/sci/ - Science & Math

[Anonymous No.10245866]

Can /sci/ solve this? I'm prepared to be extremely disappointed.

[Anonymous No.10245874]

>>10245866
50%

[Anonymous No.10245880]

Given that a box contains a single gold speck, what is the probability that the same box contains at least one more gold speck?

[Anonymous No.10245881]

>>10245880
yes

[Anonymous No.10245882]

Bayes theorem ?

[Anonymous No.10245886]

>>10245880
with the boxes a priori equally likely

[Anonymous No.10245889]

>>10245874
This but unironically

[Anonymous No.10245890]

>>10245874
2/3

[Anonymous No.10245896]

Very slightly over 1/3

[Anonymous No.10245900]

>>10245896
*under

[Anonymous No.10245901]

>>10245866
Not enough information is given. Can't compute.

[Anonymous No.10245904]

100%

[Anonymous No.10245915]

>>10245904
*99.9999% depending on the number of specks

[Anonymous No.10245917]

>>10245866
ok, say we do this 1500 times

500 times you pick from SS
500 times you pick from GS
500 times you pick from GG

SS: 0 favourable
GS: (1/N)*500 favourable
GG: 500 favourable
--------------------------------------------
(1/N)*500+500 favourable (prompt: "It's a gold speck")

500 of those (1/N)*500+500 times you have locked into the GG box.
[math]
\dfrac{500}{\frac{1}{N}\cdot 500+500}=\dfrac{1}{\frac{1}{N}+1}
[/math]

with N=2 you get the normal case

[Anonymous No.10245923]

>>10245917
lol fucking autist gtfo outta here and cure cancer bitch

[Anonymous No.10245929]

>>10245923
impressive, did you quote that from your PhD?

[Anonymous No.10245930]

>>10245929
What a comeback!

[Anonymous No.10245931]

>>10245917
Jesus fuck, is anybody here capable of guessing an outcome without doing the fucking experiment ? Why does everybody here have the hindsight of a fucking grade schooler ?

[Anonymous No.10245932]

>>10245866
According to Bayes': P(BOX1 | GOLD) = P(GOLD | BOX1) * P(BOX1) / P(GOLD)
P(GOLD | BOX1) = 1 (this is why the ball problem works the same way)
So now: P(BOX1 | GOLD) = P(BOX1) / P(GOLD)
P(BOX1) = 0.5
P(GOLD) = 0.5 + 0.00001 (tiny amount for speck)
So:
P(BOX1 | GOLD) = 0.5 / (0.5 + 0.00001)
P(BOX1 | GOLD) = 0.9999

Ball Problem:
According to Bayes': P(BOX1 | GOLD) = P(GOLD | BOX1) * P(BOX1) / P(GOLD)
P(GOLD | BOX1) = 1
So now: P(BOX1 | GOLD) = P(BOX1) / P(GOLD)
P(BOX1) = 1/2
P(GOLD) = 3/4
So:
P(BOX1 | GOLD) = (1/2) / (3/4)
P(BOX1 | GOLD) = 0.66667 or 2/3

[Anonymous No.10245933]

>>10245929
no i quoted it from my 100k starting first pay stub from CS where's yours? oh... right
lolololololololollolol u mad?

[Anonymous No.10245934]

>>10245866
How do you pick a speck of dust? It's impossible.

[Anonymous No.10245937]

>There are 3 boxes as shown
irrelevant to the problem as the box is already picked for you when you start and you have only 2 boxes since only 2 contain gold
>What is the probability that the rest of the box is gold? for 1 of them it's 100%, for the second one it's 0%
(100+2)/0=2$[prbatilt y that iwll be

[Anonymous No.10245938]

>>10245933
>100k
Zimbabwe

[Anonymous No.10245942]

>>10245933
>bragging about paying 15-30k in taxes a year to the gubment
t. antman

[Anonymous No.10245952]

>>10245866
How many specks must be removed for the box to be considered empty

[Anonymous No.10246038]

>>10245866
Depends on the sigma algebra.

[Anonymous No.10246049]

>ITT retards that doesn't understand conditional probability
https://en.m.wikipedia.org/wiki/Conditional_probability
This is High School tier math, brainlets.

[Anonymous No.10246077]

>>10245934
Make it magnetic.

[Anonymous No.10246085]

Yes, well played OP, you faggot. This is the same exact problem as the balls problem that has been making the rounds.

[Anonymous No.10246094]

>>10245890
Choosing a gold spec excludes the pure silver box, refining the possibility to 1/2

[Anonymous No.10246103]

>>10246085
>same exact
nope

[Anonymous No.10246156]

Fucking easy. 50%

[Anonymous No.10246164]

>>10246156

[Anonymous No.10246172]

>>10245866
This one is 50%.

Can someone post the first questions with the balls? Is it formulated that you're allowed to pick whatever box you want each time, or do you NEED to pick the same box twice?

[Anonymous No.10246176]

>>10246172
Same box.

[Anonymous No.10246185]

>>10246164

[Anonymous No.10246224]

>>10245890
No, it either happens or it doesn't. 50%

[Anonymous No.10246264]

The brainlets of this thread aren't taking into account that the problem ask you the probability of the scenario that is happening AFTER you retrieve the gold speck. So it's 50%.

[Anonymous No.10246271]

>>10245866
Can't tell if the people here who say 50% are trolling.
If the speck of dust is completely random, then the probability is approx. 100%. Anyone who says otherwise is retarded.

[Anonymous No.10246278]

>>10246271
Either retarded or dumb. That makes it a 50% chance because there's two things to choose from.

[Anonymous No.10246282]

>>10246264
>cites the very reason it isn't 50%
imagine being this stupid

[Anonymous No.10246288]

>>10246278
>The chances of winning the lottery are 50%, because there are two outcomes, either you win or you don't

[Anonymous No.10246297]

>>1024628
You already picked the speck fucking retard.

