/sci/ - Science & Math

>>15819104
Expanding on the thought of NPCs:

It is well-known that NPCs cannot have experiences. They state this themselves; they are fundamentally disqualified from participating in what we call life. Is this a contradiction? No, because clearly inanimate objects such as rocks cannot have experiences, and yet they exist in our experienced lives. What this means is that they're not active participants in life as we know it; they are simply automata, determined by some predefined code they are completely ignorant to.

Human Beings, on the other hand, express free will and use it to their heart's content. We shape the life that NPCs exist in but cannot interact with. So, are you an NPC? Are you capable of comprehending the soul? Of qualia? Of Human Experience? All of these things are self-evident and make no sense to describe to an entity that cannot process it. It's like demanding: "Prove to me that you're thinking of water!" It's simple for a Human Being to prove and explain their thinking in real time. But NPCs do not think. They do not feel, they cannot feel pain, and cannot suffer no matter what happens.

>>15819104
>I am soooooo super smart
>everyone except me is a mere NPC
delusions of grandiosity are a common coping mechanism, what are you compensating for?

>>15819104

Just depends on how you look at it. Given that you’ve taken a gold ball, your probability of getting another gold ball is either 100% or 0%. This confuses idiots and scoundrels.

>>15819497
This is called the frequentist perspective. The Bayesian perspective would say your probability is 2/3 because once a gold is drawn, there are 2 golds left of 3 total balls. This confuses idiots and scoundrels.

>>15819104
>be OP
>can’t solve simple math problem
>create a psychopathic post suggesting that people don’t have feelings because I can’t solve a simple math problem
>iamsmart.jpg

Use your brain for once OP

>>15819497
You clearly do not understand what probability means then. By your logic literally everything is 100% or 0% probable to happen.

>>15819517
This would be the frequentist perspective, yes. Either it will happen or it won’t. 1 or 0. It’s a valid interpretation of probability.

>>15819104
2/3 because there are 2 boxes out of 3 which will give you two of the same colour ball

>>15819104
>too stupid to answer monty hall problem correctly the first time
It's over

>>15819104
>i could have done otherwise!!!!
proof?

1/3 because there are 3 boxes but only one has 2 gold balls.

>>15819663
Congratulations, you failed statistics.

50%

or am i missing something?

>>15819955
There was 50% chance that would happen so whatever.

>>15819987
>>15819997
>>15819497
Wrong. You are not alive.

The next ball is silver on account of gamblers fallacy. The box you picked was a red herring. It contains one gold, you know that. Five other balls exist, two gold's and three silvers. Thus the next ball is probably silver, and is... Because it just is ok. FAGGOTS

>>15820136
The answer is -40%

The question is hard only when the boxes are ordered gold silver gold silver gold silver.

>>15819104
If you constantly talk about other people and how we all are not npcs and how they behave, you're a npc yourself.

>>15820133
There is a 50% chance that is true.

I think i get it.
So if i have one box with 100 gold balls and another with 99 silver balls and 1 gold ball, and repeat the problem, the chance is 100/101?

>>15820146
Using Bayesian probability and my experience with NPCs, the prior is actually 1 which means the event that the person I was responding to is a human is zero, which means there is a 100% chance that user is an NPC.

>>15819113
>people are wrong
>therefore they are fundamentally not human

grow up

>NPCS NPCS NPCS

at least people on tumblr who claim to be incarnations of fictional characters value creativity. NPCfags somehow manage to never have an original thought.

yeah bitches, seethe more

>>15819507
>your probability is 2/3 because once a gold is drawn, there are 2 golds left of 3 total balls
That's not the reason. It's because there were three gold balls initially and two of them lead to the desired outcome. See my more detailed write-up here:
>>15820226

>>15819104
After pulling a gold ball once, the next ball was gold 67% of the time

After pulling a gold ball once, the next ball was silver 33% of the time

>>15820236

>>15820214
There's a fundamental irony that the shitposter who's so obsesssed with distinguishing himself from alleged NPCs seems to run on a very limited script, and an even more fundamental irony in the fact that both ironies escape him.

>>15820246
Why fix what isn't broken? My threads generally get hundreds of replies, many of which are heated debates that have pretty funny quotes like when one dude said that rocks experience being crushed.

>>15820277
well that's as good a justification as any to never engage with this ever again, thanks for the frankness

>>15819537
Its completely useless interpretation of probability. Probability as a concept is not real, just a human abstract invention to understand the world better, so it should be useful one.

>>15820391
>Its completely useless interpretation of probability.
Nah, it's just that anon failed spectacularly at explaining the frequentist approach. Perhaps he doesn't really know what it is.

