985228
select boxA of course

>>7985237
So you switch to door 2?

>>7985230
Yes, and if you are holding a box with a gold ball removed from it, you know it had at least one gold ball in before that ball was removed, and is therefore more likely to be the box that originally had 2 gold balls in it. The "box being gold-gold" and getting a "gold and then gold" are identical, in both cases you are really asking whether the box you are holding originally had 2 gold balls in it, and the odds of that are always 2/3, never ever 1/2

>>7985246
"gold-gold" and getting a "gold and then gold" are not identical.
You can get gold and gold in two ways as there is two gold balls in the Gold-Gold box which would make 2/3.
However if you start with a box that has a gold ball removed, it is either the Gold-Gold or Gold-Silver box. The question only starts with the gold ball removed from one of two boxes, it is not important if you removed it or not.

>>7985252
>it is either the Gold-Gold or Gold-Silver box
Correct, and its more likely to be the gold-gold box

If you are randomly given one of the 2 boxes, and told a gold ball has been taken out, then 2/3 times you will be holding the gold-gold box, and 1/3 times you will be holding the gold-silver box

>>7985150
She should switch to number 3.

>>7985257
>It is either the Gold-Gold or Gold-Silver box
Yes, and that is what I meant by being 50/50. Yes, it would be 2/3rd if the entire problem was part of the but the sentence that has the question mark.

>>7985257
>>7985252
Hang on a bit roll it back.

The key point is wwhether or not he ball is taken out before you pick the box or after. If it comes out after you pick the box, which is clearly stated to be the case in the question, then the odds are 2/3, if the ball is taken out before the box is picked, the odds are 1/2. You got me all confused for a minute there

>>7985266
That is what I meant. I'm sorry for confusing you.

>>7985274
Right. The original question does very clearly state that you pick a box then take out the ball though

"pick a box at random"
"take a ball from the box"
"it's a gold ball"

Whats the probability of the next ball from that same box being gold? 2/3

>>7985279
Yes, but as I see they were not part of the sentence that ends with a question mark, they are not to be considered as part of the question.
If it was all include in the sentence that ends with a question mark, then it would be.

>>7985196
no, when reduced to 4 balls (3g, 1 s) the problems become identical.
Both are simple 3-sceneario-probabilty questions. Only one (the boxes) is designed to trick you into viewing it as a 2 or 4 scenario problem

>>7984512
>is a weeb
>can't understand a simple explaination
Surprising.

>>7985283
Its all part of the question, the first parts describe the conditions of the sentence with the question mark in it.

The question "what is the probability that the next ball you take from the same box will also be gold?" on its own is meaningless. There is no possible way to answer that question without reference to the previous sentences. I dont understand why I have to explain this you arent 3

The problem goes you pick a box at random that has a gold ball in it. There is only two boxes that you can pick that has gold balls from it, and you have to stick your hand in it twice.
Since there is only one box among the two you can stick your hand in twice to get gold, it is 1/2.

>>7985300
Thats not even bad math its just shitty reading comprehension

>>7985290
It is not actually. Everything before the question has already been answered, the question is the only thing that has to be answered. It does not matter if the two boxes had 100 gold balls and 99 gold balls and 1 silver if they both have 99 removed. The question's outcome remains the same since everything before the question has already been resolved.

>>7985309
Actually no, your reading comprehension is shit.

>>7985309
It said you picked a box, not a ball.

>>7985310
The question asks about a box whose condition was determined by the previous statements. Its a box you picked, then took a gold ball out of it. The final sentence is meaningless without that information.

>>7985312
Yes exactly. You pick a box, and then take out a gold ball. The odds of there being another gold ball in that same box is 2/3

>>7985318
No it isn't, the question tells you that you picked a box that had gold in it. It don't matter because you could've picked only one of two boxes.

>>7985318
You picked a box that had gold in it, and then you have to take another ball out. The scenario is 50/50 chance of getting gold.

