/biz/ - Business & Finance

>>8347660
50%

2/5 probability of picking another gold ball

>>8347686
i agree you either get a gold ball or you dont

>>8347660
bout tree fitty

>>8347660
about tree fifty chance

50/50

>>8347706
While my reasoning is a little more complex than that, but yes. And you either get a silver or a gold, giving you 50/50.

2/3

>>8347694
no, you know you aren't picking from the two silver box

>>8347686
yup

2/3 is the correct answer

>>8347741
>>8347749
This isn't a monty hall problem.

It's 1/3

The second ball drawn has to come from the same box the first ball came from. Therefore the only way to pick a second gold ball is if the first box was chosen at random initially.

>>8347694
This

saged and hidden

I have now realised that only 2/3 boxes have a gold ball. So you'd have to have chosen one of those two initially.

Final answer is 1/2

>>8347686
>>8347694
>>8347724
>>8347726
>>8347775

>>8347660
1-1/3=2/3

7/256
god its fucking obvious everyone here is a fuckin dropout loser why do i even come to this website

>>8347833
Jk it's 1/2

>>8347660
66% because you picked the box with the gold ball

it's 1/3

there was a 1/3 chance you picked the box with 2 gold balls, that remains unchanged by you drawing one out

>>8347830

2/3
lrn2conditionalprobability

>>8347761
true but its still 2/3

the possible outcomes are
2 grey (1/3)
100% grey - grey => 1/3 chance
1/1 (1/3
50% grey - gold => 1/6 chance
50% gold - grey => 1/6 chance
2 gold (1/3)
100% gold gold => 1/3 chance

exclude options when you pick grey first

>>8347660

it's 2/3

>>8347917
But that's not the question..

>>8347987

the question is what are the odds you picked the box with 2 gold balls, it just appears that information OP gives you changes that but it really doesn't

this is a famous mathematical riddle called the Monty Hall Problem

>>8347951
You aren't picking the second ball from a box at random, you're picking it from the same box. So only the first (2 gold) and second (1 gold 1 silver) are of interest, the 2 silver box is discarded once we've successfully picked a gold ball (which is implied in the question).

Again, the question is not "what is the chance of drawing two gold balls", it is "what is the chance of drawing a second gold ball from a box when your first draw yielded a gold ball". This is 1/2 - by picking the gold on your first draw, you can only have 1 of 2 boxes, so your next draw will either be another gold (having picked box 1) or a silver (having picked box 2)

1/2 it is

Jesus the state of this board. To all you fucks over thinking this its literally 50/50. 2nd ball in ANY box containing a gold ball will be either gold or silver. 1/2. fuck

>>8347951

>>8347917
Last bus to literacy camp is departing in 20 seconds.

>>8348054
Retard alert

>>8348054
It isn't Monty Hall, it is 100% guaranteed that you have picked a box with a gold ball and are going to take a second draw from the very same box, the 3rd box is out of the equation. If you were able to put the ball back and switch boxes you would be right, but you're locked into the box you initially chose here.

>>8348135

it's the same probabilities how can you not see that?

you drawing one gold ball is the same as the Monty Hall host showing you one goat. It doesn't change the underlying probability that your initial choice of box was 1 in 3

>>8348058
>>8348088
You're more likely to have initially picked the gold ball from the box with 2 gold balls, given that it presents more chances for the winning condition (2/3 gold balls vs. 1/3 gold balls)

>>8347951
You just aren't thinking 4th dimensionally

>>8348182
You dont choose the box. you start with 1 gold ball and the box it came from. the 2 silver box is negligable entirely. it may as well not exist

>>8348058
>you can only have 1 of 2 boxes, so your next draw will either be another gold (having picked box 1) or a silver (having picked box 2)
Exactly. Also you might die tomorrow or you might survive, therefore you must have a 50% chance to die tomorrow. Better tell your loved ones.

Oh fuck, I better tell my loved ones too.

>>8348320

no read the OP image it says you pick one box at random

there were 3 boxes and you picked 1. therefore the odds that box contains 2 gold balls is 1 in 3.

>>8347660
I think its a 2/3 chance

2/3

>>8347741
>>8347749
>>8347761
>>8347951
>>8348058
>>8348088
>>8348088

>>8348372
>YOU PUT YOUR HAND IN AND PULL OUT A GOLD BALL

LISTEN FUCKO THIS IS WHERE THE QUESTION STARTS. WITH A GOLD BALL IN HAND. THE 2 SILVER BOX DOESNT FUCKING MATTER.

>>8348195
I didn't think of that, that's possible - but it may be arguable that the initial draw has no adherence to probability: it was guaranteed, for the sake of the question, to be a gold ball, so the initial pick was 50/50 between the 1st & 2nd box, and your draw, the only with any element of randomness, will be from one of those two.

>>8348372

It's not 2/3, the remaining balls from the boxes aren't shared ("from the same box").

You picked the gold ball, either from box 1 (which contains one more gold), or box 2 (which contains one more silver).

50/50

>>8348404
The number of balls irrelevant.

50%

Either you picked the box with 2 gold balls or you picked the box with 1 gold ball. You couldn't have picked the all silver box.

>>8348459
this was my initial thought, but
>>8348404
>>8348195
make me reconsider. So it may not be that you have two options (box 1 or box 2) but 3 (gold A from box 1 gold B from box 1 or box 2), thus you'd have three possible picks of your own, the first two yielding a gold and the third a silver so 2/3 seems to make sense (but I'm a Humanities fag so what do I know)

>>8348404

No, its 2/3rds if you switch boxes. The question says that you pick both balls from the same box, so its 1/2.

>>8348320
>it may as well not exist
>>8348430
>but it may be arguable that the initial draw has no adherence to probability
This is what happens when you ignore the whole "you pick a box at random" part. It says that very deliberately and is an essential part of the riddle. It's not telling you what WILL happen, it's telling you what DID happen after you made a completely probabilistic choice. If you were to reproduce this experiment in real life (and you should give it a try if you're unconvinced since it's so damn easy to do as long as you have some opaque cups and are capable of closing your eyes) you would find that you get the gold ball (or whatever analogous binary-state object you use) 2 out of 3 times.

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

>>8348430
We're given the fact that we picked a gold ball. Between the two boxes, one of them contains more gold balls and so was more likely to have been the one that was picked from, given this information.

Imagine if the question was reframed, so that one box was 100/100 gold, the second box was 1/100 gold, and the third box was 0/100 gold. If you randomly pick a gold ball from one of the boxes, then you can be almost certain that it was from the first box, because 100/101 gold balls come from that box. Just like how in this problem you can be slightly more certain it came from the first box because it contained 2/3 gold balls.

>>8348558
if you actually think this after looking at his photo you are really dumb, i'm sorry. I actually thought everyone saying 1/2 was memeing but you sound legit.

You have WORSE odds if you switch boxes, this isnt the monty hall problem, but it does use a similar logic.

>>8348404
>>8348428

that's not what it is though, really there were 6 initial possibilities and you are only showing 3. the overall probability is still 2 in 6.

50%

If you picked a gold ball it means you either picked the 2gold balls box or the 1 gold 1 silver box

this feels like facebook...

P(G2|G1) = P(G1 and G2) / P(G1)
(1/3) / (1/2) = 2/3

>>8348645
It didn't ask for the overall probability, it asked for the probability given that you've already picked a gold ball, which rules out 2/6 of the possibilities from the beginning

I'm about to do some real life trials with identical plastic bags and some bottle caps. I fully expect to get a result of aprox. 50% gold for the second pick.

