Is anyone here RETARDED enough to believe the probability is 50/50?

>>8603718
Its literally 50% the right box is pretty much xcluded if you know beforehand the pattern of arrangement
am i missing something?

>>8603718
I think we should add to sticky some of these threads with explanation of the answer (or just a wikipedia link) so we won't have to see the same shit over and over and over again.

>>8603718
brainlet bait
sage

>>8603729
holy fuck i thought /sci/ is where the people with at least some amount of brains go to

the condition is that no matter what, you obtained a golden ball. out of the 6 possible balls that might have come out, only 3 satisfy this condition. however, only 2 will let you fully win the game by getting 2 golden balls.

2/3

>>8603736
i got 404s on other boards and thought i'd try my luck here because seeing americans struggle with this problem is funny

>>8603738
can you even answer the question pls?

>>8603742
There aren't six possible balls. There are four possible balls. The other two are in a box with no gold balls, and therefore could not have been drawn.

>>8603742
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
Now go away.

>>8603718
Assuming the two silver balls in the right box are in the same closed system of boxes as the farthest right box and abide by stable thermal equalibrium the contents of the furthest box to the east have a 33.3% chance of becoming entagled with any 2 other balls. Assuming the first ball drawn was gold it is possible that it tunneled through either 1, 2 or 0 boxes to reach your hand. Upon the second draw the odds of the ball being gold from box 2 or 1 is 14.65% or the farthest west box being 100% due to the plank constant raised to the power of possible ball-hand permutations. What this means is that the em drive just works because it generates dark propulsion.

>>8603759
>plank constant
>plank
fuck outta here

>>8603748
Yes, four possible balls. You got a gold one (eliminating 1 out of the 4). Now the ones remaining are GOLD, GOLD and SILVER

2/3

>>8603742
Are you retarded? The question specifically asks about the probability of the NEXT set of balls, literally no other case can be made about it. Its 50% you made up a whole scenario that has nothing to do with the question

>>8603769
The next set of balls depends on the ball you currently picked, obviously.

>>8603742
Sad that you would make this thread to try and feel better about yourself by laughing at people who can't solve a simple probability question that can easily be confusing. Petty and small minded.

>>8603768
Y r they"re 3 balls in 1 bocks?

>>8603779
No, I just saw this on /pol/ and how everyone who picked 50/50 had a USA flag and then I remembered the times I was wrong about the Monty Hall problem.

The fact that you are even making any kind of assumptions about me and my psychology based on 4chan posts is funny to me as well, because I am now laughing at you too.

>>8603776
so it's 50/50, you either picked the wrong box or you didn't.

if you picked a gold ball out of the box, you have chosen one of the two boxes with gold balls in it. there are two boxes with gold balls in them. So you have a 50/50 chance of your box being the correct box assuming you picked the box randomly and you can't switch boxes.

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>>8603768
Remaining might be G/G/S, but that third gold ball is irrelevant since you would have picked it if given that you got the other box, which in turn will make the first box irrelevant and vice versa.
>math fags always trying to overcomplicate shit

>>8603788
>so it's 50/50, you either picked the wrong box or you didn't.
you wouldn't say that if I didn't tell you about the golden ball being first. You only consider the SS box to be at 0% once you are told that your box has at least 1 golden ball in it.

You now know there is a golden ball in the box you picked, and the problem now lets you know that there are (including your ball) 4 balls that can be drawn.

1 is out because it's your own ball
2 balls are gold
1 ball is silver

2 gold, 1 silver

2/3

>>8603797
Again, the ball you first picked is UNKNOWN. You know it's gold, but if they were all labeled A, B, C, you wouldn't know which one you got, only that it is gold.

>>8603802
Youre trying really hard with some low quality bait. Please return to >>>/pol/

>>8603776
But that is the starting point, nothing matters before it, this IS the new case scenario that has been provided at 100% for he question to be asked

>>8603802
Kek. But you are literally told so and are asked on that specific ground

shit tier bait sage

>>8603802
Consider that picking the correct box is a success condition. the third box with two silver balls in it is irrelevant because you haven't picked that box. you now have two boxes, one of which you have picked. the balls in the box are irrelevant, the only thing that matters is that one box is a failure condition and the other box is a success condition. Assuming you picked the box at random, you have a 50/50 chance of getting the correct box.

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>>8603802

>>8603786
It's funny because it's true pal. No assumptions were necessary.

>>8603802
3 boxes, 1:GG 2:GS 3:SS. You pick G. Only boxes 1 and 2 contain G. Your odds of having G pair in box 1 is 100%, your odds of having G pair in box 2 are 0%. Average the odds (100+0)/2=50
The odds of G pair being in a G box is 50%

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>>8603829
christians: 1 atheists: 0

>>8603718
Listen I'm going to let you in on a secret. This thread gets made all the time. Everyone knows the answer. 50/50 replies are just having a laugh watching you earnestly try to explain it again and again.

>>8603811
Yes, I remember making the same argument for the Monty Hall problem, except that whatever comes 'before' DOES matter. There is no "new case", because it is still the same problem. You already have one condition. The way you put it makes it sound like we are picking between 2 boxes where one has silver and the other has gold- then it would obviously be 50/50, but that is not the problem.