>>7985323
>>7985322
Nope, work on those reading skills

https://en.wikipedia.org/wiki/Bertrand's_box_paradox

>>7985324
The question says you already chose a box with gold, and then asks the probability of pulling gold from the same box again. It's asking about the same box, not about getting gold again.

>>7985332
Its asking about the probability of the box you chose being a certain box, given that you have already pulled a gold ball out of it.

Its not the samae as if you were offered a choice between 2 boxes you know had gold in them and then asking the odds of picking one of those boxes. The key point is that you pick the box before you know that there is a gold ball in it

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>>7985334
>The key point is that you pick the box before you know that there is a gold ball in it
Oh. Well that changes everything. Brb, I'm going to try and kill myself now.

>>7985338
Its all good, there seems to be some natural bias in people to make this sort of mistake, something like 90% do it, regardless of level of education

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>>7984151
lol

>>7984053
Nah mate, it's a 1/3 chance that you picked the double gold chest, not that your second ball will be gold.

you need to think about the problem logically.

Given the first ball is gold, what is the probability the second ball will also be gold?

There are only 2 scenarios when the first ball can be gold.

doublegold
(We have to treat picking any of the two gold balls in the same chest as the same event; really the event is selecting a gold ball so it doesnt matter if you pick the right gold ball or the left gold ball)

mixed left (this will not give you a gold ball)

among these 2 cases, you can see that there is a 1/2 chance that you will select a gold ball after selecting a gold ball.

>>7985351
Picking one gold ball or the other in the box with 2 gold balls are separate events. The odds are 2/3 that if you pick a gold ball from your box the next ball will be gold

>>7985343
Isn't that basic rationality? Like the retarded Monty Hall question where theoretically you would win a car 2/3rds of the time knowing that a goat is behind door 3 when it really just means you have a 50% pick in the end?

>>7985360
Well if you consider it a 1 out of 3 guess, then you do win 2/3 times. But if you consider it a 1 out of 2 guess, you win 1/2 times.
It's more about the whole perspective rather than just the two choice that matters.

>>7985366
But that's just kinda dumb. If you have to choose between 3 doors, and 2 of the choices will involve you getting hit in the dick with a hammer and 1 will have you fuck a hot slut, no one will choose the option of getting hit in the dick with a hammer if door number 3 is opened to reveal that.

>>7985351
>>7985359
>>7985360
>>7985366
you've all fallen for bertrand's box! The solution really is 2/3. The point of this discrepency is to show you that just looking at the events is not proper, you need to consider the probabilities of those events

https://en.m.wikipedia.org/wiki/Bertrand%27s_box_paradox

>>7985372
We all know the solution is 2/3, we're talking about how retarded it is since it really doesn't matter by the point the question is asked.

>>7985360
No in the monty hall problem you really genuinely do have a 2/3 chance at the end

>>7985366
No in the end question of the monty hall problem, if you switch doors 2 out 3 times the you will win a car, if you stick with your door you win 1 in 3 times. There is no perspective, your odds of winning are 2/3 if you switch doors in the second half of the problem

>>7985373
But thats not correct, it absolutely does matter

>>7985375
Yeah! What if we pretend the boxes are really roomsin the next saw movie, and we all have to figure which room was right

>>7985377
Or what if you were actually on the monty hall show, and wanted to win a car?

>>7985374
No you don't. Yeah, you only had a 1/3rd chance, but if you switch doors you get a 2/3rd since you're essentially making two guesses rather than 1. Regardless, you're still choosing between two doors.

>>7985383
Ive succesfully convinced at least 2 people in this thread, its by far the most productive time ive ever spent on /sci/

>>7985388
Thats right you are choosing between 2 doors, but the doors do not have equal chances of having a car behind them. The car is more likely to be behind the door you didnt choose first, than it is to be behind the door you did

>>7985395
What if I didn't choose any door.

>>7985397
Then it's 1/2.
But it is 1/3rd if you stick with it since you picked the door when you knew it was only 1/3rd of a chance of being the car. Door number 3 was revealed, meaning it took its 1/3rd and gave it to door 2.