>>8348618
Turn 360 degrees and walk away.

Can't believe there are brainlets that can't grasp that because you got a golden one first you have double the likelihood to have chosen the 2xgolden box an therefore two thirds
probably nonwhites

>>8347660
2/3

>>8348747

no it doesn't it just appears to, that is the trick

you are not changing anything after you make your initial choice of box so the scrap of additional information is meaningless to the underlying probability

>>8348272
based gimpposter

>>8347660
If you put your hand in the first box, 100%

If you put it in the second, 0%

Chance doesn’t actually exist

YOU FUCKING BRAINLETS I KNOW THIS IS BAIT BUT YOU TRIGGER ME TOO MUCH.

The answer is 2/3. Yes it's counterintuitive, but follow my mathematical proof and you will be convinced, faggot.

We want the probability of picking GG KNOWING that we picked a box with one G ball (we will call this event 1G). We denote this probability by : P(GG|1G). Now, use Bayes theorem (google it, I don't want to prove it here), which tells us :

P(GG|1G) = P(1G|GG)*P(GG)/P(1G)

Then, we have that P(1G|GG)=1 since if we picked the GG box we necessarily got 1 G ball. P(GG) =1/3 because it's simply the probability of picking the GG box without a priori info. Finally, we need P(1G). This can be viewed in two ways. You can consider you have half and half G and S balls, so it's 1/2 to pick a G ball. You can also say that to get a gold ball you have to either pick the GG box (1/3) OR pick the GS box (1/3) AND pick the G ball inside (1/2). Unsurprisingly, we get again P(1G)= 1/3+1/3*1/2 = 1/2.

PLUCK THAT SHIT INTO (1), and we get :

P(GG|1G) = (1/3)/(1/2) = 2/3

Can't believe I spend 10 minutes explaining this shit to brainlet, but at least I can sleep now.

>>8348849
okay, I'm done trying to explain basic statistics to brainlets, look up conditional probability sometime you fucking mong

>>8347660
this is monty hall problem but forced to not switch. 1/3

>>8348863
the problem is dude, you do have a priori information. So the brainlet is you here.

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

everone go home now

>>8348948
Re-read again what I wrote, but slowly

>>8348948
>>8348862
>>8348802

>>8348618
make them black please. it's easier to run over niggers

>>8348084
This was my understanding but all the circus math going on in here had me second guessing.

>>8348958
Looks like I was right, brainlets

>>8348863
>>8348923

we only made one choice, it doesn't matter that we get more information AFTER we made that choice, it cannot affect the outcome

3/6 balls are golden so it's a coin toss that the first ball you draw any given time you run the experiment will be golden

if you ran the experiment 100 times you would only pick the box with 2 gold balls one third of the time, but the first ball you draw would be gold half the time

the question is not "what are the odds the second ball is golden only of the times the first ball is golden?" it's just "what are the odds on any given experiment both balls are golden?"

its 2/3 you brainlets reeeeeeeeeeeee

>>8348802

first 10 trials, literally 50%. The ignores are ones where the first pick was silver:

1: ignore
2: silver
3: ignore
4: silver
5: ignore
6: ignore
7: gold
8: ignore
9: gold
10: ignore

also, Im a little retarded re: >>8348558

>>8348641 is right about your odds being worse if you switch, but not about this particular scenario not being 50%.

If you're allowed to eliminate the box with only silver balls you have 2/3rds. If you're not you have one third. If you don't switch you have 1/2. For some reason I assumed that in an alternate version of this question where you switch, you'd eliminate the 100% silver box.

Gonna do 10 more tests and report back.

>>8349024
>the question is not "what are the odds the second ball is golden only of the times the first ball is golden?"
It literally is, Jesus go back to ESL class you fucking pajeet

>>8349024
I don't understand a single thing about your incoherent ramblings. I defined the probabilities, used equations, arrived at the result using only logical steps.

I don't give a fuck about your "arguments", the equations tell me that you are wrong. Just check the post linked by the other anon, apparently it's a famous problem : >>8348958

>>8348658
There a 3 gold balls you could possibly pick initially.
By that fact alone there are 3 possible outcomes.

You’re not picking a box, that’s not what the question is asking of you.

>>8349061
if im wrong explain how this works
>>8349053

are you literally doing this by hand? holy fucking christ you are a brainlet. There is no way this ins't a troll at this point

>>8349053
jeez fucking code so verbose I hate you

>>8349061
>mfw brainlet try to simulate probabilities IRL
>mfw plenty of people already simulated it
>mfw 2018 and anon still can't code

>>8347660
whatever 6/9 is

>>8347660
75% chance. Congrats op you win.

>>8349024

You must be a sub 100 IQ being.

>>8347686
kek

>>8349155
i was trying to be explicit for people that don't know how to code no bully plz

>>8348390

>>8347660
There are 3 possible states and 2 end up in gold. Therefore 2/3.
It's really interesting neurologically. If I think about states 2/3 seems fine. If I think about boxes 1/2 seema like the obvious answer.

This means that there's a bug in human world modeling hardware. Seems to be genetic and universal.

>>8348980
Nice try, fag, you obviously overloaded the native print function with one that prints wrong answers. Or maybe you got lazy and just photoshopped it. Or maybe I'm wrong and you're being honest after all.

Given that there's three possibilities and you're only honest in one of them, there's a 2/3 chance you're of shit.

>>8347660
1/2

conditional probability. The question is worded differently to Betrands problem

>>8349024
>3/6 balls are golden so it's a coin toss that the first ball you draw any given time you run the experiment will be golden
The problem specifically states a gold ball has already been chosen, that is an initial requirement for the experiement, so the odds of not picking a gold ball initially are not relèvent.

You’re arguement is like saying a coin toss isn’t 50/50 because there’s a chance you don’t have a coin. A coin toss problem assumes you have a coin, this problem assumes you have already pick a gold ball, in both cases you only consider possibilities that have the initial conditions already satisfied.

>>8349053
>1 million samples, his cpu hates him
>uses virgin format method instead of chad % builtin
>values instead of truths for 2 choices
>not spyder ide
you're not going to make it

phd in Physics, astrophysics, and mechanical and electrical engineering
0% is the answer

thank me later

>>8349285
I modified it with cheatengine, it was 3/4 fag get rekt

>>8349342
Fuck you and your legible ID.

>>8349342
nice id, now check these digits

>>8349318

>The problem specifically states a gold ball has already been chosen

no that is the trick, it is not asking you to pick after showing you one golden ball, you pick the box before you have that information

if they showed you one gold ball AND THEN asked you to pick the second your odds would be 2/3 but that's not what's happening

>>8348404

>>8349267
So that's what religion feels like.
Thanks OP. Didn't expect to learn something fundamental like that today.

>>8349267
>There are 3 possible states and 2 end up in gold.
The three stater are not equiprobable (equally likely). They have probability 1/4, 1/4, 1/2.

>>8349061
>>8349141

Second 10 trials:

1: gold
2: silver
3: ignore
4: gold
5: silver
6: ignore
7: silver
8: ignore
9: gold
10: ignore

3/6, 50% again, still 50% for the whole experiment. If I'm an idiot then why am i get exactly what I expected?

Going to do a third trial

Holy shit, is /biz/ really this stupid?

>>8349470
the actual state of biz

>>8348404
DO I PUT GOLD ROCK BACK OR NO?