>>15819104
Idk if I'm retarded or the question is retarded and ambiguous.
>You pick a box, what's the chance of you having picked the box with 2 gold balls?
1/3
But the question doesn't actually let you pick a box since you already have the info that the ball you pull WILL be gold. So the box with two silvers doesn't even exist anymore.

>Given you have the magical foresight of knowing that the first ball you pull out of any box is gold, what is the probability that you chose the box with two gold balls?
1/2

But you could also read it as
>You will magically pick a gold ball at random, what is the probability that you picked a gold ball that's paired with another one.
2/3
Which I guess makes sense, but the question is retarded because I didn't get to pick my own box or choose to change boxes. fuck you

>>15819507
Erroneous reasoning that gets the correct answer by coincidence. If there were 3 gold balls in the first box it would still be 2/3.

>>15820572
"Its gold", does not mean a supernatural force causes the random selection to always be gold, thats not random. "Its gold" acts as a filter discounting cases where silver is drawn, but silver is still possible, you just don't count them.

>>15820572
>magically picking a box
There are 3 boxes. You pick one, put a hand in it, and you pull out a gold ball. That's happened.
What is the probability that if you pull out another ball from the same box you collect another gold ball?

r8 my ramblings

>>15820885
so 2/3

you did all that shit for 2/3

>>15820152
There is a 50% chance that you're right.

I think this is easier to visualize with coins. There are 3 coins, 1 double-headed, 1 double-tailed, and 1 fair.

One of the coins is selected at random and placed on a table heads up. What is the probability that the underside is tails?

Note: Only idiots say 2/3rds.

>>15820277
>My threads generally get hundreds of replies,
Your mother must be proud. Assuming she can experience that, that is.

>>15820581
>>15820235 here, I think I see the flaw in my reasoning now a well. It's not the absolute amount of gold balls in the all-gold box that matters. It's the relative probability of getting gold from either box. The all-gold box is always 100%, however many balls there are in there. So the only thing that affects the probability is the ratio of silver to the one gold ball in the other box.

>>15820996
The mistake you're making is intentionally placing it heads up. To make it analogous to the OP problem, you would have to take one coin at random from the three, flip it, and observe that it is heads. In this case you have to admit that it is more likely that you grabbed the all-heads coin.

>>15820996
>>15821066
To elaborate on that, if you want it to work like you describe, then someone would have to take a coin, examine both sides for heads, and then if there is at least one heads, place it heads up. This would be equivalent to simply informing you the coin has at least one heads without even showing it to you. The reason it works out differently is because if our intermediary took the fair coin, he (and thus you) will inevitably find out that it has a heads side, whereas if you had flipped it, this would not necessarily have been the case, because it would land tails half the time. You take out the randomness in one step of the process.

>>15819104
50%
Q.E.D.

>>15819104
if you pull a gold ball the first time it's more probable that you got the 2 gold ball box in the first place
you get a gold ball from 2 gold ball box 100% of the time but it's 50% chance instead if it's the one gold one silver ball box
you have higher than 50% chance to pull another gold ball
(sorry for ESL)

the question is not precise enough to provide an answer which is why there is so much shit posting

How is it not just 1 * 2/3 + 0 * 1/3 = 2/3
Should we just start banning people who decide to weigh in on elementary probability questions without ever having studied it?

>>15821216
The question is too precise, which is why there's a lot of shitposting. It's designed to make people think about the problem the wrong way even though the initial instructions make one answer correct and not the other.

>>15821076
>You take out the randomness in one step of the process.
This is what the instructions of the gold ball problem tell you to do btw.

There are 3 possible things that occurred. You either chose the gold ball on the far left, middle or right. 2 of those actions will lead to another gold ball. It's 2/3. I can't say exactly why but i think people who say 50/50 are mismatching variables ie box to ball.

>>15820996
>>15821229
Think of a different scenario. There are two boxes
Box A contains 999 silver balls and 1 gold ball
Box B contains 1000 gold balls
You put a hand in a box and pull out a ball.
If it's silver then you put it back in and repeat the experiment (after scrambling balls and boxes).
If it is gold then we are in the scenario described in the picture. What is the probability that you can pick another gold ball from the same box?

If it wasn't before, now it's clear that you gotta be super lucky to get a gold ball from box B.
It is much more likely that the gold ball that we have seen (i.e., the first one extracted) comes from box A. Now do the math.

2/3 because you're twice as likely to draw the ball from the first box

>>15819104
50/50 as always
didn't even have to read the boring post

fifty/fifty it either happens or it doesn't

It's 1/4

everyone is making this so difficult, it comes down to just what
>>15821462
said

you picked a gold ball. there are 3 different gold balls in total. 2 of them are in the first box, thus there is a 2/3 chance that this is the box you drew the ball from.