>>8603814
That's exactly the reason why it goes from "anything is possible" at the beginning to "some outcomes are more probable than others", such as the chance of the outcome of having 2 silver balls becoming 0%

>>8603816
The balls in the box do matter, because they are what the win condition is- 2 golden balls. I know it's hard to understand, especially since I've been on the other side of the argument, but I hope you can come around to it. Maybe Wikipedia will help.

>>8603818
Can you tell me which of the golden balls it was? Left, Middle, or Right? No, you can't. It is an unknown golden ball.

>>8603823
>more assumptions

>>8603829
You are not calculating probability. Only possibility under the assumption that all outcomes have equal probability, which they do not.

I can rephrase the question:

There are boxes numbered 1-3
1: G, G
2: G, S
3: S,S

You picked a box, and you were told it had a golden ball in it. What are the odds that the box you picked is Box 1? The gold ball you were told about might be any of the G's, but box 1 (with 2 G's) is more likely.

>>8603809
make me

>>8603845
>but box 1 (with 2 G's) is more likely.

Why is it more likely?

You reach into box GG or box GS. Either way, you get a gold coin.

If you reached into box GG then you have a 100% chance to pick another gold coin. If you reached into box GS then you have 0% chance to pick another gold coin. You can't know which box you picked. You only had two options of boxes to pick. 50% chance.

People that say 2/3 assume there's a chance to pick a silver coins first, and if that happens then the coin is put back in the box, the boxes are shuffled, and the problem resets.

You can't pick a silver ball first. You can only choose between 2 boxes, not between 3 gold coins. You have no way of knowing which box you drew from, but you have a 50% chance of having picked the GG box.

>>8603718
> The boxes are chosen at random, if there is a golden ball in it is removed

you're not getting the two thirds GG to 1 third GS box rate, so it's 50/50

>>8603844
I assumed a few of these guys would be trolling like
>8603834
but I consider the amount of mental gymnastics required to write extensive posts where you attempt to give a solution you know to be wrong to a probability problem to be beyond the capacity of a normal well adjusted human.

I'm sure there might be a few guys who earnestly don't know

anyway thanks for telling me

>>8603718
The experiment starts when you already have eliminated the third box. So it is 50:50

>>8603859
>You can't know which box you picked
since you picked one with a gold coin, it's more likely to be box 1

>>8603859
I think the spin this brainino is trying to put on it is that everything is made up and the boxes dont matter. Im your host, Drew Carey.

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>>8603845
>Can you tell me which of the golden balls it was? Left, Middle, or Right? No, you can't. It is an unknown golden ball.

>Left, Middle, Right

It is either the GB with another GB as a couple OR ot is a GB with a SB as a couple.
Theare are no Left, Middle, giraffes, dark energy and pagan magic involved.

50/50

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>>8603873
>>8603844

ok fine, at least 2/3 of you are trolling

i leave this thread in shame

>>8603868
Why?

You pick the box, then you pick a coin, and that coin is gold.

You have an equal probability of choosing either box.

Getting a gold coin is a certainty.

Therefore it's as likely you choose the mixed box as the pure gold box.

The framework of the false paradox guarantees the first coin drawn is gold.

You aren't twice as likely to pick the pure gold box, and the first time you pick the mixed box you're certain to draw the gold.

And obviously you can't draw from the pure silver box because then you defy the framework of the scenario.

>>8603868
Picked ball is could be any one [G]
Box 1. Box 2. Box 3.
([G][G]) ([G]S) (SS)

What are the odds that within each (box) one picked [G] shares the (box) with another [G]?

100% for box 1, 0% for box 2, box 3 is not applicable as it contains no [G].

What is the average of 100% and 0%?

50%

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>>8603880
>at least 2/3 of you are trolling
got me


>>8603883
this


It was made to troll the fags that fucked up on monty hall and are now damaged forever.

>>8603858
Not op and cant explain in mathematic terms but imagine having a sea of gold balls and a sea of silver balls with 1 gold ball n them. You shove your hand and pick a gold ball. Its more likely that you picked it from the sea of gold balls than he sea of silvers with 1 gold

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>>8603718

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>>8603889
amazing

>>8603889
You are picking a gold ball. It is irrelevant what the other contents of the set are as long as you can select 1 gold ball. The original selection isnt probable, it is static. There was 1 gold ball selected. There couldve been 69 billion rainbow collered balls and one gold ball in one set and 69 trillion black balls and 1 gold ball in the other, the odds of you selecting a gold ball if ypu must select a gold ball is always 100% given the set contains a gold ball.

>>8603898
Thank :▪)

>>8603889
It's more like your hand can only hold gold balls, so regardless of which sea you shove your hand blindly into, it's guaranteed to pull out a good ball.

You have an equal chance of choosing either sea.

>>8603908
You asked why it was more likely to pick a gold ball, that means you need the probability before you pick the gold ball and its very unlikely that you are gonna pick the gold ball from the countless silvers

>>8603912
There is no such factor you made that up

>>8603883
>You have an equal probability of choosing either box.
No, you don't.
The part about "picking a box randomly" becomes irrelevant, old information as soon as you exclude the box with only silvers. It's extraneous information.
The problem explicitly states that you picked a gold ball at random, and 2/3 of the gold balls are in the box with 2 golds.