>>8349141
>>8349470

1: ignore
2: silver
3: silver
4: gold
5: ignore
6: ignore
7: silver
8: ignore
9: gold
10: ignore

2/5. That's 40% for this trial.

When averaged across all three trials, that's 46.67%. A little less than 50%, but that's just because of the limited number of trials. If I did more, it would tend towards 50%

>>8349594
no, it would tend towards 66%, as has been demonstrated in numerous computer simulations in this thread using millions of trials

>>8349424
>>8349594
>>8349467
>>8349285
Every fucking one of you fags never return to my board again. You're all fucking retarded. The answer is 2/3. It's understandable you might have missed it at the start, it is a riddle. Now it has been explained multiple times and you can't learn, you are all retards. Face it please. And to the dumbass who did this by hand, please never ever speak in public without being spoken too, the world can do without your mouth flatulence on a daily basis. Now all of you GET THE FUCK OFF MY BOARD.

>>8348802
>>8349061
>>8349470
>>8349594

jfc /biz/ it's a two second math problem.

>>8349467
No, you know you hold a gold ball as a fact. There are three possible gold balls. Two lead to another gold ball.

>>8349640

in both of the simulated cases, they only ever pick the first of the two options from the box they pick from, which increases the odds to 2/3rds

>>8349649

this is what happens when you prove autists wrong

>>8349770
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox

NOW LEAVE!! AND NEVER RETURN!

>>8348618
Thrust myself onto the lever impaling myself to death AND flipping the switch at the same time BUT also doing it in such away that positions my body so that when i empty my bowels postmortem it will shift the lever back into its original position depending on what and how much food i ate the previous day. Next Dubs decide the food and amount. Trips indicated I ate a trolley and now there are two trolleys but still dependent on food from dubs because either they crash into each other or safely murder everyone on the track. Side note the box with two eggs is making me hungry for eggs.

>>8347660
The only randomization event is the first choice. The first choice logically dictates that if there is a gold ball chosen, it must be either the box with two gold balls or the box with two silver balls. As you must reach into the SAME box again and pick out the REMAINING ball, what is the chance that that ball is gold? 50%, and anyone who says otherwise is a "statistician" who failed to understand the simple logic of the question.

And yet you're only allowed to pick from the same box. Not both. If they were pooled together and you picked again sure. Then it's 2/3

>>8347686
thread should've ended here
sage

Its 50%
You get a gold ball first try, so that mans you have a [gold gold] box or a [gold silver]
Your next pick will be either another gold, or a silver.
It's 50% chance

>>8349770
>in both of the simulated cases, they only ever pick the first of the two options from the box they pick from
This doesn't matter since boxes were shuffled so that the order of elements was randomized

>>8348980
Your program demonstrates that you don't understand the concept of "conditional probability."

You don't have to model picking the first ball in your program. We already know it is gold. Checking the metal of the first ball should not be in your program.

>>8349770
they didnt in mine you dumb dumb, not that it matters, as the other anon shuffled the balls while I shuffled the choice. Notice the first if/else block
>>8349053

>>8347686
this

>>8348862
This

>>8349825
>play the lottery
>your ticket either wins or it doesn't
>the probability is 50/50
in other words confusing the number of outcomes with the probability of said outcome

>>8347660
pretty good

>>8347830
It’s 50/50 you’re the fucking brainlet

>>8350124
This is an age-old statistical problem that people way smarter than you figured out hundreds of years ago, hence why the people saying it's 2/3 can use mathematical proofs and simulations to back up their arguments while all you can do is shitpost

Let me dumb this down for you brainlets
You have two boxes with balls inside like so:
[GOLD GOLD] [GOLD SILVER]
You reach in and pick a gold ball out.
What are the chances your next ball from THE SAME BOX will be gold?

>>8350243
well there are 3 gold balls and 2 of them lead to picking out another so 2/3

>>8350243
2/3

>>8348645
Learn how to read retard

>>8350273
>>8350278
Good work guys you get a special star, don't forget to show your mommy!

These math posts always remind me how fucking stupid people on biz actually are. No wonder the do-the-opposite-of-biz strategy works so great.

Jesus I never knew so much of /biz/ was just this fucking slow, now I know why you guys fall for so many ETH ponzis and pump and dump shitcoins

>>8350351
If I gave you this scenario how would you respond?

A man buys a lottery ticket. He must match 10 numbers in a row, ranging from 0 - 9, meaning his odds of winning are 1 in 10^10.

The man is watching the lottery drawing on tv. He has matched the first 8 of the 10 numbers so far. Knowing this, what are his odds of having a winning ticket?

By your logic, the answer would still be 1 in 10^10. If you still think that, I don't know what to say anymore and you are beyond helping

You 2/3rds retards seemed so sure of yourselves I tested the scenario in code just to make sure my logic was correct. I was beginning to doubt my own sanity.

It was correct, you 2/3 guys are retarded. This isnt even all that complicated really.

>>8350602
do you actually think this logic is correct or are you trying to trick people?

I'm pretty sure you know, but if not, invert the position of the two balls in the second box......

>>8347660
So heres my formulation:

A person first picks a box from the 3 and then draws both balls from it one at a time. Let E be the event that the second ball he draws is gold and G be the event that the first ball he draws is gold. We are looking for the probability

P(E|G)=P(E,G)/P(G)

P(E,G) = 1/3 because it would mean that the person chose the first box out of 3.
P(G) = 1/3*1+1/3*1/2 = 1/2. If the person chose the first box then it is 100% chance that 1st ball is gold. If the person chose the 2nd box then its 50% chance the first ball is gold.

so the final answer is (1/3)/(1/2)=2/3

>>8350642
you literally cant. you cant. holy fucking jesus christ god damn you niggers are stupid.

YOU ARE HOLDING A GOLD BALL. IN YOUR HAND. THE FIRST BALL IS ALREADY DRAWN. YOU CANNOT EVER DRAW A SILVER BALL FIRST UNDER ANY CIRCUMSTANCES. EVER. EVER EVER EVER. NEVER EVER. NOT EVER.

>>8350602
>>8350708
Your simulation is incorrect because if it chooses the second box it always picks the first ball no matter what, which is not what is happening in the problem.

>>8350708
yeah but you arent accounting for the ball being picked. I know you cant pick a silver ball. But the fact that you picked a gold ball has statistical significance. 50% of the time that you pick the second box you wont draw a gold ball, meaning that drawing a gold ball will be more likely occur when the first ball is picked.

I said change the positions becuase you clearly aren't account for the ball being picked. You are assuming the first gold ball is always picked when it can also be the second gold ball. There is a difference in the two. That's why rolling a 2 with 2 dice is a 1/36 chance but rolling a 3 is a 3/36 - 1&2 and 2&1 are not the same thing.

Look at the python script I wrote and notice the difference. I wrote it to be as explicit as possible, showing that every ball can be picked, and the simulation will only continue if a gold ball is picked. If not, the whole thing resets. That;s how it would actually work in teh real world. You wouldn't always pick the first ball. If you think your logic is still right after looking at what I put you are just dumb, idk what else to say. You need to read a little about statistics before you argue shit like this.

>>8349053

it does the whole anlaysis here as well
https://en.wikipedia.org/wiki/Bertrand's_box_paradox

idk how after reading all that you can still think you're right

>>8349649
>being this mad
>while being wrong
lol brb just bought 100k

>>8347660
2/3

t. Millionaire self educated Neet who reads Wikipedia everyday

33.33(repeating of course) percent chance.