>>7985397
Then you arent playing the game so who cares?

>>7985405
Because I'm betting after the goat is revealed.

>>7985407
But to get to that point you have to have already picked a door

>>7985150
Tewi already drank the antidote because she's a liae.

>>7985414
I'm in the audience.

>>7985420
Then whoever is playing the game chose a door and its a 2/3 chance the car is behind the door he didnt chose

>>7985422
But I don't know what he chose. I put the bet after door 3 is revealed.

>>7985430
What you know is irrelevant, the odds are not dependent on your perspective. The door he didnt pick will have a car 2 out of 3 times regardless of what you have seen

>>7985431
But I don't know that. I just know there are two doors. Which one should I pick if I don't know which one he initially chose?

>>7985433
The choice is between "stay" or "switch" rather than between door x and door y. If you are somehow unable to tell which one he is staying on then you dont have enough information to make a good choice, it would appear to be 50/50 even though in reality it isnt

>>7985286
>it happens or it doesn't
Dumbass.

It's 1/3

>>7985218
Yeah it would have been better to seed the RNG

>>7986047
Yeah, dumb brainlets don't realize you only had a 1/3rd of a chance to pick the right one to begin with.

>>7983991
It's 1/3 because you can't switch. You're stuck with door 1.

>>7985047
why explain your right answer wrongly?

>>7987419
Whats wrong with my explanation?

>>7983991
>Only one box has 2 golden balls
>Durr its fiddy% right?

Kill self

>>7984512
Maybe you should go back to your Asian studies major. They seem to accommodate retards.

>>7985831
>Dumbass
how so?

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for the people still in denial.

Since the first ball is gold, we must have picked either box1 or box2.
The next ball will be gold only if we picked box1, and will never be gold if we picked box2, ergo probability is 50% - the probability to select box1 out of two.

Find a flaw.
Hint: you cant

>>7987550
Java random generator is an NSA-planted bug.

>>7987570
You can pick two different golden balls from box1 but only one from box2, so box2 will only count half the time (when you pick the golden one)

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>>7987570
>The next ball will be gold only if we picked box1, and will never be gold if we picked box2,
Of course.

>ergo probability is 50%
No, box 1 is twice as likely to provide the "gold ball first".

>>7987570
>only if we picked box1
pick box 1 by getting left ball
pick box 1 by getting right ball
pick box 2 by getting left ball

do you see that there are 3 posisble scenario's?

>>7983991
The question is intentionally badly worded, so that most people assume that the ball that you pick isnt put back. That's why most people come up with 1/2, and they are right, you get 1/2 if you dont put the ball you picked back.

The 2/3 answer is correct, too, but under ANOTHER set of assumptions. This is basically the meme dress of mathematics, where people assume diferent things, then endlessly debate about it. Stop. There's nothing else of interest about this crap.

>>7987592
It's not put back. But it's 2/3. >>7984151

>>7987597
You dont pick balls. You pick boxes. Again, its badly worded to cause people to believe those two things at the same time.

>>7985161
Still 1/3

>>7987592
This is the most relevant post in this thread.

>>7987601

>>7987576
>>7987591
>>7987550

>>7987647
read again the post. The people you quote are right, too.

>>7987632
no it is not. It is just as stupid as all the other replies who try to push ½ as the correct answer.

>>7984947
What's the chance in this problem with 20 balls?

>>7985025
no.........

>>7987591
this
this is the answer
you have said it very concisely like no-one else has

>>7985372
Wrong. One of the parameters is that you select a gold ball.

There is only 2 boxes with gold balls

What is the probability your next ball will be gold?

>>7988284
Sorry, forgot to mention the other parameter: you take the second ball from the same box as the gold ball you got at first

>>7987525
It's pretty clear from applying the same reasoning to >>7984947 that the method >>7985025 suggests is flawed and only gets the correct answer by coincidence. You can't just say things like "there are three options, two of which satisfy the condition; therefore the probability is 2/3." You have to have a reason why those options are equally probable.