>>8603919
Try reading the original problem. You pick a box, then you grab a random ball, and the random ball is gold.

You can't operate on the framework that the random ball might not be gold. The random ball is certainly gold. You only picked between 2 containers that had any number of gold balls.

That is a plainly stated factor.

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>>8603895
You don't calculate by balls, you calculate by boxes,
>What is the chance that the second ball that you pick is gold.
This is the question.
If the balls were not seperated by boxes, then "2/3" would make sense.
They are seperated. Go fuck yourself.


>to smart to stop responding in bait threads

>>8603928
I think you're confused. You pick a gold ball at random OUT OF the box you picked at random prior. You're not picking from 3 gold balls assigned to two different boxes, you're just taking a gold ball out of whichever box you picked.

>>8603931
Ok if we are to discuss solely on the problem then the question asked has as answer 50%

Isnt it?

>>8603939
Your brain is up your ass, btw.

>>8603916
But you do pick the gold ball. 100% of the time. Even if the probability of selecting the gold was 100% or 0.00000000000000000001%, the gold WAS picked. A set containing all gold or almost no gold are equal candidates of having a gold ball.

>>8603945
no, it's 2/3, see >>8603895

>>8603959
That diagram assumes you didn't select a box before selecting a ball, or that there was a chance of selecting a silver ball.

Either way, the diagram is fallacious.

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>>8603959
>no, it's 2/3, see >>8603895

>>8603959
But the problem asks what the probbility of the NEXT ball being gold is, it doesnt take into account anythig else. The way the problem is worded its obviously 50%

>>8603941
>you're just taking a gold ball out of whichever box you picked.
Nope. You can't see inside the boxes. There's no way to guarantee that the ball you draw will be gold unless you're only choosing among the golds.
The silver ball inside the mixed box isn't an option, so you're not actually picking between the all-gold box and the mixed box as illustrated.

>>8603779
In the thread he made on /b/ he would just blandly reply "wrong" to everyone who made an argument that wasn't a verbatim copy of wikipedia.

One guy made a perfectly sound argument but he used a roundabout way and used 1/6 in his calculations somewhere. Because the small minded OP never saw that number on wikipedia he just claimed it was "obviously wrong and you don't even understand the problem" without trying to actually understand the approach that person took. Fuck him.

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>>8603718

Assuming the golden ball was picked from the GS box, and the ball is not returned, then there are two possibilities

If you pick from GG you'll pick gold
If you pick from GS, you'll pick silver

1/2

Assuming that the golden ball was picked from the GG box, and the ball is not returned, then there are three possibilites

If you pick from GG, you'll pick gold
If you pick from GS, then
a) you'll pick silver
b) you'll pick gold

2/3 chance of picking gold

[math]\frac{1}{2} * \frac{2}{3} = \frac{1}{3}[/math]

The answer is [math]\frac{1}{3}[/math]

>>8603969
>anythig else
read again, it says 'same box'

>>8603973
You pick either the gold gold box or the gold silver box, because you pick a gold ball and there aren't any in the silver silver box.

We all understand that.

The same logic continues to apply.

Whether you pick the gold gold box or the gold silver box, you still pick a gold ball.

Since you already picked a box, it's just as likely your box has one silver left as one gold left. You were no more likely to favor the gold gold box because the constraints make either box as likely to give a gold ball the first time around.

>>8603990
>You were no more likely to favor the gold gold box because the constraints make either box as likely to give a gold ball the first time around.
Here's where you're getting confused: there's no "constraint" that magically changes probability. The problem is misleading you when it suggests your choice was truly random.
Your 50/50 choice was overruled, and a gold ball was taken from one box and placed in your hand. Anything else is impossible.

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>>8603718
How is this wrong?

Didn't read the thread but going to have a go anyway.

If you pick a gold ball, chances are 2/3 it was in the left box and 1/3 it was in the middle box.

If it was the left box you're guarenteed to pick another gold. If it was in the middle box its guarenteed to be silver.

So the answer is 2/3

fight me faggots

>>8604084
>If it was the left box you're guarenteed to pick another gold. If it was in the middle box its guarenteed to be silver.

so 50/50

>>8604065
P(X=0)=0

>>8604091
>If you pick a gold ball, chances are 2/3 it was in the left box and 1/3 it was in the middle box.

The people in this thread really suck at exlaining it, but it is indeed 2/3. Just read the fucking wikipedia article as >>8603752 said

This is why I love probability theory. All these counterintuitive results

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>>8604227
OK brainlets, try this

>>8604379
0%

>>8604406
Wrong.

>>8604379
2/3

>>8604426
Wrong.

>>8604379
50 %. Gee, it's not that hard...

>>8604434
Wrong.

>>8604436
>"1" in the top left corner indicates that there has to be exactly one mine in the adjacent fields
>There's only two fields left
>The others do not contain the mine
>P=1/2=0.5=50 %
YOU DENSE MOTHERFUCKER

>>8604406
>>8604426
>>8604434
OK since this basic as fuck question seems way too hard for you brainlets, just give an argument for what the best move in this situation.