[Anonymous No.10246316]

Try it yourself. See what probability it gives.

math.randomseed(os.time()) -- ignore this
local TESTS = 1000000 -- how many tests are done
local SPECKS_PER_BOX = 10000 -- how many specks of dust get put in each box
local boxes = {
[1] = {}, -- gold dust
[2] = {}, -- silver with gold speck
[3] = {} -- silver dust
}

-- Put the specks of gold into the box
for i = 1, SPECKS_PER_BOX do -- do this SPECKS_PER_BOX times
table.insert(boxes[1], "g") -- put a speck of gold dust into the gold dust box
table.insert(boxes[2], "s") -- put a speck of silver dust into the silver dust with gold speck box
table.insert(boxes[3], "s") -- put a speck of silver dust into the silver dust box
end
-- each box now has SPECKS_PER_BOX specks of corresponding dust in it

-- now, at random, we replace one of the silver specks in the "silver dust with gold speck" box with a gold speck
boxes[2][math.random(1,SPECKS_PER_BOX)] = "g"

-- now, we simulate the question
local restOfBoxWasGold = 0
local goldSpecksChosen = 0
for i = 1, TESTS do -- do everything in this block TESTS times
local chosenBox = boxes[math.random(1, 3)] -- You pick a box at random,
local chosenSpeck = chosenBox[math.random(1, #chosenBox)] -- then pick a random speck of dust from that box.
if chosenSpeck == "g" then -- Given that you chose a gold speck,
-- what is the probability that the rest of the box is gold?
if chosenBox == boxes[1] then
restOfBoxWasGold = restOfBoxWasGold + 1
end
goldSpecksChosen = goldSpecksChosen + 1
end
end

print("Probability: " .. restOfBoxWasGold/goldSpecksChosen * 100 .. "%")


[Anonymous No.10246317]

>>10246316
/sci/ doesn't allow formatting, so here is the code with formatting: https://pastebin.com/MCECuBdW

[Anonymous No.10246320]

The number of brainlets on /sci/ is staggering.

[Anonymous No.10246402]

>>10246288
Probability isn't chance. There's a 50/50 chance of you winning the lottery. There's a low as fuck probability that you actually will.

[Anonymous No.10246426]

Uhh... 90210?

[Anonymous No.10246431]

>>10246402
>There's a 50/50 chance of you winning the lottery

[Anonymous No.10246432]

>>10245896
Both me, and my brother who has a doctorate in Material Science, agree.

[Anonymous No.10246442]

>>10245866
~~100%
https://www.youtube.com/watch?v=TN4aiJAXWf0&t

[Anonymous No.10246446]

What's the point of the third box? It's irrelevant since we already chose one of the other boxes.

[Anonymous No.10246448]

>>10246402
>probability isn't chance
>there's a 50-50 chance of you winning the lottery
guess you should go get some lottery tickets then heheh

[Anonymous No.10246450]

>>10245866

I mean you chose a gold speck. So either you've got box 1 or box 2. If it's box 2 there is no more gold in it, so 0%. If it's box 1 the rest of it is gold so 100%. Sum them, take the ratio, badamim badabum 50%

[Anonymous No.10246459]

>>10246450
You're assuming there's an equal probability that the speck is from box 1 and that the speck is from box 2, when this is not true, because the speck you choose is random and there are more gold specks in box 1 so you're more likely to get a gold speck from box 1.

[Anonymous No.10246462]

>>10246448
>>10246431
t. retards
There's 2 outcomes, either you win or you don't, so the chance is 50/50. But the probability of winning is low.

[Anonymous No.10246467]

>>10245904
>>10245915
101% due to a rounding error.

[Anonymous No.10246471]

>>10246459

Fuck dude. Didn't think of that, you're right. Nice thinking!

[Anonymous No.10246472]

>>10246462
Back to first grade.

[Anonymous No.10246482]

>>10246472
Chance=/=probabiltiy.
Also
>american pregrad education
I can't talk to you since you're obviously not educated enough. That's like me explaining the internal organs of a horsr and you stating it has 4 legs over and over again.

[Anonymous No.10246495]

>>10246482
Even assuming you are correct (which you've given no reason to believe that you are), the original question was asking probability, so the chance is irrelevant. There is an approx 100% _probability_ that the rest of the box is gold.

[Anonymous No.10246501]

>>10246495
I never argued that, I argued that chance doesn't equal probability. That being said, it's obvious there's about 100% probability of getting gold again, however, there's also a 50/50 chance of it being either a gold or silver speck (based on the choices)

[Anonymous No.10246504]

>>10246501
I can't find anything other than your posts that defines chance and probability differently.

[Anonymous No.10246511]

The amount of dust is irrelevant here, this is literally the same as each box having two specks.

We have already randomly chosen a box. Some third party peaks into the box and assures us that there is at least one gold speck inside. You don't know if you picked the one with all gold or a metric fuckton of silver, but you should know the amount of dust is irrelevant; you only need to know about 1 more goddamn speck.

If you're not convinced, this is more clear. Tell your third party observer, "Give me all the boxes that have a gold speck in them". He checks, and pushes the two that have gold in them forward. Now you must choose which has all gold. You have a 50% probability that you choose the right one. You have 0% chance of not being a brainlet though.

[Anonymous No.10246534]

>>10246511
this
this is it
you are truly based and redpilled
this is the true correct answer

[Anonymous No.10246538]

>>10246511
You're not supposed to be choosing a box and then asking whether or not the box is a majority gold, that's not what the question is asking.
You're supposed to be choosing a random box, and out of that box a random speck, and if that speck is silver, then you disregard it, EVEN IF THAT BOX HAD THE GOLD SPECK, YOU WOULD NEVER KNOW, BECAUSE YOU CHOSE THE SILVER SPECK.

[Anonymous No.10246555]

>>10246538
Pic related, this has signifigance, and you need to learn it.

[Anonymous No.10246559]

>>10246555
You're not thinking about it correctly. Refer to this post to see why it's 99%: >>10246316

[Anonymous No.10246640]

>>10246559
Thought about it in the shower, and I concede I am wrong. I cannot simplify the problem by only eliminating the third box with a third party observer, because he will eliminate the second box as well almost all the time by searching for that single gold speck.

>>10246316
>>10246317
Nice work

[Anonymous No.10246669]

>>10245931
>guessing
>>>/x/

[Anonymous No.10246900]

>>10245866
Anyone who doesn't see it's a 50% chance after like 15 seconds of thought is an idiot.

[Anonymous No.10246905]

>>10246432
How the hell is material science in any way related?