>>8350834
I hope for your sake you're larping

>>8350708
Read it closer, retard. You pick a ball at random and it happens to be gold. That is not what your code does, your code looks inside the boxes after the first choice of box, finds the gold ball, and picks it up deliberately.

The reason why doing this leads to the flaw is that you're actually counting the times that you would have picked a silver ball from box 2 as picking a gold ball instead. Understand? You actually failed to properly eliminate all situations in which you would have picked silver and thus not ended up with this final choice in the first place, which is why you end up with the wrong answer.

>>8350905
good rebuttal

>>8350602
Just scanned through the thread holy shit lol, you're a codelet

>>8350834
>mfw anonymous retards on /biz/ think they know maths better than Joseph Bertrand and every statistician since
It's just too precious, and also living proof that the Dunning Kruger effect is real

Just admit you were wrong. It's a problem designed to be counter-intuitive. There's no shame in being wrong.

Theres actually a higher chance of it having a gold ball because there are two remaining gold balls but only one silver, hence 2/3. If youre a dumb faggot its 50/50

Everyone saying 1/2 needs to go back to highschool and review their conditional probability.

>>8350798
it literally is happening in the problem. It will always pick the gold ball first because the problem DIRECTLY SPECIFIES THAT YOU HAVE ALREADY DRAWN A GOLD BALL FIRST.

>>8350834
100% of the time that you pick the second box you will get a silver ball second. You are guaranteed to get the gold ball first because the problem FLAT OUT STATES YOU DREW THE GOLD BALL FIRST. THIS IS NOT A MATTER OF CHANCE, IT ALREADY OCCURRED. THE ONLY WAY TO CHANGE IT WOULD BE TO USE A TIME MACHINE, WHICH IS AN ENTIRELY DIFFERENT PROBLEM.

What second gold ball? What are you talking about? If you have the box with 2 gold balls, you have a 100% chance of the 2nd ball being gold. If its the box with a gold and a silver, you have a 100% chance of the second ball being silver.

>You wouldn't always pick the first ball.

You literally would. Because the problem says it already happened. How can things that have already happened not happen? Is time not linear where you are from?

Im being kind of a dick here but im beginning to think this is more of a reading comprehension problem than a math problem. Is english not your first language? The problem says you have already drawn a gold ball, so you dont have to calculate the odds of that happening. Since it already happened the odds are 100%. You only need to calculate the odds of the 2nd ball being gold as well.

>>8348618
I like these trolley dilemmas

>>8351000
The problem does not specify that you always pick the first ball. It simply says that the result of your first random pick was gold. There is a difference, in that if you had picked the silver ball from the 2nd box then the trial would be considered a fail.

refer to >>8350665
and >>8350979

>>8350914
Its picking up the gold ball deliberately because the problem starts only after you have drawn a gold ball. There is no possibility of that not occuring since it already occured. You have the gold ball in your hand already. There is only one ball left in the box.

You cannot select silver first. Its impossible. Just forget about it.The problem already states you have selected gold first.

>That is not what your code does, your code looks inside the boxes after the first choice of box, finds the gold ball, and picks it up deliberately.

Yes. Thats how its supposed to work. You already have the gold ball in your hand. You dont need to worry about drawing silver, you cant ever draw silver first.

Maybe I should make a second simulation that makes it more clear to you guys. Ill post in a second.

>>8351059
>If you picked a silver ball from the second box the trial would be a fail
And? Then you just try again until the first ball picked IS gold. Then the problem starts

>>8351000
gold ball A is not gold ball B. They are different entities. You wouldnt always pick the 'first' gold ball, ie gold ball A because you could also pick gold ball B. They are statistically different. You must account for this difference.

Tell me what is wrong with my script. Where is its logic wrong, and why did I get a different answer than you if its not wrong? Read the wikipedia page. Tell us how the wiki page is wrong and explain how you are better at stats than Joseph Bertrand.

Everyone else pointed out the error in your logic and you can't address it. Change your code so that the ball choice is random and eliminate instances of silver being picked first and see what happens.

>>8351000

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

I don't know how you can continue to be this stubborn about it after already shown to be wrong multiple times. Honestly it just makes you so much dumber than someone who's willing to learn and accept when they're not an expert in the subject at hand. Do you think the mathematician who originally came up with this box riddle was wrong about its own solution?

>>8351123
you are correct. Now if you go with that idea you can imagine that you will be picking from the first box more often than the 2nd because half time when you pick from the second you already fail. That is the intuition behind why its not 1/2.

2/3

>>8351108
>Its picking up the gold ball deliberately because the problem starts only after you have drawn a gold ball
Right, which makes it all the more concerning that you feel the need to cheat by looking inside the boxes. Why not test your answer properly by making sure you only include situations in which you would have actually chosen the gold ball first?

In your simulation, if you WOULD have picked up a silver ball, then you cannot include that scenario in your calculation. All you're doing is picking up the silver ball, putting it back, and picking up the gold ball instead and saying it was your first pick all along. I hope you're as good at sleight of hand as you are bad at coding, since you'll need to be if you want to pull that off in a real experiment.

>>8351108
Ok here is updated code to better illustrate a fucking coin-toss.

Cmon guys. Just re-read the problem really carefully. Real carefully, word by word if you have to.

>>8350834
oh shit nigger, you're right
I thought it was 50/50

what ide are you using for python?

>>8351215
Because those are the only situations that matter. I didnt calculate situations where I decided to pull out nothing, or both at the same time just to fuck with the guy doing the testing, or there was a spider in the box that bit my hand because that shit doesnt matter and isnt part of the problem.

I have already drawn a gold. Why would I need to calculate situations that do not apply to the problem at hand?

>>8351260
you should stop posting and go read an intro to probability book before you embarrass yourself further.

>>8351300
just using pycharm with the darkula theme friendo

>>8351260
>>8351314
that was too far this is just a confirmed troll. I'd be mad if I had anything better to do

>>8351352

>>8351314
Ok fuck it you win, I put in code that can draw a silver first even though thats not part of the problem. I then ignored it because its not part of the problem.

Its still 50% odds. Nothing has changed.

>>8351020

>>8351260
nigger did you just use a float as an array for an index?

>>8351260
Max, you're just a troll, right?

Trick question. The rules are you need to draw two golden balls from the same box.

Though your odds improve if you calculate them after drawing the first golden ball from your chosen box, overall your odds are a straight 1/3.

It’s 50/50 I don’t care what some douchebag statician trying to ask what he thinks is a trick question when really he’s just a moron.....VEGAS would be on my side you ducking shitlicking faggots

>>8351805
Stealing someone else's example: You buy a 10 digit lottery ticket and watch the results on TV. After seeing them read the first 8 digits and having them all match your ticket, are your odds of winning 1/100 or 1/10^10?

Never has a thread so clearly revealed the absolute state of /biz. If you think it's anything other than 50% - congratulations, you're fucking retarded

>>8351805
You have a box with 999 silver balls and one gold ball and another with all gold balls. You pull a gold ball out of one of the boxes. What are the chances that you pulled from the silver or the gold box?

>>8347660
2/3.

Here's another way to phrase the question. You pick a box. You pick out a ball, and it's gold. What are the odds the second ball in that box is gold? Think about it.

>>8351903
1:999 or 0.001%

>>8351972
So when the problem is scaled back to the original size, why do you think it's 50%?