>>8604438
Wrong. The two fields do not have equal chance of containing a mine, due to the other information you have.

>>8604445
That would only be true for two or less overall mines.

It's 2/5 retards.

>>8604449
Wrong. Calculate it yourself and show your work.

>>8604379

[math]\frac{5}{14}[/math]

>>8604462
Wrong.

>>8604379
1/3

>>8604379
Sounds annoying to do.
10 mines over 76 squares, some of which are mutually exclusive.

>>8604469
Wrong.

>>8604471
It's really not that hard.

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Well I guess /sci/ really is full of underage brainlets. I'll post the answer since you apparently think this is some kind of trick question.

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>>8604379
Interesting.

I think the answer is again 2/3

>>8603718
DESU famalams I would've said 1/2 before I read https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox, but they actually convinced me.

For those who aren't convinced yet:
What is being done here is we're putting the three boxes, and selecting a box randomly (each box has 1/3 a chance of being selected) and taking a ball from it randomly; if it's a silver ball you'd repeat the experience, but if it's a gold one you'd continue.
Now repeating the experience a bigger and bigger number of times, the following happens with an approximately equal number of times:
1-GG box selected and the ball picked is first gold.
2-GG box selected and the ball picked is second gold.
3-GS box selected and the ball picked is gold.
4-GS box selected and the ball picked is silver.
5-SS box selected and the ball picked is first silver.
6-SS box selected and the ball picked is second silver.

Since the picked ball is golden, 4,5 and 6 are eliminated, and 1,2,3 happen with equal probabiliy, so the GG box gets selected 2/3 of the time, meaning that the second ball taken is golden 2/3 of the time.

>>8604481
Nope, you incorrectly assumed that each of those cases is equally likely in a randomly generated board. You have to take into account the fact that there are more ways for 8 mines to be distributed in the rest of the board than there are for 7 mines to be distributed in the rest of the board. See >>8604476 But you did start out correctly.

>>8604094
But 1/3 of all boxes have X = 0.

>>8604490
Yep, true. But for the purposes of playing a game of minesweeper I'd happily accept the 2/3 approximation.

>>8604483
The question doesn't say you selected a box at random, you selected a ball at random

Your 1 and 2 are the same event

>>8604536
I'm talking about after you select a box and take a ball out of it.

>>8603718
Are we taking a random ball out of the box or are we taking the first (left) ball out of the box?

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>>8604483
yeah but, thats bullshit.
it says in the problem that when you take the ball from the box, its gold, already supposed within the problem itself is that you either pulled the first box, and it doesnt matter what ball you took, or you took the seccond box, and the universe makes you take the gold ball, every time you pick up that box.

and so, since you will pick up only box one and two[in order to pick up a gold ball first] and you will pick up both of those boxes an equal number of times, because you pick them at random, you have a 1/2 chance of picking gold and 1/2 chance for silver.

>coming to a science board without understanding math problem mechanics.

Suppose you are on a game show, and the host brings out these three boxes. Each box has a left and right compartment holding one ball. The host has full awareness of the position of each ball.

The aim of the game is to pull out two balls of the same color.

You first pick a box and open a compartment at random.

The host then opens a compartment in another box revealing a ball of a different color.

He then gives you free reign to pick any remaining compartment, from your box, his, or the completely unopened box.

What is your best option?

>>8604563
The problem says you pick a ball at random, not a box at random. This is such a common and well documented problem how people can still argue in favour of the 50:50 answer is beyond me

>>8604564
2/3 of the time, staying with your box will win.

7/9 of the time, going with the host's box will win.

5/9 of the time, switching to the unrevealed box will win.

Therefore you should open the host's box.

It's 50/50, you either pick the golden ball or you don't.

Can't believe you brainlets are struggling with this.

>>8604692
That doesn't sound right. (Assuming the host chooses from the available balls at random.)
A = Stick
B = Open the host's box
C = Open the unopened box

2/3 of the time you'll pick from a double
-2/3 of those time he'll pick the from other double.
>A You win.
>B You lose.
>C You win 1/2 the time
-1/3 he picks from the mixed box.
>A You win.
>B You win.
>C You lose

1/3 of the time you pick from the mixed
-Host has to choose from the other double.
>A You lose.
>B You lose.
>C You win.

P(Win|A)=2/3
P(Win|B)=2/3*1/3=2/9
P(Win|C)=2/3*2/3*1/2+1/3=5/9

Picking from the unopened box is the best strategy.

>>8604836
2/3>5/9, idiot.

Sticking is the best strategy.

(Replying to myself.)

>>8604836
Ah I interpreted the question as you winning when you end up with a box with two balls of the same color, not the two balls you chose being the same color even if they are in different boxes.

>>8604864
That might be the more interesting question. I was just making it up as I went, hoping something counter-intuitive would pop out.

I'm guessing this problem exists as an explanation of why the Monty Hall problem works to brainlets? Because it's absolutely clear that this problem and that one are the same; pulling a golden ball is clearly equivalent to the host opening a door with a goat behind it.