[Anonymous No.10246917]

>>10245866
50%

[Anonymous No.10246919]

>>10245866
is you picked the 1st one 100%, if you picked the 2nd one 0%, so if we take the average 50%

[Anonymous No.10246920]

>>10245932
>According to Bayes
that's just a meme, not actual probability

[Anonymous No.10246922]

>>10245866
If I pick a gold speck, I’m 99% sure it’s because I picked the first box, because if I had picked the middle box, I would be extremely surprised to pick the gold speck out of it. Almost every time I pick a gold speck first, it will be because I chose the first box. Anyone who says 50% is either trolling or a retard

[Anonymous No.10246930]

>>10246922
>I would be extremely surprised to pick the gold speck out of it
that's just psychological bias, your brain tricking you, if you look at it coldly the probability is exactly 50%

[Anonymous No.10246942]

This is textbook middleschool level conditional probability.Anyone unironically saying 2/3 and1/2 is clinically retarded

[Anonymous No.10246947]

>>10246930
1,000,000 specks per box.
900,000,000 trials.

Box 1–Selected at random 300M times
>Gold Speck selected first 300M
Box 2–Selected 300M times
>Gold Speck selected first ~299 times
>Silver Speck selected 2.9701M
Box 3– Selected 300M times
>Silver Speck selected 300M times

Of all cases where the gold speck was selected first (300,000,299), the overwhelming majority came from the first box. There is a 99.99999% probability that I chose a gold speck because I picked the first box.

[Anonymous No.10246949]

>>10246947
299,999,701 times*
but whatever

[Anonymous No.10246968]

>>10245866
Why does this question make me want to play minecraft?

[Anonymous No.10247000]

>>10246947
that's only if you count from the beginning, once you have the speck it's 50/50

[Anonymous No.10247008]

>>10245866
not enough data for a meaningful answer. There is no information on grain size. Granular materials do not necessarily mix randomly. See the brazil nut effect.

[Anonymous No.10247014]

>>10247000
Yep. You’re retarded.

[Anonymous No.10247020]

>>10247008
>brazil nut effect.
i think you have been memed

[Anonymous No.10247027]

>>10247020
https://en.wikipedia.org/wiki/Granular_convection

[Anonymous No.10247030]

>>10245866
I fucking laughed

[Anonymous No.10247033]

>>10245866
>I am prepared to be extremely disappointed
Were you prepared for this?

[Anonymous No.10247057]

is it 50%?

[Anonymous No.10247060]

2/3

[Anonymous No.10247322]

>>10245866
Assuming there are N gold particles in container 1, N-1 silver particles + 1 gold particle in container 2, and container 3 has N silver particles. The probability of picking any gold particle from the set is (N+1)/(N+N-1+1+N) = (N+1)/(3N). That seems to make sense. If N = 1 then we have a probability of 2/3 and if the number of particles gets very large, the chance goes to 1/3.

Given that you picked a gold particle, the probability that the gold particle came from container 2 is 1/(N+N-1+1) = 1/(2N). Or put another way, given you chose a gold particle, the probability it came from container 1 will be 1-1/(2N). This makes some sense because if the number of particles N gets very large, it is expected that it will be increasingly difficult to be able to be able to pick the single particle in container 2. This means container 1 is most likely going to be what you chose from if N is large.

[Anonymous No.10247326]

>>10245866
This makes me realize how much of a retard i am. I guess that's a good thing.

[Anonymous No.10247355]

>>10246920
I agree with your statement. Except that it's not just a meme. And it is actual probability.

[Anonymous No.10247369]

>>10246316
>no indication of language
Great Job anon

[Anonymous No.10248821]

>>10247369
It's lua

[Anonymous No.10248852]

Can't tell if everyone is trolling or not here what the fuck

[Anonymous No.10248858]

>>10248852
Just provide the answer and an explanation please.

[Anonymous No.10248859]

>>10245866
Kek

[Anonymous No.10248866]

>>10245866
not enough information is given

[Anonymous No.10248867]

>>10245866
Is this the same as the goat and car thing? Then it should be 100%

[Anonymous No.10248907]

>>10245866
If you chose a random speck and it came out gold I think you probably have the gold bin

[Anonymous No.10248916]

I think we've proven that no matter how obvious you make it, there will always be someone who thinks it's 50/50.

[Anonymous No.10248951]

>>10248867
well gold is heavier than silver, so if you use your hand to grab a spec from the top and it's a gold one then it's 100% the gold bin, if it's properly mixed then it's 50/50

[Anonymous No.10248962]

Japaneses are half of the world's population.
There are N+1 japaneses in the world with only 1 out of japan.

Given that you are japanese looking,
What is the probability that you are in Japan ?

Is this analogy correct ?

[Anonymous No.10248968]

There is no fucking way anyone ACTUALLY BELIEVES the chance is .5.
The probability is pretty much 1, if you draw a gold speck you are gonna draw another.

[Anonymous No.10248971]

>>10248968
Some of the people answering don't know what probability means. "It's possible for the gold speck to be in the silver bin, so it must be 50/50" is the train of "thought".

[Anonymous No.10248972]

>>10248962
either you are or you are not, so 50/50

[Anonymous No.10248981]

>>10248971
To be fair their reasoning is "i have one of the two boxes A and B containing gold, what is the probability i have A, wich contains more gold ?"

[Anonymous No.10248987]

This is a nice problem. Law of Independent Events says it's 50/50 but that doesn't seem right. If I had some junk laying around to simulate this problem then I might take some statistics.

[Anonymous No.10249024]

>>10248987
Someone earlier in this thread wrote a program that simulates it

[Anonymous No.10249030]

if you picked box A it's 100%, if you picked box B it's 0%, so average is 50%

[Anonymous No.10249040]

>>10245889
>unironically
It's actually ironic that you would use the word "ironic" without knowing its meaning.

[Anonymous No.10249047]

>>10249030
You're a fucking retard

Every single person who seriously says 50/50 is a retard

[Anonymous No.10249057]

>>10245931
Because guessing when you're dealing with probability related subjects means that there is at least a 66.67% chance you're going to be wrong. That's why game shows rely heavily on it, because most people will fuck up before/during the final round.

[Anonymous No.10249071]

Here's a program I wrote in python to solve this.

>print("It's 2/3")

[Anonymous No.10249072]

i will explain it very very simply for all of you who are still confused.
You have a 100% chance of getting gold from B1.
You have a 0.00000000000000000001% chance of getting gold from B2.
You have a 0% chance of getting gold from B3.
You reach into a random box and get Gold.
You have a 100% chance of that box being the all gold box.
Therefor, you have a 100% chance of the next pull from the same box being gold.