For a correct explanation of the answer see >>7985047. In that case, it's clear from the description
>You pick a box at random. You put your hand in and take a ball from that box at random.
why the scenarios there are equally likely.

Honestly I think it has to be somewhere inbetween 1/2 and 2/3.

>>7988417
ruse?

>>7987592
You do not result with 1/2 probability under 'no replacement' assumption for this question. calculations must be off to get this.

>from the same box
>already took a gold one
Its a 50% chance, it all comes down to getting the right box, and the one with two grey balls is discarded since you already took a gold ball

>>7988519
need to account for there being two events from drawing from box A. Draw first gold ball, draw second gold ball. These are two events in which you succeed. Box B has one event from drawing. Drawing the only gold ball. Three events total, two successes. 2/3

First reply was correct
Still 166 posts going on 300

>>7985047
No. You shouldn't label the balls, it confuses you.

You either chose the gold/grey or the gold/gold

>>7985047

Wrong.

>1.You picked the box with a gold and a grey ball and drew the gold
>2.You picked the box with 2 gold balls and picked ball A
>3.You picked the box with 2 gold balls and drew ball B

The probability of 2 and 3 are 25% each.

Because of the parameters of the question.

Your dick is either in the gold/gold box or the gold/grey box

Labelling the balls achieves nothing

Just to clarify:

Either:
a.) You pick a box out of the two with gold in them and then answer the question. In which case 50%.

b.) You pick a gold ball from either of the two boxes with gold in them in which case the answer is 2/3 because you pick the box with two gold balls twice.

>>7983991
1 l 0
1 l 1

Only two possible outcomes if the first ball is always gold
50%

>>7983991
There are three different cases in which you will pick a gold ball.

In two of those cases, you will pick another gold ball on your second pick
In one of those cases, you will pick a silver ball on your second pick

Therefore, the probability of picking a second gold ball should be 2/3

>>7987550
this should've been the first post to stop people from debating.

>>7990512
>>7988519

Think about it this way.

There are 1 million balls in each box.
In box 1: all the balls are gold.
In box 2: ONE ball is gold, 999,999 are silver
In box 3: all the balls are silver.

You've just successfully chosen a gold ball. You celebrate.
You think to yourself. What are the chances that I chose from box 2? Pretty low.
Therefore, you'd be smart to bet that your next pick will be a gold ball.

>>7990534
Did you read my post; I said that either you choose the box based on the fact that we know their is a minimum of one gold ball OR you choose a gold ball; in which case there is 2/3 chance because there is two outcomes where you pick the first box.

In your example the chance would be either:
a.) 1,000,000/1,000,001 because there would be a million and one ways to pick a gold ball only one of which would not result in gold on the second pick.

OR

b.) 1/2 because you either you picked the box with 1 million gold balls or you picked the one with a million-1 silver balls.

It all depends on the wording.

>>7990532
The program chooses a gold ball from 3 and in two of those situations the next ball is gold. 2/3 chance.

If it was programmed such that it picked a box with a gold ball in it and then displayed the colour of the other ball the chance would be 1/2.

File: golfclap.gif (2MB, 450x345px) Image search: [Google]

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>>7990515
>Only two possible outcomes if the first ball is always gold
>50%
I'm going for a walk today.
I'll either get hit by lightning or maybe not.
Only two possible outcomes.
50-50

>>7990508
>The probability of 2 and 3 are 25% each.
No, the probability is 1/3 each because of the parameters of the question.

>Your dick is either in the gold/gold box or the gold/grey box
Correct, but its twice as likely to be in the gold/gold box

>Labelling the balls achieves nothing
Labeling the balls highlights the fact that pulling one ball or the other out first are separate events with equal probability of occurring

Like what this >>7990521 guys says

>>7990564
You randomly choose a box, you know nothing about the contents of that box, it clearly states this in the question, there is no ambiguity

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>>7990564
>If it was programmed such that it picked a box with a gold ball in it and then displayed the colour of the other ball the chance would be 1/2.