>>8603742
second ball is from the same box my dude.

This has to be the saddest troll thread in the history of 4chan.

>>8603718
yes

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To the 1/2 fags.

Let's assume a world with perfect probabilites.

We do this test with 90 people.

There are 3 boxes. 1/3 chance. How many get box A? 30. Box B? 30. Box C? 30.

30 people are out of the game already, they picked the box with 2 silvers.

30 people picked box A. There are 2 coins inside. 15 pick coin 1. Gold. 15 pick coin 2. Gold. All 30 stay in the game.

30 people picked box B. There is 1 gold coin inside. 15 pick coin 1. Gold. They're in the game. 15 pick coin 2. Silver. They're not in the game.

Okay so we have 45 people in the game at this stage.
30 people have box A with 2 gold coins.
15 people have box B because those are the lucky 1/2 that picked the gold coin from box B to stay in the game.

What's the probability the next pick is gold??

>Hurr its 50/50 cos you either pick the coin or you don't. 22.5 people will win.

Nope. There are 30 people in the game with box A. Only 15 who chose box B were lucky enough to stay in the game because they needed luck to not draw the silver, and they will lose on their next draw.

=> 2/3 chance of winning.

The chances of having box A and box B are not equally likely, they were equally likely to be chosen by the player initially, but then 50% of the box B pickers were culled from the game by chance. There are twice as many ways to pick box A and stay in the game than B, and box A pickers are the guys who win.

This is not a difficult concept.

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There, I made a brainlet version of it.

Don't even try arguing with it. Use conditional probabilities if you don't believe it, or write a Matlab script to simulate the experiment and do 100k draws.

>>8603859
Look at it this way. Box 1 contains Gold1 and Gold2; Box 2 Contains Gold3 and Silver1.

All you know is that you picked out a Gold ball.

If you picked Gold1, the other ball is Gold2
If you picked Gold2, the other ball is Gold1
If you picked Gold3, the other ball is Silver1

2/3 is the probability of the other ball being gold.

I feel like you guys are overcomplicating this.

You can only pick the first two boxes. Once you remove the first gold (which is a guaranteed event) there are 3 balls left.

2 of which are gold, 1 of which is silver.

So 2/3 chance you'll pick another gold.

>>8603718
It is a trivial matter to determine which box contains the gold balls by lifting said box. Gold weighs more than silver

>>8605122
you mean mass.

Also how do you know that gold balls have such a radius that make them weight the same as the silver balls? mass = density*volume my friend.

>>8605134
to be fair, since gold has a higher mass, he's still correct in saying it weighs more

Weight = mass x gravitational acceleration

>>8605122
no one has said the gold balls aren't hollow.

>>8605148
Who said it's gold and not Gol D. Balls?

>>8605119
No, there aren't 3 balls left. If you picked a gold ball, that means you are looking at the left 2 boxes. If you got the gold ball from the left box, then you'll get a golden ball the second time. If you got the first ball from the right box, then your second ball will be silver. That means the two possible outcomes are equal. Therefore 50/50

>>8605162
god, seriously look at this >>8605083
and stop spouting nonsense.

>>8605083
No. The probability to draw the second time is 50/50 since you're drawing from the same box as you did the first time, meaning that there are only two possible boxes.

>>8605166
Can't we completely ignore the third box? Since our getting a gold ball the first time is a given

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The fundamental point here is how the question is worded.

If the questions was: IF you get a gold ball, what is the chance the next ball is gold as well? The answer to that is 2/3. It's the question described here: https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox


However, in this question, the first gold ball is a certainty, so the question is: You got a gold ball. What is the chance the next one is a gold ball as well? It's 50%.

It's really the same principle as monty hall you fags

>>8605167
you aren't taking into account that half of the GS boxes fall into "first ball is silver so discarded" category. That's literally the trick of this.

>>8605174
If you got a gold ball you already skewed the distribution.

I also believed it couldn't be until I made the pic.

>>8603718
>I know basic probability, look how much of a genius i am.

>>8605178
>at random
>a certainty
I can't tell if you're trolling or retarded.

>>8605185
You are already past the point of randomness for the first ball, because we're only looking at situations where the first draw was gold.

This post >>8605181 has it right with the "first ball is silver so discarded" category, but I'm arguing we're allowed to discard that category because we're only looking at the cases where the golden ball has been drawn AND we already know that.

It's a shitty worded question

>>8605194
I wonder if they gave Rusell the Nobel prize for his ability to making simple problems impossibly difficult just by using the appropriate wording.

He is still making autists rage like 80 years after.

>>8605181
No, the first ball is never silver. It's a given that our first ball is gold, and then there are only two configurations: GS and GG

>>8605213
read the problem again. You take one ball at random. In the case of the experiment it's golden but in other experiments will be silver.

When thinking statistics you can't think of a single occurence, you need to look the whole picture.

>>8605213
There are three gold balls. You know you've picked one of them. Two of them have another gold ball in the same box, one doesn't. Two out of three.

2/3

>>8605213
When you pick the golden ball, you know that the chance of this box being SS is 0.