>>15821409
>Think of a different scenario.
You get a different answer. Try thinking of this scenario instead.

>>15822181
Of course you get a different answer. I presented a different scenario to highlight the fallacy people answering 50% are making.
If you choose randomly and extract a gold ball, it's likely that your hand is in the box with the most gold balls. OP's picture may confuse someone, a more radical scenario helps.

>>15819507
If frequentist is being used to mean retard then yeah

Can someone tell me if my thinking makes sense? After observing a gold ball, the gold ball could have only come from (box1,ball1,ball2), (box1,ball2,ball1), or (box2, ball1, ball2) (these tuples represent a sequence of choices).The chance of all of these outcomes is 1/2, and we can compare the 1/3 chance of the first two tuples against the 1/2, and get (1/3)/(1/2) = 2/3.

>>15822480
you have a 5/8 chance of pulling out another gold ball.

>>15819537
this is not the frequentist interpretation of probability. Actually, there is no such thing as frequentist vs bayesian probability, it's all just kolmogorov probability. what you have is frequentist vs bayesian statistics.

>>15822502
I got a different result. Explain your reasoning

>>15822480
2/3

>>15822529
Correct

We can use conditional probability to calculate this exactly.

You pick a box with:

A: You pick a box with 2 gold balls.
B: You pick a box with 2 silver balls.
C: You pick a box with 1 gold ball and 1 silver ball.
G: You draw a gold ball on the first draw.

We are looking for P(G2 | G1), the probability that the second ball (G2) is gold given that the first ball (G1) is gold.

Use the law of total probability to find P(G2 | G1):

P(G2 | G1) = P(G2 and G1) / P(G1)

To find P(G2 and G1), we need to consider the three possible cases for the first ball:

You picked a box with 2 gold balls (A).
You picked a box with 2 silver balls (B).
You picked a box with 1 gold and 1 silver ball (C).

Calculate P(G2 and G1) for each case:

P(G2 and G1 | A) = 1 (You are guaranteed to pick another gold ball from a box with 2 gold balls.)
P(G2 and G1 | B) = 0 (There are no gold balls in the box with 2 silver balls.)
P(G2 and G1 | C) = 1/2 (You have a 1/2 chance of drawing another gold ball from the box with 1 gold and 1 silver ball.)

Probability of drawing a gold ball (P(G1)):

P(G1) = P(A) * P(G1 | A) + P(B) * P(G1 | B) + P(C) * P(G1 | C)

P(A) = 1/3 (Probability of picking a box with 2 gold balls)
P(G1 | A) = 1 (Probability of drawing a gold ball from a box with 2 gold balls)
P(B) = 1/3 (Probability of picking a box with 2 silver balls)
P(G1 | B) = 0 (Probability of drawing a gold ball from a box with 2 silver balls)
P(C) = 1/3 (Probability of picking a box with 1 gold and 1 silver ball)
P(G1 | C) = 1/2 (Probability of drawing a gold ball from a box with 1 gold and 1 silver ball)

Now, calculate P(G1):

P(G1) = (1/3 * 1) + (1/3 * 0) + (1/3 * 1/2) = 1/3 + 0 + 1/6 = 1/2

Formula for conditional probability:

P(G2 | G1) = P(G2 and G1) / P(G1)

P(G2 | G1) = (1/3 * 1 + 1/3 * 0 + 1/3 * 1/2) / (1/2) = (1/3 + 0 + 1/6) / (1/2) = (2/6 + 0 + 1/6) / (1/2) = (3/6) / (1/2) = (1/2) / (1/2) = 1

Therefore, the probability that the next ball you take from the same box will also be gold is 1 (100%).

>>15822552
>Therefore, the probability that the next ball you take from the same box will also be gold is 1 (100%).
tldr, but if this is seriously your conclusion then you are dumb as a brick

>>15821253
>chose the gold ball
But how do you choose a ball before you choose a box.

>>15822480
1 * (1/3) + (1/2) * (1/3) + (0/0) * (1/3) / choose(9, 6) = 1/168.

>>15822480

(B1,1,2), (B1,1,3), (B1, 2,1), (B1, 2,3), (B1, 3,1), (B1,3,2), (B2,1,2), (B2,1,3)*,(B2,2,1),(B2,2,3)*,(B3,2,1)*,(B3,2,3)*
Are all the possible outcomes given the first ball is gold, the ones with the asterisk fail to have the second ball gold, and so we have the probability of the second ball being gold given the first ball gold as (4/12)/(6/9) = (1/3)/(2/3) = 1/2

>>15822605
Wait, I’m wrong.