Ok I was wrong. It really is 66.6% odds. What is happening here is because you already grabbed a gold, you have much higher odds of the box you chose being the double gold box. This skews the results in favor of the second ball being gold as well. So you have 3 possible outcomes that result in a gold ball first: box 1 ball 1, box 1 ball 2, box 2 ball 1.

This means you have a 2/3 chance of the box you have just drawn from being the double gold box and only a 1/3 chance
of it being the mixed box. You have a 0/3 chance of it being the double silver box.

>>8351610
No, Math.Floor rounds down to the nearest integer. I dont think it would work if it was a float.

>>8352030
Include me in the screencap

>>8352030
yeah i saw that after you posted

so you weren't trolling all along?

>>8352068
after I posted*
jesus my brain is turning to mush today.

>>8352030
good job anon, I'm proud of you.

>>8352068
It's a pretty common troll question on sci. People are certain about their answer because they don't take the time to include all the elements of the problem.

>>8352095
This thread is linked on /sci/ right now, probably by OP
>>>/sci/9591739

>>8352068
No not trolling.

In my defense it was a tricky question.

>>8351972
>trolling

>>8348084
This. The question doesn't begin until you've already picked a ball, so the silver box is completely removed from the equation and might as well not exist. Since a gold was already removed from either box you have a single gold and silver left

IDK why this is so hard

Holy cow many autistics does it take figure out a 4th grade math question?

>>8351967
A better way to rephrase the question:
You pick a box. You pick out a ball, and it's gold. What are the odds you picked the first box with 2 gold's?

2/3.

P(G_2|G_1) = P(G_2G_1)/p(G_1)

P(G_2G_1) = 1/3

P(G_1) = P(G_1|B_1)P(B_1) + P(G_1|B_2)P(B_2) + P(G_1|B_3)P(B_3)

P(B_1) = P(B_2) = P(B_3) = 1/3

P(G_1|B_1) = 1
P(G_1|B_2) = 1/2
P(G_1|B_3) = 0

P(G_1) = 1/2

P(G_2|G_1) = 2/3

1/3 as the decision you made is pick a box not a ball

>>8347660
50%
2/3 if the problem stated "If it's a gold ball." instead.

1/3 as the decision you made is pick a box not a ball

OMFG THIS THREAD IS STUPID

OMFG YOU ARE THE REASON WE ARE CRASHING YOU ARE SO GODDAMN STUPID AND RETARDED


EVERYONE IN THIS THREAD IS PART OF THE GLOBAL CANCER THAT IS KILLING THE EARTH

THE ANSWER IS 1/3 AS YOU CHOOSE A BOX AT RANDOM, NOT A FUCKING BALL YOU DAMN SISSY MANCHILDS

>>8349425
But you're not taking into account that If I picked at random a box with a gold ball, that box is already more likely to be the first box than the second box.

some people just want to watch the world burn

>>8352229
was it though?

>>8351610
>as an array for an index
am I becoming dyslexic? I did breath in a cloud of mold dust by accident the other day while I was attempting to clean my neet dungeon the other day, am I going to be ok?

>>8347660

It's 2/3rds.

Look at it this way, if the first ball you take is gold, there's a better chance it's the one with 2 gold balls instead of 1, right?

>>8350243
>dumbs the problem down according to his own agenda
>problem asplodes in his face

>>8347660
I take the first box which, as the image clearly shows, has two gold balls, and then I take the gold ball from the 2nd box too. Then I take the silver balls.

>>8352665
why the fuck would that be the case? jesus christ I am shocked at how retarded biz is, and I've been listening to you dumbfucks on crypto advice... jesus, where's my noose?

>>8352773
see >>8352655

>>8352615
Like 90% of /biz/ still thinks its 50/50. Comparatively im like a genius.

Also its so tricky it has its own wikipedia article. Its so tricky its used as Guaranteed Replies™ on /sci/. Its safe to say its fairly tricky.

>>8352773
Sorry bro, you're the dunning kruger here.

>>8352817
i'm pretty sure I've literally inhaled vast amounts of neurotoxins within the last 12 hours and I got the right answer in 15 seconds.

You guys who think it is 2/3 are wrong because you got tricked by the monty hall problem (which is not a case here).

Here's a simply analogy:
Question 1:
What are the odds of a coin landing heads-heads?
Answer: 1/4 (1/2 * 1/2)

Question 2:
What are the odds of a coin landing heads-heads given it already landed heads after the first flip?
Answer: 1/2

>>8352925
Maybe you've actually learned and understood probability unlike most people?

>>8353086
Thats the gamblers fallacy mang. Also it really is 66.6%, I ran a simulation and everything.

The tricky part is that because you know the number of gold and silver balls, the information gained by drawing the gold ball means that you have a 2/3 chance of being in the double-gold box, because 2/3 of the gold balls are in that box.

>>8353086
This isn't Monty Hall. It's 2/3 anyway, it's explained many times in this thread and it has its own wiki article.

Fuck I may just start posting probability riddles to trigger the brainlets on /biz/. Maybe extend this to other uncertainty models, game theory and decision making to teach you fuckers something

You fucking idiots. Why do I come to this piece of shit board.
It’s 50%. Actual statistician here. This is not Monty hall. This isn’t a riddle.
Anons, I’m sorry. You won’t make it.

>>8352773
See my math proof >>8352481

It's 2/3. Tricky problem though. But this is a bait thread and someone's gonna reply by saying "brainlet" or with a brain dead wojak because it's humorous to them for some reason .

>>8353166
If you were an actual statistician that's just another proof you should go back to your silly regressions, samplers and models and let the big boys play with actual uncertainty modeling

>>8353198
Man no one even knows what that crap means. Its like all that nonsense black hole math they post on singularity brainlet wojaks. This is why no one believes you, including me at first.

Also someone said it was the monty hall problem which im fairly certain has nothing to do with this, which really put me off from reading any further links. Just explain it in plain english and I think people will understand better.

>>8353137
>actual statistician
https://en.m.wikipedia.org/wiki/Bertrand's_box_paradox

>>8353198
>>8353255
My math proof was first and its also more brainlet friendly than his
>>8350665

>>8353311
>>8352481
I made this for you guys.

>>8353255
>Its like all that nonsense black hole math
It's literally some of the first formal probability mathematics you learn in a college setting.

The identity for conditional probability is: P(A|B) = P(AB)/P(B), where P(A|B) is the probability of A being true given B, P(AB) is the probability of A AND B being true, and P(B) is of course just the probability of B being true.

That's my first line.

When you have disjoint sets that, when unioned, will create the space you're working in, you know that P(A) = P(A|S_1) + P(A|S_2) + ... + P(A|S_N), where S_1,...,S_N are the disjoint subsets.

Using this idea and the identity above, you get my 3rd line.

The rest is algebra.

>>8353345
kek nice.

btw I never understood that brainlet wojack. doesn't the black hole mean his brain is incredibly massive. Seems like the brainlet is the guy that made the pic.

>>8353375
Sorry, the 3rd line should read

P(A) = P(A S_1) + P(A S_2) + ... + P(A S_N)

>>8348618
Nigger

>>8347686
retard alert!

>>8353382
Its a singularity, a single point in space. His brain is so small it has become mono-dimensional and can no longer be measured in terms of length, width or height. Its the smallest object physically possible.

Also black holes dont have to be big. (in terms of mass, not volume. No black hole has any volume at all.) Most of them are tiny. The sun makes millions of tiny black holes every day. They are so small they are unstable and wink out of existence within a few femtoseconds because the smaller a black hole is the faster it loses mass due to hawking radiation.