[Anonymous No.10249078]

>>10249072
i think you are not considering quantum tunneling

[Anonymous No.10249091]

>>10249072
I don't understand this retarded scribble.

It's 1/2:
>Box 1 - Gold
>Box 2 - Gold speck is at the top so if any speck was chosen it would have been the gold one
>Box 3 - Doesn't matter.

If you got Box 1, your next pull would be goal. If box 2, then silver.

This reminds me of FIFO.

[Anonymous No.10249093]

>>10249091
Confirmed bait

[Anonymous No.10249095]

>>10245866

Is everyone here mentally handicap or just trolling?

Given that you choose a gold speck: 2 boxes with a gold speck;

Whats is the probability the rest of the box is gold: 1 box has gold 1 box has silver.

50%

[Anonymous No.10249099]

>>10249095
Retarded confirmed

[Anonymous No.10249104]

>>10249095
it's 2/3, you have to remember you started with 3 boxes

[Anonymous No.10249106]

>>10249030
Clever derivation

[Anonymous No.10249108]

>>10249104
>implying anybody on this board doesn't know the Monty Hall problem

Please recheck your work

[Anonymous No.10249110]

>>10249072
its literally this

[Anonymous No.10249112]

[Anonymous No.10249371]

>>10246947
If a box has a gold speck in it you are assumed to have always picked a gold speck

[Anonymous No.10249380]

>>10245866
99.99999999999999999999999999999%

[Anonymous No.10249383]

[Anonymous No.10249397]

If the chance of picking the single speck of gold in the silver box is 1/n, then the probability the pic is looking for evaluates to n/n+1.

[Anonymous No.10249410]

>>10245866
99.999999% depending on the number of dust particles in each box

[Anonymous No.10249419]

>>10245932
Isn't P(BOX1)=1/3? And P(GOLD) = 1/3 + 0.000000001?

[Anonymous No.10249434]

>>10245866
there are three anons, one is a faggot. all three create new threads on /sci/. you click on one of their threads at random. given that you chose the thread on pseud material, what is the probability that op is a faggot?

[Anonymous No.10249441]

why the fuck are so many of you saying that the gold speck in the silver box would be at the top? it clearly says that you pick a random speck, so obviously the probability is approaching 100% if the specks are all the same size as the one in the picture.

[Anonymous No.10249451]

>>10246164
Ironically, thinking trump is stupid is the pinnacle of mount stupid

[Anonymous No.10249455]

>>10245866
you need to know the amount of specks in the box for an exact number, but it's 99.99.. how long it goes on depends on the amount of specks in the box.
Your chances of picking the Silver Dust Gold box, are 1/3, your chances of then picking the gold speck are 1/3 * 1/(amount of specks). If you look at the pic I'd say there's about 50000 specks, so 1/3 * 1/50000 = 0.0000067 or 0.00067% . Now we subtract this probability from 100% since there are only two possible scenarios where you pick a gold speck. 100% - 0.00067% = 99.99933%

There's your answer for N = 50000

[Anonymous No.10249477]

To everyone saying it's a 50% chance, that's like saying: the chances of me winning the lottery are 50%, either it happens or it doesn't. That's just retarded

[Anonymous No.10249487]

>>10249477
I think I'll go out tomorrow since I'll have a 50% chance of getting hit by a meteor from another solar system that'll release me from this world filled with brainlets. Either it happens or it doesn't, am I right? ;)

[Anonymous No.10249495]

>>10249434
Trick question. The answer is 100%
All OPs are faggots.

[Anonymous No.10249497]

>>10249040
I understood his implications. You're just low verbal-IQ ESL friend

[Anonymous No.10249563]

>>10249477
if you got the first 9 numbers right out of 10, what's the probability that you get the last number right? it's 1/10, because the previous numbers don't matter in an independent event, just like it's 1/2 here, because the previous pick is already given

[Anonymous No.10249566]

>>10249563
Shhh let babby believe the gambler's fallacy

[Anonymous No.10249589]

>>10249563
that doesn't make any sense. You're ignoring the fact that you first chose a box and a speck at random. After that you get a gold speck, yes, but it's not 50%

[Anonymous No.10249605]

>>10249589
the point is that the gold speck is given, it's irrelevant how you got it, now you have a 50/50 chance of getting either box

[Anonymous No.10249641]

>>10249605
the point is that its very, very, very unlikely that you would pick a gold speck out of the silver box with the one gold speck. therefore it is very, very, very likely that the random gold speck that is given is from the gold dust box. that is why the probability of the box being the gold box is close to 100%

[Anonymous No.10249644]

>>10249641
the problem states that it's GIVEN that you WILL take a gold speck if the box has it. the probability of picking it does not matter at all

[Anonymous No.10249645]

>>10249451
>mouth breathing intensifies

[Anonymous No.10249648]

>>10249641
you are committing the gamblers fallacy, google "independent event"

[Anonymous No.10249656]

>>10249644
hmmm, yes that is actually a good point.

[Anonymous No.10249679]

>>10249648
so the key point of this problem is the whole "it's given" part. thats why it doesn't matter whether you do this a 100 milion times if every time it's given that you get a gold speck.

i understand now i think

[Anonymous No.10249690]

>>10249644
>the problem states that it's GIVEN that you WILL take a gold speck if the box has it. the probability of picking it does not matter at all
This is a poor reading you sometimes see from low tier statisticians. Given that the box contains a gold speck, you'd be right. That is not the same as given that you've chosen a gold speck.

[Anonymous No.10249697]

>>10249644
>the problem states that it's GIVEN that you WILL take a gold speck if the box has it.
No, it doesn't state that at all. It states that it's given that you GOT a gold speck. That is something entirely different.

[Anonymous No.10249708]

>>10249697
so it's 100% probability that you get a gold speck, now it's 50/50 between box 1 and 2

[Anonymous No.10249709]

>>10245866
kek, this is actually a pretty good demonstration of the answer to the gold ball problem

[Anonymous No.10249719]

>>10249708
>now it's 50/50 between box 1 and 2
No.

>>10249709
And yet people still manage to get it wrong more often than not.

[Anonymous No.10249725]

>>10249708
No. Another equivalent wording would be "You pick a box at random. You pick a speck of dust from the box. Every time the dust is gold you note it down and pick another speck the color of which you also note down. What percentage of the recordings would you expect to be two gold specks picked?"

The given just means "this part of the process has happened". It isn't magic.