Nope.
Pic related.
Similar program, but I didn't include the silver-silver box.
Out of a million tries, about 250k are disqualified because a silver ball is picked first.
Of the remaining ~ 750k, 2/3 are gold-gold.

>>7990581

>>7985149

>>7990608
This is a 181 post thread and there is no ambiguity. It is intentionally deceptive. I highlighted the distinction clearly in my other comment.

>>7990616
This is the same. Your program picks a gold ball and then records how often the other ball in the box is gold. 2 out of three times this is the case.

The distinction being made is between the aforementioned program and one where a random box is picked, a gold ball is removed and the colour of the other ball is recorded; in which case the ball would be gold 50% of the time.

>>7990630
The question itself is completely clear, you are adding ambiguity that doesnt exist

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>>7983991

>>7990632
So if I reworded the question thus:

(With the same 3 boxes) Upon picking a box that contains a gold ball, what is the probability that the other ball is gold?

How would you answer. Because this is how other people are interpreting it.

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>>7990630
>Your program picks a gold ball and then records how often the other ball in the box is gold.
No, my program picks a RANDOM ball, and discards the cases where the first ball is silver.

>one where a random box is picked, a gold ball is removed and the colour of the other ball is recorded
That's EXACTLY what my program does.

>in which case the ball would be gold 50% of the time.
Look at the output.
Out of a million tries, about half are gold-gold, 25% are gold-silver and 25% are silver-gold.
BUT, the silver-silver cases don't count towards the total, so half a million gold-gold out of 750k qualifying cases makes a 2/3 ratio.

How about instead of making vague pronouncements, YOU write a program that illustrates your point?

>>7990646
Then its 1/2, but since thats not what the question was, it only goes to show that people are morons

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>>7990646
>(With the same 3 boxes) Upon picking a box that contains a gold ball, what is the probability that the other ball is gold?
>How would you answer. Because this is how other people are interpreting it.
see:
>>7990669
>Out of a million tries, about half are gold-gold, 25% are gold-silver and 25% are silver-gold.
>BUT, the silver-silver cases don't count towards the total, so half a million gold-gold out of 750k qualifying cases makes a 2/3 ratio.

>>7990669
>BUT, the silver-silver cases don't count towards the total,
Oops: meant the silver-GOLD cases don't count
sorry

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>>7990669
Your program picks a golden ball from box 0 twice as much as it does from box 1 because there are two golden balls in box 0.

I rarely deploy Carrot memes but you are pushing me.

>>7990730
Just hope you don't get a KILLER!

>>7990730
Thats the point though

>>7990735
Yes and the people who think it is a half interpret the question to count golden balls in box 0 and 1 equally.

I don't know about you but I'm really in the mood for some Golden Balls. Shame it stopped.

>>7990741
And those people are interpreting it wrong. The question is not ambiguous, even if a lack of reading comprehension makes you think it is

>>7990741
>I don't know about you but I'm really in the mood for some Golden Balls. Shame it stopped.
It was an interesting concept but I think the execution was lacking. The idea that you need to balance taking someone trustworthy but also with money is pretty unique.

>>7990745
ok.

>>7990760
Yeah. That final round game theory though. I only really like it because of Jasper Carrot.

>>7983991
I'd lift the box and see which one is heavier

>>7985184
can I pick door 3?

>>7985184
No, because I want a pet goat.

>>7983991
While it certainly took me a while to get it, the conceptual gist of it is this:
Before you picked any ball, you're much more likely to pick a golden ball from the gold-gold box than the gold-silver box, so after picking a golden ball, the likelihood that you have picked the GG box over the GS box is higher. That larger likelihood needs to be taken into account.

>>7983991
Why is this so fucking debated? There's only one box that satisfies the 2 gold balls scenario. The chance of choosing the correct box to do this is 1/3, plain and simple. Remember that you're taking both balls from the same box, so no matter what the sample space is, there's only a one fucking third chance of choosing the correct box for two gold balls to come out of it! It says the ball must ALSO be gold, clearly implying that the first ball that comes out of the box must be gold, so anybody thinking 2/3 is WRONG!