>>8353452
shut up nerd before i give you a swirlie and shove you in a locker

>>8353086
Nope, you know that the box you already drew from is not the double silver because you have a gold ball in your hand meaning it can only be the double gold box or the gold silver box, this isn't even remotely the same question as flipping a coin brainlet

2/3 chance cause im a smart ass

how its it not 1/2?

>>8347660
Master’s math student here
It’s 50%

>>8353534
Because the double silver box is eliminated, you have a gold ball in your hand, that is eliminated, the remaining balls are 2 Gold and 1 Silver, its 2 out of three gold, your chance to get gold are 2 out of 3

>>8353554
What subfield did you study?

50%
1/3 the first box is chosen (success), 1/3 the third box is chosen (failure), in case of 2nd box you have 50% chance to get gold ball as second so 1/3 * 1/2 = 1/6
overall 1/3 + 1/6 = 1/2 = 50%

>>8347660
Two out of three, so 66.66666666...%

You got a golden ball, so it's not the box on the right with the two silver ones.
That means only the left and middle box are in play, and after you take out one golden one, all that's left in the middle box is two golden and one silver ball. Hence: two out of three.

Debate me.

>>8352773
>>8353255
https://en.wikipedia.org/wiki/Bertrand's_box_paradox

>>8353616
nevermind, I'm a brainlet, didn't read the question properly, it's 1/3, you have to pick the box with 2 golden balls which is only the first one
read carefully "you pick a ball at random and it's golden, what are the chances you take another golden one out of the same box"
2nd box is not applicable because you can't take 2 golden balls out of it

>>8353580
but you have to reach into the same box..
So you have either reached into the double gold box, or the silver/gold box.
which is 1/2 chance to get another gold ball...

>>8347660
Two out of three, so 66.66666666...%

You got a golden ball, so it's not the box on the right with the two silver ones.
That means only the left and middle box are in play, and after you take out one golden one, all that's left in the left and middle boxes combined is two golden and one silver ball. Hence: two out of three.

Debate me.

[edited because I forgot a few words]

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

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

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

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

>>8353554
Oh good, you must be comfortable showing a proof then,

Are you srsly retarded? Those saying 2/3 should just kill themselves, useless brainlets. How can you pick another golden ball, if you picked one from the middle box already? You either pick a silver or a gold one, hence 50%. Jfc

>>8353688
>if that happens to be a gold coin
Is not the same as
>It's a gold ball.
Different problem.

>>8353693
>How can you pick another golden ball, if you picked one from the middle box already?
Lol, that's why it's called probability.
2 out of 3 you'll pick out a golden one.
That means 1 out of 3 you'll pick out a silver one.

>>8353667
Intereseting stuff. Unfortunately my brain just doesn't understand logic

>>8353707
If it's a gold ball, the probability the next ball will be gold is 2/3.

The first ball is gold, so the probability the next ball will be gold is 2/3.

It's the exact same fucking problem you god damned retard.

>>8353688
So exactly like I said in >>8353685
(and probably a few people before me)

How is this even a paradox?

>>8353737
Or did most of you miss the part about having to pick another ball from the SAME box you picked the first one from?

Simple explanation for the brainlets.

>>8353305
>Actual statistician

>>8348618
Are the 5 people white?

>>8353775
That doesn't matter. You got a golden ball, that means you got it from either one of those boxes.

All that matters is how many remain for you to pick; and the answer to that is two golden and one silver.
So the odds of picking another golden one is two out of three.

Alright let me put down some brainlet-proof evidence.

You picked a ball. It's gold. What just happened?
You had a 3/6 chance to pick that golden ball. Now that you've picked it, that removes the golden ball from what's left to pick, making it a 2/5 chance to find another golden ball if you could pick any of the other boxes. But hold up, you can't do that, and you know for sure that you aren't in the box with the 2 silver balls, so you can remove those as well, making the chance to pick another golden ball in the same box 2/3.

Holy shit. This board is full of literal brainlets.

I mean, the answer 33.3% must be obvious to any sane human being.

>>8353671
You don't know which box you have though because 2 boxes have at least 1 gold ball, so you have to assume it could be either one giving you a 2/3 chance

>>8353775
I like this. I made something similar here >>8352655

if you still don't understand why it's 2/3 read the answer on; https://math.stackexchange.com/questions/187909/statistics-bertrands-box-paradox

>>8347660
It's 100% because I picked it up out of a box that said chain link on the side.

having already taken a gold ball means you've chosen either box 1 or 2.
the question is about the next ball in the box you already chose.
had you chosen box 1 you'd have one gold ball left in the box; had you chosen box 2 a silver ball remains.
I'm going for 50%.

>>8353808
that doesn't make sense tho
i picked up a gold ball meaning there's 2 boxes i could have picked from.
my other ball (from the same box) is either going to be the other gold ball from the 2x gold ball box, or the silver ball from the 1xgold and 1x silver box.

the trick is I have to take my second ball from the same box, it's 1/2 it's not 2/3

>>8353789
If you choose 1 it's a double gold. If you choose 2 it's a double gold. If you choose 3 it's a silver. 2 ways to get double gold vs 1 way to get silver. There is no way to simplify this for you further.

>>8353723
No matter what If you select the box with Gold-Gold, the odds of picking gold first is 100%, the odds of picking gold second is 100%

With the Gold-Silver box is where "If" matters.
>"If" first ball is gold.
50% chance of choosing Gold ball first, 50% chance of choosing Silver ball first. If gold then 100% silver second. If silver then 100% gold second.

>It's a gold ball.
100% chance of choosing a gold ball first. 100% chance of choosing a silver ball second.

With the original question choosing either Gold-Gold or Gold-Silver will always result in choosing a gold ball first. Every pick in the Gold-Silver box must be gold first, then silver after.
With "If" you have the possibility of choosing silver first in Gold-Silver boxes.

>>8348618
Why do you need to complicate things, I just take the gold and run, anon.

>>8353844
It makes perfect sense you don't know which box you have so logically you must assume it could be either the box with two or the box with 1 gold and one silver, thus adding up the probability of both boxes

>>8353835
You got gold, so it's either from the left or middle box.

The question is what are the odds of another gold if you pick from the SAME box.

All that remains in the left and middle boxes are two gold and one silver. Your odds are 2/3.

>>8353854
>If you choose 1 it's a double gold
Yes. That is the 2 in the "2 out of 3"

>If you choose 2 it's a double gold
No. If that first golden ball came from box 2, then the next ball is going to be silver.

>>8353874
well i guess im just retarded

>>8353881
I'm not talking about box 2 im talking about gold ball 2. 1 and 2 both come from box A. Gold ball 3 is from box B.

>>8353898
So your answer is also 2/3?
That's what I'm saying.

>>8350902
I will use Intimidating Shout.

>>8353920
Yeah, I never implied otherwise. I explained it in that picture to better illustrate that the outcome is decided depending on which of the 3 gold balls are picked.

>>8353868
>With "If" you have the possibility of choosing silver first in Gold-Silver boxes.
"If a gold coin was withdrawn in the first step"
There is no possibility of silver first with "if."

>>8353868
If A, then B.

A is true, so B must be true.

There are three doors; A, B, and C.

Behind one door is a million dollars.

You get to choose one door, and you pick A.

Door C is opened just because; there is nothing behind it.

So the million dollars is behind A (your pick) or B.

You get to choose: stay with your pick (A) or change your pick to B.