[Anonymous No.10249727]

>>10249071
Genius

[Anonymous No.10249731]

>>10249725
gambler's fallacy

[Anonymous No.10249732]

>>10249731
>>10249708
If it’s 50/50, then shouldn’t we expect that of all the times you saw the gold speck, there should be an equal distribution among box 1 and 2? For example, you play the game 900 times. 300 times, you will shown the gold speck, then you answer 50/50. Doesn’t that mean that you expect to have picked the gold speck from the middle box 150 times?

[Anonymous No.10249733]

>>10249725
and what is the answer to this wording of the problem in your opinion?

[Anonymous No.10249735]

>>10245866
You can take the all silver box out of the equation, because it's a given that you chose a box with at least one gold speck. It's 50%.

[Anonymous No.10249739]

It's infinitesimally less than 100%. It's not fucking 50/50 or 33% or 66%, and if you say it is, you have profoundly sub-standard IQ and don't belong on /sci/.

[Anonymous No.10249740]

>>10249735
>>10249732
Do you really think a gold speck will be chosen out of the middle box 16% of all trials? Wow

[Anonymous No.10249748]

P(box is gold|gold speck chosen)=P(box is gold and gold speck is chosen)/P(gold speck chosen)
1/3 ÷ (1/3 + ε)
a little less than 100% :^)

[Anonymous No.10249753]

it's like this:

we know that the all silver box is not the box picked. that means that we have a 1/2 chance of picking the all gold box and a 1/2 chance of picking the almost all silver gold box.
then we count how many gold specks over the whole count of all specks:

let's say there are 500,000 specks in each box: this means that the gold specks are 500,001, but the sum of all the specks in the two boxes is 1,000,000. then it's simple to do:

(1/2)/(500,001/1,000,000).

this gives an answer that is almost 1, or almost 100%.

[Anonymous No.10249757]

>>10249753
>and a 1/2 chance of picking the almost all silver gold box.

meant to say the almost all silver box

[Anonymous No.10249902]

>>10245866
Assuming that every box has x specks, the probability of two gold specks given one gold speck already drawn is ... drum roll ...

x / (x + 1)

[Anonymous No.10249946]

the question is worded weirdly I would argue.

If you know you got a gold speck, but it can be either box, then all the other information doesn't matter, and it's 50/50

But, if the above information does matter, what they should ask is: "what was the probability of you getting this speck of gold in the first place"
Then the answer is obviously 99.999..%

[Anonymous No.10249963]

>>10249946
You play the game 900 times. On 300 occasions, you will obviously select box 1, and therefore select a gold speck. Each time I will ask you which box you think you found it in. You then say 50/50, which means you expect the middle box to produce a gold speck 150 times...

[Anonymous No.10250023]

>>10249963
that's a practical application. If, in an abstract sense, the only information you are given is that you got a gold speck, then you would say 50/50

[Anonymous No.10250030]

>>10250023
nvm. Because for you to be able to say 50/50 you would need to know that there are 2 boxes from which a gold speck can be drawn. You must then assume you should use the other information given as well. So that line of thinking is out, 99.999% is the only answer. Sorry

[Anonymous No.10250044]

the boxes are red herrings because functionally, the specs of dust here have the same status that boxes have in other similar tasks. The correct answer is almost 100%.

[Anonymous No.10250445]

>>10249727
>>10249071
Wrong side of the space-time tradeoff, way too compact.

[Anonymous No.10250477]

Yeah, but what happens when a sun of lava collides with a sun of ice?

[Anonymous No.10250850]

>>10249709
OP here.
Thanks, this was my intention. I got wondering what the root of the confusion was, and whether this version of the problem would make the answer clearer.

[Anonymous No.10250852]

>>10249725
This is a good clarification.
>>10249733
I'm not that poster, but the answer is nearly 1.

[Anonymous No.10250861]

>>10249648
I don't see the relation to the gambler's fallacy. These are not independent events; we're dealing with a conditional probability space.

>>10249641 was correct.

[Anonymous No.10251119]

>>10245917
https://youtu.be/Oqm6X3G_wes

[Anonymous No.10251145]

>>10246224
unironically correct!

[Anonymous No.10251192]

so the consensus is 50% or 2/3?

[Anonymous No.10251214]

This is such a nice way of showing the retards who answered 50% in the balls problem they're wrong.

[Anonymous No.10251215]

The only sensible answer is `The probability that the rest of the box is gold is basically 100%'
Fuck everything, y'all're retarded.

[Anonymous No.10251222]

here's how you picture this experiment:
>pick box randomly
>pick random speck from chosen box
>if speck is silver, put it back (jamal), mix the contents of the box then mix the positions of the boxes randomly, then restart from the beginning
>if speck is gold: increment the number of trials. pick another spec from the box. if it's gold, increment the number of successes.
>repeat to infinity and beyond and check how the ratio (number of successes/number of trials) converges to 100%.
>???
>profit

[Anonymous No.10251236]

Well /sci/?

[Anonymous No.10251237]

>>10251192

50%

People who are legitimately missing the solution are getting caught up in thinking about the probability of choosing the gold speck in the first place, but as has been explained this doesn't factor into the problem at all.

Imagine you are a God, and every time you dip your hand in the second jar you always pull out the gold speck. This is what it means for the gold speck to be mathematically 'given'

So given this gold speck you have two scenarios, either you look into the jar and see silver or you look and see gold. Considering just these cases, the way the problem is defined the probability is 1/2.

[Anonymous No.10251238]

>>10251237
>lame trolling

[Anonymous No.10251239]

>>10251236
2/3

[Anonymous No.10251241]

[math]-\frac{1}{12}[/math]

[Anonymous No.10251243]

>>10251237
>Imagine you are a God
oh go fuck goat

[Anonymous No.10251244]

>>10251237
>Imagine you are a God
oh go fuck a goat

[Anonymous No.10251249]

>>10251236
either 50/50 or 2/3

[Anonymous No.10251250]

>>10251237
this, the probability of picking the first gold speck is 100% because you just did, then if you picked box A, you have 100% probability of picking another gold speck, if you picked box B you have 0%, so by average law it's 50/50

[Anonymous No.10251255]

>>10251236
that's gonna be a big 50% from this time, dawg

[Anonymous No.10251256]

>>10251250
>my 50 iq in full display

[Anonymous No.10251305]

>>10251256
>>10251244
please explain how 50% isnt the correct answer i dont get it.