>>7993082
Its not asking the odds of initially choosing the g/g box. Its asking how likely it is that you are holding the g/g box if you draw a gold ball out of the box you chose

>>7993105
Oh. now that I read it again and actually understood what it was asking, I agree that it is 2/3. My bad! Maybe that's why it's so debated.

Everyone who says its 2/3 is retarded.

1)You pick a golden ball yet pick a box at "random" - nonsense this is not random, the 3rd box is useless
2)Picking the golden ball effectively means you only have two boxes with one silver ball in it or one golden ball.

Therefore the whole problem set is simplified into picking one of two boxes which either hold a silver or gold ball, i.e 50%

go fuck yourselves autists

>>7983991
36%

>>7993143
No you moron, it asking how likely it is that the box you picked is g/g if you pick a box then pull out a gold ball. 2/3

>>7993166
Thats the thing, there is no "how likely" in you picking - because its predetermined for you, no matter how many trials you conduct the fact remains that the first thing you pick is a golden ball, there is no choice in picking a box. Hence the actual choice is only choosing a box after the first golden ball has been removed, but then that only leaves a golden ball in 1 box and a silver ball in another, but notice how you were forced to pick a golden ball at first, this means the probability derives from the predetermined action that was given to you i.e picking a golden ball the first time round.

There was 50% chance that you picked golden ball from box 1 or box 2, and all thats left is a singular golden ball in either box 1 or box 2, same goes for the silver ball

Prove me wrong.

>>7993185
>There was 50% chance that you picked golden ball from box 1 or box 2
This is where your mistake is. Since box 1 has double the gold balls as box 2, it's twice as likely your chosen box is box 1 if you pick a golden ball.

>>7993185
>that the first thing you pick is a golden ball
No no no the first thing you pick is a random box. You seem to have totally confused what is happening here.

This is what has happened before the question is asked

1. You picked a random box out of the 3
2. You pulled a golden ball out that box

You now want to know how likely it is that the box you already picked had 2 gold balls in it.

>>7983991
"You pick box at random. You put your hand in and take a ball from that box at random. It's a gold ball."

This is redundant statement. It's either a gold ball or it's not. Since it is given to be a golden ball, there are only two possible outcomes. 1/2

>>7993207
>>7993217
ohhh fug. thanks family

>>7993219
Its not a given. You could just as easily have pulled a silver ball out of the box you randomly chose, but the question isnt asking about those scenarios

>>7983996

wdf am i missing i must be fucking retarded that s it i quit science

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>>7987550
This is a basic problem, you only need basic code. If you're trying to prove a point, you should either comment your code, or not write it so weirdly; otherwise people can't be certain you haven't made a silly mistake like making a box with more gold balls more likely to be picked (in which case, the boxes in pic related would be 66% 33% 0%)

Seriously, why would you use "Random generator = new Random();" rather than "Double randomNumber = Math.random()" when the latter is common in many languages whereas the former is Java-only?
That and basically everything else about your code is incredibly strange.

>>7993331
So long as you accept the odds are 2/3

Alright, I've found the solution to satisfy everyone:

If your procedure is that if you pick a random box then you pick a random ball and you start over without counting anything if that first ball is silver, then that means that you're effectively twice as likely to have your second pick come from the first box, meaning you end up with a 66% chance of the second ball being gold.

If your procedure is that if you pick a random box and there's a guarantee you'll have picked a gold ball if there is one, then you're equally likely to have picked box 1 or 2 thus there's a 50% chance your second ball will be gold.

There's no clear way to settle this since the language of the OP can be interpreted to mean either.

It's 1/2, because the all-silver ball box is out of the question at THAT point. It's a trick question.

>>7993386
The original question is not ambiguous at all

>>7983991
yep its 50

>>7994776
wait no 1/3

>>7994779
The question is essentially asking which box is it possible to take two balls out of.
The possibility exist in one box, because its the only one with two gold balls

>>7983991
I would say 1/2, because if you took a gold ball, you either took the box with 2 gold balls or the box with one gold one silver.