Would changing to B increase your odds, or would the odds remain the same?

>>8353881
>all that remains in the lef and middle boxes are 2g and 1s.
you removed 1g only from box2 and solved as if you can still switch to box1 where there are 2g. That is not the question; the moment you choose a box you have to check the contents and see if there are 2g in it and only box1 has 2g so your odds are 1/2.

>>8354036
The odds that you picked gold from the left box (and not from the middle) are two to one though.

>>8354025
Changing increases your odds fgt

>>8353961
"If" in that case would be used exclude outcomes where silver is picked first. Both silver first then gold, and gold first then silver second both are possible outcomes although only one passes the "If" check.
Without the "if" you have a new problem where gold must be picked first. So silver first then gold is not a possible outcome.because after Box B was picked a gold ball must have been selected.

>>8354036
>you removed 1g only from box2
That's if the gold you picked came from box 2. You don't know that though.

>>8354036
Think about it this way, theres three gold coins to pick first from the left box and from the right box.

2 out of those 3 will yield you a gold ball on the second draw, only one will give you a silver ball the second time

100%
Because I’ll remember the position of the ball

>>8354054
although I don't understand the answear I'm not gonna go agains the general consensus. Didn't major in maths so fuck it, I'll just take my 13,(3)%error and leave.
Thx 4 the time to answear me anon

The overall probability is indeed 2/3, however the question is asking the probability after (keyword after) picking the first ball. The question is asking for the local probability, which is 1/2 because there are only two choices left after eliminating the first one.

It's a trick reading comprehension question.

this thread must be a jewish trick
They are trying to lower the inhibitions of the general population by making them believe that all of their peers are way dumber than they actually are

>>8354149
Here's an explanation.

>>8354218
If you picked Box 1 you have a 100% of choosing a gold ball second.
If you picked Box 2 you have a 100% chance of choosing the silver ball second.
You are choosing boxes not balls. And the problem already stipulates you will choose gold first.

>>8354218
I was blind but now I see.
Good luck and great fortune to you anon!

>>8354268
Those three options at the bottom are all equally possible under the premise.

That means you have two chances of picking another gold, and one chance of picking silver.

>>8354287
And you.

>>8354268
So you're suggesting that this scenario:

Someone puts two boxes in front of you, one with two gold balls, and one with one gold and one silver. They then look into each box and take a gold ball out and ask you to choose a box.

is equivalent. Is that correct?

>>8354292
>pick box 1
>pick a gold ball
>pick another gold ball
>win

>pick box 2
>pick the gold ball
>pick the silver ball next
>lose

Both Box 1 and 2 equally possible to pick and therefore 50% chance of success.

66% you fucks

>>8354322
There are indeed two boxes, but under the premise there are three possibilities.

1) you picked the left golden ball in the left box

2) you picked the right golden ball in the right box

3) you picked the one golden ball in the middle box

Under possibilities 1) and 2), you're going to pick another gold ball.
Under possibility 3) you're not going to pick a gold ball.

Hence: the odds of picking another gold are 2/3.

>>8347660
2/3 you crypto kikes.

Made a mistake writing that out.

>>8354322
There are indeed two boxes, but under the premise there are three possibilities.

1) you picked the left golden ball from box 1

2) you picked the right golden ball from box 1

3) you picked the one golden ball in box 2

Under possibilities 1) and 2), you're going to pick another gold ball.
Under possibility 3) you're not going to pick a gold ball.

Hence: the odds of picking another gold are 2/3.

>>8354319
Not at all. If you could switch boxes the boxes have no meaning in the first place and all the balls could be put in the same box.
The equivalent problem would sealing two boxes, one Gold-Gold, one Gold-Silver, choosing one at random and giving it to person. That person then removes a gold ball from the box and gives it back to you.

>>8354380
Regardless, you're solution comes down to dumb semantics. You assume the problem is saying the gold ball is absolutely guaranteed to be picked before you pick it, which is an ass-backwards assumption that has no bearing in the real world. You're splitting hairs and you know it.

>>8354375
You have an equal chance of picking each box. For every time you pick Box 1 twice you would be selecting Box 2 twice. So yes the number of unique possibilities is greater the probability is unchanged. To put it another way in 4 expected attempts you are picking GoldR once, GoldL once, and Gold(Box2) twice.

>>8354446
>You have an equal chance of picking each box.
No.
Under the premise, you are twice as likely to have picked box 1.

>>8354455
>pick a random box

>>8350602
>>8351260
We'll never know for sure if you're trolling or an actual brainlet. I choose to believe you're an actual brainlet thus making me feel better about myself. Thanks.

Ok I just mapped out the trees in my head. I thought it was 50% but now I see it is 2/3rds. I see now that you could pull out ball 1 or ball 2 from the double gold box and thus those each have their own probabilities.

>>8354458
What?
The premise is "you pick a golden ball".

Box 1 has two of those; box 2 only has one.
Thus, it's twice as likely that you picked that golden ball from box 1.

>There are people on this board who unironically think the answer is 50/50
>This is what I'm trading against

>>8354375
This poster made me see the light.

>>8354438
Maybe read what OP's problem said first, complain second. Problems like these literally all hinge on the exact words used. Without an "if" it's a different problem and has a different solution.

>>8354500
English isn't your first language, is it?

>>8354485
The premise is you "pick a gold ball" yes.
If you pick Box 1 you will pick a gold ball first. If you pick Box 2 you will pick a gold ball first.

>>8354512
I'm Anglo, therefore I know what "If" means. There is nothing implied in these probability problems

>>8354545
Okay, got it, English isn't your first language.

>>8354545
There is no "if" when it comes to the first golden ball.
The premise says "you pick a golden ball".

There are two golden balls in box 1, and one golden ball in box 2.
So the odds that the first golden ball you picked came from box 1 are twice as high.

It's 50-50
Please keep these coming I love these threads. Almost as much cringe as the "she steals $100 from the register" one yesterday.
Serves as an indispensable daily reminder to never take crypto advice from /biz/

>>8354609
see>>8353688

>>8354564
Please read >>8354199
The whole point of OP's bait image is to encourage this exact discussion. I guess some people really don't understand or are extremely dedicated to playing up the act.

>>8354639
No, the overall probability for picking the box with 2 gold balls is 1/3.

Besides, conditional probability (i.e. P(G_2|G_1)) Already assumes the first gold ball has been picked.

Here's the problem explained for cryptoniggers

>You saw the three boxes and noted the balls and their colors in the three boxes
>You pick out a ball from a random box that you don't know about
>It's a gold ball
>You remember that only two boxes have gold balls
>The first box has two out of three gold balls, meaning you had a 2/3 chance of picking this box
>The second box only has one gold ball, meaning you had a 1/3 chance of picking this box
>You are asked to guess the probability picking ANOTHER gold ball
>Well if you picked the first box, you have a 1/1 chance of picking a gold ball
>If you picked the second box, you'd have a 0/1 chance of picking another gold ball
>So a 2/3 * 1 = 2/3 chance of picking a gold ball from the first box and a gold ball again
>And 1/3 * 0/1 = 0/3 chance of picking a gold ball from the second box and a gold ball again
>Add the probabilities up: (2/3 + 0/3) = 2/3 chance of picking a gold ball on the second try, given that you chose a gold ball on the first try

Was that so difficult?

Dude, it's 50/50. You HAVE picked the gold ball, so you picked a Box with a gold ball in it.