However, the chance of the box being GG or GS is NOT equal.

There is a higher chance of it being GG.

Imagine a similar problem.

There are 3 boxes. They contain a BILLION balls. One box only contains silver balls, on the other box, only one ball out of a billion is golden, and the other box only contains golden balls.

If you stick your hand in one and pull a golden ball, it's almost impossible for it to be anything but the box with nothing but golden balls.

>>8605194
>You are already past the point of randomness for the first ball, because we're only looking at situations where the first draw was gold.
Yes, and that is exactly what Bertrand's Box says. Just because something certainly happened doesn't mean it had to happen. If I flip a fair coin and it lands heads, that doesn't mean the coin wasn't fair. You were never destined to get the gold ball just because it happened that way. And it's more likely that the gold ball you saw was from the box with two of them. You don't understand conditional probability, so I suggest you read a bit more about it.

>>8605232
I see your logic, but it's still wrong. We have to look at the outcome. Since it's a given that our first ball is golden, we need to see what the result would be if you take one golden ball from each of the boxes. One of the boxes would have a golden ball left and the other would have a silver ball left.
>>8605222

>>8605241
Holy shit that makes a lot of sense. It's more probable that you got a golden ball from the left box....
Of fuck thank you I feel very stupid now.
Sorry everyone else that I annoyed...

>>8605246
Fuck, you're right.
Thanks

wtf I hate statistics now

>>8605248
>I see your logic, but it's still wrong.
Brainlet, please.

>>8603718
There is a 66% likelihood the gold ball was picked from the leftmost box, and a 33% likelihood it came from the middle one.
Thus, a 66% chance the next ball will be gold.

Brainlets need to get the fuck out of sci

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From the pol thread

Draw the second ball from the same box. It's 50/50 whether it's the gold or silver while eliminating the third silver/silver box.

Sounds like that Eubanks theory.

What if whenever you picked the right box, you were AUTOMATICALLY handed the gold ball, every time?

>>8603718
It is 50%.

However the problem in OP is in fact not https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox which is 2/3.

The main difference here is that OP clearly states it is a gold ball that you picked out, while the 2/3 solution applies to the problem where a gold ball is not a premise.

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>>8605356

That is a lot of work for an incredibly basic concept.

66% chance

>>8603718
when it clicks it clicks

66% chance

>>8605413
>>8605470
fucking retards

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You're at a game show

You just won 100k and got to the bonus round where you get to bet your prize money in a gimmicky game of chance

The host explains OP's boxes setup. You can bet however much money you want on a box, and if that box contains two golden balls you get 3x the money back

You don't really give a shit, so you put 5k on a box as a token bet

The host spins a fair three-sided die to pick a random box. It lands on a different box than the one you picked

The host walks up to the box the die indicated, sticks his hand inside without looking, and takes out a silver ball

He then offers you to change your bet on the box you initially chose - you may increase or decrease it however you like, but you may not switch box

Also at that point you remember that your great great grand aunt died yesterday and left you 4m so the "100k is a unique opportunity to me"-factor doesn't apply to you. You only care about maximizing your expected winnings

What do you do?

>>8603742
>seeing americans struggle with this problem is funny
Wanna know how I know this is b8?

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>>8603718
After reading this thread, the answer appears to be yes.

To the 50/50 retards: can you at least document yoursef first? There's an article on wikipedia that explains everything in detail. It's not a scientific paper, so it should be accessible even to you, maybe.

It has been proven even mathematically for god sake.

/sci/

>>8603718
why there is silver balls box? it seems redundant

>>8603845
>box one is more likely because it has two gold balls

What? The condition for "a gold ball" means at least one. Two is irrelevant.

If you roll a dice, what is the probality it lands on a side with at least two black dots? Is a 6 more probable than a 2 because 6 has more black dots?

>>8606696
one might have thought that, choosing a box before choosing a ball would make the odds 50/50.

however, the observation of what box was chosen is not made before the ball is chosen; thus rather than the criteria collapsing 3 boxes into 2, it instead collapses 6 balls into 3

>>8605083
But conditional probability tells me the answer is 1/2.

The people who say that the chance is 50/50 are dumb as fuck. The first choice, which gives you a chance of 1/2, is important. If you taked a gold ball, that means that the third box (silver and silver) can't be the box from you taked the ball. BUT, it's more likely that this box is the first box (gold and gold), because you taked a gold ball at once. So, you had two options: GG or GS. You can see that, if you have now a gold ball, there is more chance that she came up from the GG box.

It's too obvious that the answer can't be 1/2, and who said this has low IQ.

>>8603718
P(GG|G) = P(G|GG)*P(GG)/P(G)
= (1)*(1/3)/(1/2)
= 2/3

>>8604065
It's wrong because you didn't condition on all the information you had.

Drawing a ball at random and getting a gold is more information than just learning that the box that had a gold pulled out of it has X >= 1. It might be intuitive to compare a situation where I will intentionally look into the boxes and pull a gold ball from one of the gold-containing ones at random, and then you have to decide on the likelihood that then next ball from the box I picked will be gold.