>>7985149
I see, the problem didn't say that that balls, other than their color, were distinguish able. Thanks.

>>7994917
But it's more likely that you chose from the first box since it has more gold balls.

Replace the first box with a box that has a million gold balls and the reason becomes clear.

it feels good to be intelligent

i solved this in my head in under 30 seconds

its 2/3

i feel bad for anyone who struggles with this sort of thing

>>7994934
Yes, that's another way to think about it...in that extreme case.

>>7994943
It's 1/2 fuckwhit.

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i know i am smarter than like 99% of the rest of humanity, but stuff like this i dont understand how it could be considered difficult.

here is a picture

File: proof.png (51KB, 804x656px) Image search: [Google]

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i'm just a genius, but here is a rigorous proof to supplement my drawings

really the trick, as with any problem like this (eg monty hall), is to recognize conditional probability and account for it.

once you do that, any question like this can be solved in seconds.

>>7983991
50. if you get gold, one box is eliminated

two boxes. either now one box has only a silver left, and one box untouched with two gold, or now there is a box with one gold, and another with a gold and silver.

if you took it from the heterogeneously mixed box, you will not get gold. but, there was a 50 percent chance you got that box out of the two possible boxes.

if you took it from the box with two gold, you will get another gold. there was a 50 percent chance you picked the box with two gold out of the two possible boxes to get a gold ball.

>>7995060
If you are holding a box that you took a gold ball out of, 2/3 of the time that box will have originally had 2 gold balls in it

the box with two grey balls isn't even part of the question because the question assumes the box you picked already had one gold ball in it. Therefore there is a 50/50 chance you picked the mixed box and a a 50/50 chance you picked the all-gold box, making the probability that the next ball is gold = 50%

>>7994958
But for all intents and purposes the 2 right ones are identical...

>>7995196
No they arent, they are entirely separate events

>>7995087
elaborate, the way i see it, it depends on the box, and if you dont know whats in the box, there is a 50 percent chance you get the one that will guarantee gold.

>>7994955
agreed

>>7995284
The question is not asking the odds of picking one box or another. Its asking the odds that you have ALREADY picked the g/g box if you reach into the box you picked and pull out a gold ball

>>7994958
"i know i am smarter than like 99% of humanity"

stop, if you were, you wouldnt say that. quit being an arrogant ass. you are one reason why i rarely visit this board even though it is the most interesting topic

>>7995340
im sorry the bigitude of other peoples intelligence intimidates you and drives you away from intelligent discussions

but reality is reality

>>7995354
>bigitude

Brainlet confirmed

>>7995358
>not informed of popular meme on mega society forums

140 IQ from iqtest.com confirmed

>>7995381
>unironically taking iq test

Mega-brainlet confirmed

>>7995284
There are two countries, country A and country B, with the same population. Country A has 50% purple people and 50% green people. Country B has 100% green people. You pick a random green person. What are the odds that they are from Country B?

It's the same problem worded differently.

>>7995386
>lacks basic reading comprehension

multiple tries to get 129 on iqtest.com confirmed

>>7995397
Well I assumed you were talking about yourself even if it didnt make sense, because why would you try to compliment me?

>>7995401
>thinks 140 IQ on feel-good IQ site is a compliment

proud of 115 on IQtest.com confirmed

>>7995403
Actually I scored 156, brainlet

>>7995407
>boasting about IQ score from IQtest.com

confirmed 110 IQ on iqtest.com after looking up the answers

>>7995463
I just re-did it and scored 164, take that brainlet

>>7995469
>having to retake IQ tests on iqtest.com and not immediately hitting the ceiling

trogoldyte confirmed

>>7995478
>making spelling mistakes

sub 220+ IQ confirmed

>>7995478
Yeah well my professor told me my work was "adequate" and that means really good so im probably going to get a PhD at finals

>>7983991
1/2