>>8351853
You rephrase the question after 8 correct are drawn, so 1/100.

>>8354639
Let me ask you this: if the question was rephrased to this:

"You put your hand in and take a ball from that box at random. Turns out, it's a gold ball"

Would this change the question?

>>8354375
Implying you can put your hand in box 1 twice. It's more that box 2 is a half chance after you discard the possibility of choosing silver.

>>8354694
You picked one of three golden balls.

Two are in box 1, and one is in box 2.

So three scenarios:
1) you picked golden ball 1 from box 1 ====> next ball is again gold
2) you picked golden ball 2 from box 1 ====> next ball is again gold
3) you picked golden ball from box 2 ====> next ball is NOT gold

So the odds are 2/3.

>>8354694
There's still three gold balls you could have chosen, and 2/3 happen to be in one box that has a 100% chance of having a second choosing to be gold, while the second has a 0% chance. 2/3 of the times you choose a gold ball you'll get another gold ball the second time.

>>8354721
>Implying you can put your hand in box 1 twice.
The premise says you have to put your hand in the same box twice.

Read it carefully.

>>8354668
>there are three possibilities
>picking Box 1, Box 2, or Box 3
>pick gold ball first
>box must have a gold ball contained
>Box 3 is not possible because no gold balls exist there
>Box 1 and Box 2 are possible and fit conditions needed (have one gold ball)
>therefore Box 1 and Box 2 are equally likely and encompass all possible outcomes
>Box 1 50%, Box 2 50%

>if Box 1 we can choose gold1 or gold2 first
>choose the other second
>2 possibilities
>for every 10 pulls of Box 1 we get gold1 first 5 times and gold2 first 5 times

>if Box 2 we choose gold first,as stated, silver second
>choose silver second
>1 possibilty
>for every 10 pulls of Box 2 we get gold first 10 times

End probabilities of first ball taken after 20 results.
Box1 chosen 10 times: 5 times gold1, 5 times gold2
Box 2 chosen 10 times: 10 times gold

gold1 = 1/4 taken first
gold2 = 1/4 taken first
Box2 gold = 1/2 taken first

>>8354811
>therefore Box 1 and Box 2 are equally likely
No.

There are two golden balls in Box 1, and only one golden ball in Box 2.

The odds that the golden ball you picked came from Box 1 are twice as high.

>>8354811
Answer this >>8354714

>>8354818
Odds of picking a golden ball are 100%. If the second box had 99999 silver balls and you picked Box 2 it would always be gold first.

>>8354829
The first ball you pick is gold, yes.
That's in the premise.

That means you picked one of three golden balls.
Two of those are in box 1.
One of those is in box 2.

That means the first golden ball is twice as likely to have come from box 1.
Box 1 and box 2 are not "equally likely" as you claimed.

>>8354829
>Odds of picking a golden ball are 100%
No they aren't. This is a retarded assumption from someone who doesn't understand English.

Answer this >>8354714

>>8354844
He's probably referring to the first golden ball from the premise. For some reason.

>>8354827
>>8354844
No. Random events that occurred in the past are present facts.
I flipped a coin and got heads is a fact.
If I flipped a coin and got heads is a probability.

>>8354839
You have the order mixed up. You pick a random box THEN a random ball. The only premise is that the ball you pick must be gold.

>>8354854
He's assuming the hand of god is magically giving him the gold ball and/or causality is broken and you're guaranteed the gold ball before you even pick it. It's a retarded assumption to make.

>>8354879
>You pick a random box THEN a random ball.
Yes.
And that random ball is gold according to the premise.
That means that the random box you picked is twice as likely to be box 1 than box 2.
Why? Simply because box 1 has two golden balls, and box 2 only has one.

>>8354888
Well the first ball is gold according to the premise.
So you could describe that as "the hand of god gives you a golden ball", or as "the odds of the first ball being gold are 100%", or as "a bald eagle flies into the room and picks a golden ball and drops it in your lap".
It doesn't matter how you describe it; the premise says the first ball is gold. Done.

So why he's focusing on this is a mystery.

>>8353688

so, you take into account that if you draw a gold ball, the probability of it being from the box with two gold balls is higher than the probability from it being from the box with a gold ball and a silver ball, for the second draw? is that it?

>>8347660
Daily reminder that the mouth breathing knuckle dragging brainlets in this thread trying to argue the answer is not 50% are also participating in the crypto market

>>8354879
>Random events that occurred in the past are present facts.

So now you're claiming that picking the gold ball was, in fact, random, i.e., had a probability less than one? Because if so, then the example of a person taking out a gold ball you gave is not equivalent.

You seem to think that this is the same as roulette logic, where landing on black in the past doesn't change the probability of landing on black in the present, but you can't apply that logic in the same way here.

>>8354912
Not sure why you said "for the second draw" at the end, but yes.

If you have two boxes, and "box 1" has two golden balls and "box 2" has only one; and you pick a golden ball from one of the boxes, then the odds of that box being "box 1" are twice as high.

>>8354912
But this >>8354929

isn't even really all that necessary or relevant to finding the solution.

You simply look at all the options that are left after having picked one golden ball.

There were three golden balls, so that first golden ball was one of those three.
That leaves three scenarios:

1) you picked golden ball 1 from box 1 ====> next ball is again gold
2) you picked golden ball 2 from box 1 ====> next ball is again gold
3) you picked golden ball from box 2 ====> next ball is NOT gold

So the odds of the next ball from the same box being gold are 2/3.
Because remember: you don't know if you had box 1 or box 2 until you pick the next ball.

A simple, common sense explanation, without the use of symbols, and without any arrogant attitude:

Let's start first with the fact that there are 6 balls in total. 3 of those balls are gold. So what is the probability of your first ball you pick being gold? 3/6, or 50%.

Now, we know the first ball we ended up picking was gold, but also ask yourself: How does picking a gold ball change what I have to now consider?

There were originally 3 gold balls, but you've now picked one, and so 3-1 = 2 gold balls remaining. There has also been a change to the total number of balls remaining. You've removed one ball from the total, and so 6-1=5.

So you might think that the probability of then picking a second gold ball is 2/5, 40%. But the actual answer is 2/3, why is that?

It's because we know an entire box contains only silver balls, and in this box there are 2 silver balls. It would be incorrect to include this box in our consideration because it has no way of contributing to the probability of picking a second gold ball.

So we remove 2 silver balls from the running total we're looking at: 5-2 = 3.

Therefore, the probability of picking a second gold ball is now 2/3.

>>8348272 keep this picture in mind, when reading my explanation
>>8355276

>>8355276
Wrong, it's 50%.

If you gave this question to every man in this thread, every single ball chosen from bucket 2 is gold.
For all intents and purposes there is one gold ball in bucket 1 that is replaced when the first ball is removed, as you can only choose one ball from bucket 1 in the first round.

Sorry brainlets but this question is designed to trigger people that follow the rules of probability, rather than original rational thought. It's not a schoolroom exam question, children.

T. Masters level education

>>8355413
You're wrong.

There were three golden balls, so that first golden ball was one of those three.
That leaves three scenarios:

1) you picked golden ball 1 from box 1 ====> next ball is again gold
2) you picked golden ball 2 from box 1 ====> next ball is again gold
3) you picked golden ball from box 2 ====> next ball is NOT gold

So the odds of the next ball from the same box being gold are 2/3.
Because remember: you don't know if you had box 1 or box 2 until you pick the next ball.

>>8355433
WRONG!

>>8355439
no u