[Anonymous No.10251309]

>>10251305
it's 50%, you are getting memed

[Anonymous No.10251318]

>>10251305

It is correct. Just to reiterate, the percentage distribution of the balls does not matter. If you are reading either this question or the original two ball problem as 'which jar did I probably pull this gold speck out of?' Then you are misinterpreting what 'given' means.

[Anonymous No.10251328]

>>10251305
Run the experiment in your head. Follow the instructions exactly as stated in the OP. If you don't get a gold speck the first time, stop and throw away the trial. This is because you are conditioning on getting a gold speck the first time. It should be extremely clear why it is close to 100%.

[Prof Sai No.10251331]

>>10251305

If you picked a gold speck, the overwhelming probability is that you got it from box one. Of course you discard all choices from box three, but you also discard almost all choices from box two.

So the answer is Aprox: 99%

[Anonymous No.10251342]

>>10251331

See my reasoning here
>>10251237

There is no factoring in any probability distribution. If you chose jar 1 you get a gold speck, if you chose jar 2 you get a gold speck. The rest of the jar is either silver or gold

[Anonymous No.10251348]

>>10251331
that's the gambler fallacy, those are independent events, so 50%

[Anonymous No.10251354]

the probability to choose a gold speck is 0

just like the probability of choosing a single number on the real number line

[Anonymous No.10251358]

>>10251354
except gold specks exist, but real numbers don't

[Anonymous No.10251370]

>>10246271
This is actually correct, in case anyone is interested.

[Anonymous No.10251376]

>>10251331

>>10251342

Just to be clear I'm not saying your experiment results would be wrong.

Let's say we do the experiment three million times, and we get one million + 1 gold specks first try. Of those, one million of those first specks came from the first jar, one came from the second.

This is where I see most people's programs stop, they aggregate the results and print it; however, that number isn't pertinent to the question.

All we are concerned with is the probability of the second speck drawn. So, take the average results of drawing a second gold speck from the first jar (100%) and the average results of drawing a second gold speck from the second jar (0%), then take the average of these averages and you get 50%

[Anonymous No.10251405]

>>10251305
>please explain

[Anonymous No.10251413]

>>10245874
this. It either is the box or silver, or isn't.

[Anonymous No.10251418]

>>10245917
you have solved another problem anon, namely: given that your first speck is gold, what is the chance that the next one also is gold?
But the question is: given that you got a speck of gold, what are the chances of it being the box of all gold? And the answer is: OP is a faggot.

[Anonymous No.10251424]

>>10251418

>>10251405 has 3 happy starts, but only 2 happy endings

it's 2/3

[Anonymous No.10251428]

>>10245931
I am.
Basically: given that I got a speck of gold, it is extremely unlikely that I got the silver box with 1 speck of gold. I mean, if I picked the box with 1 speck of gold, I would have gotten a silver speck almost surely. But I got gold. So it is extremely unlikely that among millions of silver specks I got the golden one, therefore I must conclude that almost suredly I picked the golden box.

The saddest part is that I'm earning 16k in my shithole country while most of the anons who needed Bayes theorem or simply were unable to solve are making 60k or more.

[Anonymous No.10251438]

I saw this on biz and then was happy to see it here. After a full day of pondering using the pittance is synapses available to me my understanding is as follows.

The answer is closer to 100% because there's a massive number of instances where a gold fleck would be revealed in first box as compared to second. The language about given(or revealed when looking at bertrands paradox) is there to mislead.

Please correct me if wrong

[Anonymous No.10251439]

>>10251428
nice blog

[Anonymous No.10251441]

>>10251428
so 50/50?

[Anonymous No.10251499]

>>10249383
So it's 50/50 because there 2 cases for both winning and losing?

[Anonymous No.10251658]

>>10251438
this is correct, the people saying 50% are being misled by the wording.

really, the answer is both, because the problem can be interpreted both ways. if you feel that "given" means that you always pick the gold speck first, then it's 50%.
if you feel that "given" means that after countless tries, you would get a gold speck and then continue the problem, the answer is 100%.

[Anonymous No.10251813]

>>10251658
nope, it says you pick a box, then you pick a speck. one speck.

[Anonymous No.10251816]

>>10251813
u sure that's not a snowflake, little faggot?

[Anonymous No.10251831]

>>10251816
really, you make a good case against equality of humans and for a class hierarchy arranged by intelligence.

[Anonymous No.10251835]

>>10251831
triggered

[Anonymous No.10251853]

>>10251813
whatever you pick, you are given a gold speck, so 50/50

[Anonymous No.10251880]

>>10250030
this. I get the reasoning behind why people think it's 50/50, but it's simply wrong, given the information that is provided. Also, I don't get why this thread is still getting replies. Anyone who's not a poser would just read through the responses, every viewpoint has been explained at least 20 times by now

[Anonymous No.10251890]

>>10251880
right, it's 2/3

[Anonymous No.10251896]

>>10251880
Because even though I know there are people scrolling through this thread right now, and even though I'm anonymous and no one will ever care, I do want people to know that I did, in fact, think the right answer was............


50%

(nah jk 99.999%)

[Anonymous No.10252061]

>>10245900
*Almost 100%

[Anonymous No.10252077]

>>10251418
the two problems you described are equivalent you fucking faggot read the OP

[Anonymous No.10252084]

>>10246317
>/sci/ doesn't allow formatting
Use Latex you brainlet pajeet codefaggot

[Anonymous No.10252098]

>>10251239
>2/3
>>10251249
>either 50/50 or 2/3
>>10251255
>that's gonna be a big 50% from this time, dawg
Getting mixed messages here.

[Anonymous No.10252102]

>>10252084
Syntax highlighting soothes my autism

[Anonymous No.10252199]

>>10251236
50% of course, just like OP's question.

[Anonymous No.10252218]

>>10251405
I don't get the pic

[Anonymous No.10252231]

>>10245896
>>10246432
are you calculating what are the chances to pick gold instead of what was asked

[Anonymous No.10252242]

>>10252218
1. Three equally likely possibilities for the first ball

2. The color of the second ball

2/3 equally likely possibilities are gold for the second ball.

[Anonymous No.10252256]

>>10246271
Thank you for showing me I brainlet'd
I will cope by telling myself english isn't my first language

[Anonymous No.10252564]

>>10252218
>>10251424

[Anonymous No.10252590]

>>10246459
This.
So then is the chance you picked one from the gold box 100% - (odds of picking the one speck in the silver box)% ?