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>mfw this thread is still going
>mfw the sheer number of retards and trolls
>mfw some people actually believe it is 2/3

Couldn't someone just conduct an experiment to confirm/refute the positions? Why did we need 150 posts of pointless theoretical circlejerking?

>>8607009

This. Any brainlet who is saying 1/2 can try in a spreadsheet. Probability is 2/3

>>8607020
That was done and posted and probability was 50% which is common fucking sense.

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Guys, please.

>>8603718
the probability is you will pick the silver one anon because you're one unlucky bastard

>>8605356
This is just wrong on so many levels. Mainly the fact that he divides by n in the end. Should be goldenballchosen/(silverballchosen+goldenballchosen) since the fact that the first ball was golden is a condition.

>>8605547
Bet all your money since you have 1/2 chance of winning the bet and the expected value of betting x amount is 1.5x+100000

>>8607082
Woops, that should be 0.5x+100000

It's funny that most people agree on the math, but the dispute is in the wording/framework of the problem.

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it's 50 percent, either u pick up a gold ball or u dont

Overall there are only gold two balls which can be picked from the same box as another gold ball.
These are the two gold balls that share a box.
There are a total of six balls.
The probability is 2/6=1/3.

>>8607216
...then incorporate the condition that a gold ball was initially chosen:
There are six gold balls of which three are gold.
The probability of initially choosing a gold ball is 3/6=1/2.
Now divide my initial (incorrect) probability by the probability that the condition is true:
(1/3)/(1/2)=2/3.
So everybody else is right and I'm not the only non-brainlet in the thread after all.
Sorry.

>>8603718
No way, surely nobody is THAT retarded these days. Everyone KNOWS it's 2/3 Gold 1/3 Silver, right? This is elementary stuff.

>>8603718
Apparently you can read the problem in 2 different ways...

If you are forced to take from the same box as the problem seems to imply, it's 50%

If you can take the second ball from every(included the previous one) box, it's 2/3

>>8607387
no you fucking retard

just fuck off

the answer is 2/3

plain and simple

66% chance the next ball is gold
pretty obvious if you ask me

Ok guys fuck this shit i want to end this thread, someone should get a probability simulator or make some program and see if the probability converges to 2/3 it's not that hard you fucking faggots.

>>8607393
Explain without failing for the Gambler's Fallacy.

It's a given that you already obtained the first gold ball, so you either picked from the GG or the GS box.

Now, if you have to pick from THE SAME BOX, you either picked from the GG or the GS back previously
GG has now 100%
GS has now 0%
You couldn't possibly take another ball from SS if you are forced to pick from the same box that gave you the first golden ball

If you aren't forced to pick from the same box as the previous one then it's 2/3 as everyone says and it was already explained enough.

>>8607403
no you more likely picked from the GG box

retard

there's no difference between picking a ball at random and 'picking a box' followed by a ball like the pic says

>>8607408
>no you more likely picked from the GG box
And that's the Gambler's fallacy I am talking about.

If it's already a given you obtained a golden ball and you must grab from the same box, then you can only win in the case you didn't take the GS box, hence 50%

>>8607412
you're a fucking idiot

have a think for a while and come back

>>8607412
you have 2 box where you can pick the gold first, one of them contains a silver ball as well. It is more likely that if you picked gold you are in the GG box, understand?

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I mean it was obvious, but I though I'd put this to rest once and for all.

>>8607425
this

think of the boxes as mean grouped into pairs in tune with the op pic after you have picked a ball at random from 6, should be clear to anyone that the answer is 2/3

>>8607419
Read the problem please.

You people are retarded if you think it's the box paradox, it's different for 2 reasons.

>already grabbed 1 golden ball
>probabilty that you will obtain another golden ball from THE SAME BOX

Try to imagine the problem in your head or something - you have a golden ball in your hand right now and you will pick from the same box.
You either picked from GG or GS, so you will either pick a golden ball or a silver ball now, with the same chance.

>>8607425
And again, it's like saying that if you already flipped a coin and got tails, then it's 2/3 you will have heads.
It's the same box, it doesn't matter if you had a 100% or a 50% for the first golden ball, you either fucked up by picking GS or you didn't.

2/3 works if it's not already a given that you obtained the first golden ball and you aren't supposed to take the next from the same box

>>8607441
*being grouped

There there really people so stupid they don't understand this, or are they just trolling?

>>8607443
you more likely picked GG, if you are picking a ball at random from 6, which is just the same as 'picking box first'. the picking a box first is redundant and is what is throwing you off

and as for the thing about the coin you really are retarded if you think that is a sound analogy

2/3 is the answer

you are wrong

>>8607443
>You people are retarded if you think it's the box paradox, it's different for 2 reasons.
>already grabbed 1 golden ball
>probabilty that you will obtain another golden ball from THE SAME BOX
That's exactly what happens in Bertrand's box.

>Try to imagine the problem in your head or something - you have a golden ball in your hand right now and you will pick from the same box.
>You either picked from GG or GS, so you will either pick a golden ball or a silver ball now, with the same chance.
No, because the fact that you got a gold ball makes it more likely you got it from the box with two gold balls vs. the one with only one gold ball.

Saged.