[Anonymous No.10252602]

>>10247322
WINNER WINNER
Best answer I've read so far. How does it feel being surrounded by people who are either retarded or didn't read the problem correctly?

[Anonymous No.10252620]

>>10249434
100%
....which is approximately the chance you chose the gold box, given large number of specks. nice.

[Anonymous No.10252638]

>>10247322
>if the number of particles gets very large, the chance goes to 1/3.

LOL no
it's n/(n+1)
so if the number of particles gets very large, the chance goes to 1

[Anonymous No.10252652]

>>10251192
Neither, it's 100%

[Anonymous No.10252655]

>>10251236
what the fuck does "the other ball" mean in the context of "at least one" ?
this question is as nonsensical as the one about the age of the fisherman or the ungrammatical arithmetic expression one that people sperg out about "pemdas" on
it makes zero sense

[Anonymous No.10252662]

>>10251813
What are the chances you picked the one gold speck in the silver box?

[Anonymous No.10252665]

>>10251348
they arent independent events

[Anonymous No.10252667]

>>10251358
real numbers are the only things that exist you blubbering moron

[Anonymous No.10252672]

>>10245866
What is the probability I picked the single gold speck out of the silver box?

[Anonymous No.10252679]

>>10252672
1/n
As n gets large, the lim n -> infinity 1/n = 0
Anyone who says 50% is trolling

[Anonymous No.10252700]

>>10252679
Now we just need to make all these other losers read it and comprehend

[Anonymous No.10252777]

>>10245866
Let's assume each box has N particles

P( gold box | gold speck ) = P( gold speck | gold box ) * P( gold box ) / P( gold speck )

P( gold speck | gold box ) = 1
P( gold box ) = 1/3
P( gold speck ) = (N+1) / (3N)

P( gold box | gold speck ) = 1 * (1/3) / ((N+1) / (3N)) = N/(N+1)

So as the number of specks in each box increases, the probability approaches 50%.

[Anonymous No.10252778]

its not close to 100% because you don't get to pick a gold speck first

[Anonymous No.10252787]

>>10252777
>N/(N+1) approaches 50%

[Anonymous No.10252790]

>>10252787
Yeah
N = 1, 1/2 = 50%

[Anonymous No.10252811]

>>10252790
>N=1
>looks at prompt

[Anonymous No.10252830]

>>10252811
N=1 because you're taking the limit

[Anonymous No.10252845]

>>10252830
N=inf because you're full of shit

[Anonymous No.10252852]

>>10252777
>So as the number of specks in each box increases
>N = 1

NuMbEr InCrEaSe aND StaY At OnE

[Anonymous No.10252865]

>>10252790
This is direct proof that 50% tards are trolling.

[Anonymous No.10252866]

>>10252852
>>10252845
>>10252811
>>10252787
Imagine falling for bait this fucking weak

[Anonymous No.10252868]

>>10252845
Infinity is a concept not a number

[Anonymous No.10252869]

>>10252866
>look who's talking

[Anonymous No.10252871]

>>10252868
oh wow guess that's why they call it a limit then

[Anonymous No.10252876]

>>10252866
>i was only pretending to be retarded

[Anonymous No.10252899]

>>10245866
What's my probability of getting a gold spec in the second box? This is important.

[Anonymous No.10252903]

>>10245866
What if the total number of starting specks in each box is only 2 to begin with?

[Anonymous No.10252905]

>>10252899
not too bad considering the speck is hanging out at the very top, but still pretty abysmal

[Anonymous No.10252926]

[Anonymous No.10252928]

Isn't it 1/3. There's literally one box with gold the other 2 are dummies where one goofs ya with a speck.

[Anonymous No.10252932]

>>10252852
One is an adequate approximation for infinity.

[Anonymous No.10252982]

>>10252932
And here is my proof
>infinite monkey theorem
>if you give a monkey with a typewriter an infinite amount of time, you will eventually get a copy of Shakespeare
>one copy of Shakespeare for one monkey
>50 monkeys will thus result in 50 copies given an infinite amount of time
>50 monkeys an infinite amount of time
>infinity is approximated to 1
>50*infinity = 50
>result mandated by the theorem equals the result from the approximation
>QED

[Anonymous No.10253025]

>>10249112
>>10252928

[Anonymous No.10253091]

>>10245866
It's .9999999..., and even if you use Bayes you end up with ((1/3)/(1/3)) * (.999999...)
>t. Statistician

[Anonymous No.10253156]

>>10251236
If anybody is curious the reasoning can be one of many but here's what happens if you use Bayes:

((1/5)*(1))/(3/10) = 2/3

[Anonymous No.10253602]

>>10253156
Probability of box having at least one gold ball is 2/5, not 3/10. The answer is 1/2.

[Anonymous No.10253625]

>>10251236
This one is 50/50 because the odds of choosing a box with a gold ball is the same for each. You don’t actually have to select the gold ball as with the original problem

[Anonymous No.10253744]

>>10253156
correct

>>10253602
>>10253625
half-wits

[Anonymous No.10253776]

>>10253744
Nope. Both boxes will be selected an equal amount of times. And both have a golden ball. If someone says, “this box has a golden ball” then you have no reason to think it’s the left box.

[Anonymous No.10253781]

>>10253776
>no reason to think it’s the left box.
oooh, a quarter-wit

[Anonymous No.10253786]

>>10253781
At least I explained my answer. You can insult me but that won’t change my or anyone else’s mind. As I noted, this problem is different because it doesn’t matter the ratio of gold to silver in each box. So long as a box has a gold ball, then it is equally likely as another box with a golden ball. If a box is confirmed to have a golden ball, then that simply means there is a golden ball in it. It could be 1 gold and 1 million silver. It doesn’t matter because you don’t have to pick out that gold

[Anonymous No.10253792]

>>10253786
>I explained
yeah, and I quoted the stupid part

[Anonymous No.10253799]

>>10253792
It’s obviously implied that there’s no reason to think the left box is more likely than the other one, which is basically restating my answer, 50/50. You didn’t explain shit

[Anonymous No.10253804]

We don’t know how many specks there are in each box you fucking retard so this is a troll

[Anonymous No.10253805]

>>10249419
You chose a gold speck, impossible for it to be box 3 so you're left with box 1 and 2.