>>8607450
>the picking a box first is redundant and is what is throwing you off
this

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>>8607401
>someone should get a probability simulator or make some program and see if the probability converges to 2/3 it's not that hard you fucking faggots

This really shouldn't be necessary, but here you go. Anyone can run it themselves:

https://repl.it/FKky/0

imagine balls GG GS and SS arranged in those pairs randomly

you're told to pick a ball at random, which is just the same as picking a particular ball of a a 'box' at random, you're better off sticking with its pair (which means picking the 1st box if you chose the 2nd box and vice versa, 4th box if you chose the 3rd box and vice versa, 6th box if you chose the 5th box and vice versa) than switching

2/3

simple as

>>8607443
explain this then
>>8607427
>>8607028
you're a genuinely a fucking dipshit if you can't see this intuitively

>>8603742
>at least some amount of brains
>seeing americans struggle with this problem is funny

>someone told me the answer and now I go around acting like I figured it out for myself

People who figure it out for themselves (a small minority, even among intelligent people) find it obvious and aren't impressed by or interested in it, so they don't go around showing it to other people. Only people with limited intelligence and serious personality defects try to validate themselves this way.

>>8607479
Funny thing is that I could tell intuitively it was 2/3, but I thought I was wrong and there was a trap in the way the problem was presented to get 1/2

Should have trusted the apparently obvious solution

>>8607465
why would you initialize the boxes inside the while loop, you wasteful cunt?

100%

Because.

If I pull another gold ball I win. If I pull a silver ball it's a do over.

>>8607507
Because I'm popping items out of the boxes, dumbass.

And that's a good idea in order to make the steps in the program look very similar to the statement of the problem - a good thing if you want the retards on this board to understand a simple program.

>>8607387
>If you can take the second ball from every(included the previous one) box,

"the next ball you take from the same box"

jesus fucking christ you are stupid

>>8607465
You count getting the first gold ball as a successful trial, you retard.

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>>8607589

>>8603718
Given that one of the balls is golden, what is the probability that the second ball is also gold?
Given that the box is either A or B, and assuming each box has an equal chance of being chosen, what is the probability the box is box A? Hot fagdick that's pretty easy it's 1/2 ffs this bait is so fucking obnoxious 8/8 for making me reply I HATE THESE FUCKING PEOPLE REEEEE

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You assholes made me so mad with this shit,
I scripted this scenario on my phone.

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>>8607778
jet fuel cant melt steel beams

>>8607785
/sci/ BTFO

>>8607778
>>8607785
phone niggers confirmed for retards.

>>8607778
After picking a gold ball the g-s and g-g boxes aren't equally likely, so randomly picking one like you're doing doesn't model the scenario properly. A fix would be to model the first pick like here: >>8607465

>>8607814
You're right. Missunderstood the scenario that grabbing a 'g' at the first grab is required to count as an attempt which it is not.
It's 66%, damn statistics.

>>8603718
[math]\displaystyle \frac{2}{3}[/math] because you have a 2 in 3 chance of getting a box with a gold ball and the information on how you pick up a ball is vague.
>inb4 american

>>8603729
no youre right it's definitely 50% i dont know how the fuck people are getting this other shit

I think 33%

>>8603718
i haven't read all the answers in this post but i have calculated it's 40%.
My explanation is the next (Excuse me for my bad english):
First, we haven't pick up the first ball. We have 3 boxes, so 1/3 to pick one of th boxes. If we pick the first one we have 2/2 to pick a gold ball. If the second it's 1/2 and the third it's 0/2. If we plus the three probabilities and multiply them by the 1/3 from pick a box we have ...3/6 to pick at first a gold ball.
Then, after picking up the gold ball, we have a gold ball less, so there are 2 balls, and we ahve a ball less, so we have a total of five. The result it's 2/5, 40%.

If there's a mistake pls tell and explicate me my error.

>>8607971
okey, i missread the last sentence. I didnt read "from the same box"

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draw a tree

>>8607976
so, it would be 1/3? Because if we have to pick up the ball from the same box it has to be a full golden ball box. And there's only one tht satisfy this condition

>>8607985
When the first ball you choose is gold, there is a 66% chance you chose a ball from the double-gold box, and therefore a 66% chance you will be choosing from the double-gold box again.

Can you suggest me a good stochastic processes book?

>>8603718
Effective odds are different than odds. The odds are always random, 50/50. Flip a coin a trillion times head and the odds are still 50/50 on the next flip.

Effective odds are in predicting a specific chaotic futures.

Even the effective odds of picking a second gold ball seem 50/50. In picking a gold ball you've already limited the selection to two boxes: there's no sense in further consideration of the silver-only box.

Either way, I'm slow but not slow as the masses are slow and ignorant.

>>8603718

LOTS of retards cant get past thinking that the probability of an outcome is equal for all possible outcomes.

Like if you have 3 possible outcomes then that's 33.333 for all of them even though one may be 5% another 15%% and the last 80%, they will insist that its 33.333% each.

I think its just a lack of brain power for the extra level of abstract thinking.

[spoiler]then they come on the /sci board and think they have something useful to say.[/spoiler]