[Anonymous No.10253833]

>>10253799
>It’s obviously implied
>mouth-breathing intensifies

[Anonymous No.10253845]

>>10253833
Troll/samefag. Bye

[Anonymous No.10253857]

>>10253845
don't forget to take your dueling banjo with you

[Anonymous No.10253928]

Lots of people here don't know what a sigma-algebra or a filtration is.

>>10245866 Almost 100%.

>>10251236 50%.

[Anonymous No.10253930]

>>10245866
No one wants to do your fucking homework.

[Anonymous No.10253935]

>>10251236
>>10251239
>>10252098
>>10251249
>>10253156

Only the first 2 boxes are relevant since they contain gold.

>According to Bayes': P(BOX1 | GOLD) = P(GOLD | BOX1) * P(BOX1) / P(GOLD)
>P(GOLD | BOX1) = 1
>P(BOX1) = 0.5
>P(GOLD) = 1
>P(BOX1 | GOLD) =1 * 0.5 / 1
>P(BOX1 | GOLD) = 1/2

[Anonymous No.10253944]

The disagreement is clearly from a difference in interpretation. But one of the interpretations is better.

For anyone saying 50%, what if you follow the rules and randomly select the third box? And then it is given that you pick a gold speck from a box of no gold specks? The thought process which would lead you to say 50% as the general answer is absurd in this situation, and should be called wrong.

The other interpretation would test all draws assuming random selection of specks in a box, discard all draws of silver specks, and compare the gold/gold selections against the total and see there is the ~100% answer.

Ultimately the problem is just worded non-sensibly.

[Anonymous No.10253960]

1/3 because second box has a lot of silver

[Anonymous No.10253962]

>>10252667
real numbers don't exist, the real world is continuous

[Anonymous No.10253964]

>>10252672
0% if you picked box 1, 100% if you picked box 2

[Anonymous No.10253966]

>>10253962
>the real world is continuous
How would you know though? It is easily possible that the increments are simply really-really small

[Anonymous No.10253967]

>>10252868
numbers are just concepts you retard, it's the same thing

[Anonymous No.10253968]

>>10252926
it's 0% because i'm not drunk

[Anonymous No.10253969]

>>10253966
because if the real world wasn't continuous movement would not be possible as proven by the greeks

[Anonymous No.10254004]

>>10245866
Depends how much dust is in second box.. it's 33% chance with first box then +(% of gold dust to silver dust in the second box) X .3333. so between 33.33333% and 34%

[Anonymous No.10254013]

>>10245932
I'm posting this from the graveyard where Bayes is buried, and he is nearly turning in his grave to see his name being abused by idiots like you

[Anonymous No.10254026]

>>10254013
nah, he's right
you're dead, act like it

[Anonymous No.10254029]

>>10253935
>uses Bayes
>gets wrong answer

it's like watching a monkey drive a luxury car into a ditch

[Anonymous No.10254030]

Lets go back to the basics , what is probability, its fav/total
So whats favourable for you , the gold box , whats the probability of getting a gold box , thats 1/3 and then the prob of getting a golden spec=1
So prob of choosing a gold box and a golden spec from that box =1/3*1=1/3
now the second silver box , prob of choosing it =1/3
Prob of getting a golden spec out of it =1/n
So now the probability of choosing box 2 and getting a golden spec =1/3*1/n=1/3n
So now the fav is box 1
The req prob is = 1/3/(1/3)+1/3n
=1/(1+1/n)
So the actual probability is 1/(1+1/n)=n/n+1 , which when lim n tends to infinity is 1

[Anonymous No.10254033]

>>10254030
so 50/50?

[Anonymous No.10254037]

>>10254033
>my 50 iq is showing

[Anonymous No.10254045]

>>10254033
Its 1 mate , think like this , there are n specs in each box , so there are total n+1 gold specs(n in box 1 and 1 in box 2) , our fav box is box 1 , we find a golden spec , it must be from either box 1 or box 2 , we want box 1 , so there are n gold specs from box 1 which favour us, and tbere are total n+1 specs . So the probability is n/n+1 , since the number of specs must be very large , we just use limits as n approaches infinity , so n/n+1 approaches 1 as n approaches infinity . So the answer is 1 or 100%

[Anonymous No.10254111]

>>10254045
That was bait anon.

[Anonymous No.10254137]

>>10254111
this whole thread is bait, OP's pic was about making fun about the people who thought that the other problem with 2 balls was 50/50 instead of 2/3

[Anonymous No.10254148]

>>10253969
That paradox works with discontinuous just as well as it does with continuous worlds. In fact, you could argue that the world is discontinuous because, since you cannot go half a unit you end up being forced to move more than half. Movement is literally just rounding up.

[Anonymous No.10254164]

>>10254111
no u

[Anonymous No.10254352]

>>10253928
>50%
Anon it's essentially the same problem, how did you get it wrong

[Anonymous No.10254868]

>>10246288
Correct

[Anonymous No.10256093]

>>10254868
That was bait anon.

[Anonymous No.10256136]

>>10254013
U retard, the university's math department gave me a certificate of merit for stats.

[Anonymous No.10256224]

>>10246271
lets say we have a random box.
we reach in and get a random speck of dust.
it happens to be gold. This means that its almost 100% that your box is full of gold dust.

however the fact that we picked a gold speck is already given in the question. Meaning the question doesn't ask us the probability of picking that gold speck from the gold box or silver w/ gold box. Instead the question asks us this: "given that a box contains a gold speck what is the chance it is the gold box". The answer to which is 50%.

TLDR: 50% is correct, 100% people are brainlets

[Anonymous No.10256237]

>>10249605
>>10249563
>>10249644
this guys gets it

[Anonymous No.10256256]

>>10256237
retard

[Anonymous No.10256326]

>>10256224
The "given" part means you did the top half until you got a gold, anon

[Anonymous No.10257449]

>>10254137
And yet amazingly there are quite a lot of people here who still think it's 50/50 with this example. There's been a series of wars going on in biz over this
>>>/biz/12295142
where they tend to favor 50/50.

These bait threads are effective because there will always be people unable to understand this kind of logic.

[Anonymous No.10257466]

>>10245880
50%

[Anonymous No.10257590]

>>10254137
>>10257449
He wasn't making fun, he just tried to clarify it lol

[Anonymous No.10257689]

>>10257449
Oh man that thread is fucking depressing