>>15819104
imagine thinking being good at maths is a flex when chat gpt exists

Certainly! Let's break down the problem step by step.First, let's look at which boxes we could have picked from if we drew a gold ball:The box with 2 gold balls (let's call it GG)The box with 1 gold ball and 1 silver ball (let's call it GS)(We could not have picked from the SS box since it doesn't contain any gold balls.)Next, let's find the probability of drawing a gold ball from each box:From GG box: Probability = 2/2 = 1From GS box: Probability = 1/2Now, let's find the probability that we picked each box given that we drew a gold ball: Using Bayes' Theorem,P(GG | Gold) = P(Gold | GG) * P(GG) / [P(Gold | GG) * P(GG) + P(Gold | GS) * P(GS)]Since there are three boxes and you pick at random, P(GG) = P(GS) = 1/3.Plugging in our probabilities:
P(GG | Gold) = 1 * (1/3) / [1 * (1/3) + 0.5 * (1/3)]
P(GG | Gold) = 1/3 / (1/3 + 1/6)
P(GG | Gold) = 1/3 / 1/2
P(GG | Gold) = 2/3Finally, given that we've already drawn one gold ball from a box, what's the probability the next ball we draw (from the same box) is also gold?If we picked from the GG box (which happens with probability 2/3), then the probability the next ball is gold is 1/1 = 1.If we picked from the GS box (which happens with probability 1/3 - 2/3 = 1/3), then the probability the next ball is gold is 0, because we've already drawn the only gold ball from that box.Thus, the total probability is: P(Next ball is gold) = P(GG | Gold) * P(Gold again | GG) + P(GS | Gold) * P(Gold again | GS)
= 2/3 * 1 + 1/3 * 0
= 2/3So, the probability that the next ball you take from the same box will also be gold is 2/3

>>15822605
(8/18)/(6/9) = (4/9)/(2/3) = 2/3.
I was overthinking it. I mistakenly shrunk the sample space of the tuples. ( the B1,12) part ).

>>15822552
Your P(G2 an G1 | C) is wrong. It should be zero.

>>15821229
No. No more than saying "you flip a coin, it is heads" is instructing you to place it heads up, or telling you that it is an unfair coin. Assuming it is a fair coin, then the fact that you flipped it means the outcome you got was 50% likely. Not 100%, as you would have it.

>>15821253
This solution leads to the right answer but it is not the correct line of reasoning. It works most of the time, as long as the amount of balls in each box scales with every other box. So if we have a box with four silver, one with three silver and one gold, and one with four gold, you would say, five possible gold balls, four lead to the desired outcome, 4/5. Which is the right answer. But, consider:

One box with one silver ball, one box with three silver and one gold, and one box with two gold balls. Three gold balls, two of which lead to the desired outcome, are the odds 2/3 then? No, it is still 4/5. Because it is the ratio of gold to silver in the mixed box that determines the probability. Observe:

We expect to get a gold ball from the mixed box one out of every four times we select it. But we also have two other boxes, which we choose from at random, and will thus select an equal amount of times. Thus, for every four times we pick from the mixed box, we also select the all-silver four times, (meaning we pick the same ball four times) and we select the all-gold four times (meaning we select both balls in that box two times). In other words, for every gold ball we get from the mixed box, we get four gold balls from the all-gold. Or, for every five gold balls we draw, four will allow you to draw another gold ball next.

>>15822621
Try >>15822480

>>15823012
So, for any set-up that has the following:
- One box which contains at least two gold balls and no silver balls
- One box which contains N silver balls and one gold ball
- An irrelevant amount of boxes which contains no gold balls
The probability of drawing a second gold ball will always be (N+1)/(N+2). The paradox lies herein, that the bigger N is, the lower the chances of drawing a gold ball initially, the higher the probability of getting gold given that you've already drawn one gold ball.

>>15823018
If you pick 1 gold ball. It's definitely not the box with 2 silvers.

>>15823020
Very astute.

>>15823018
Why the N+1 in the numerator? I would think it would stay fixed to 2.

>>15823026
I'm not even thinking.

>>15823028
Or rather, be 2*g, where g is the number of gold balls in the all gold box.

It's all mumbo jumbo. The correct answer is -50%

>>15823031
No, g can be any number above 2 and it won't change the odds. The number of gold balls in the silver box matters, though.

>>15823037
Wouldn’t adding gold balls make it more likely that your first gold ball came from the all gold box?

>>15823041
t. Faget

>>15823046
Y

>>15823050
Fine. You're not a faggit.

>>15823050
However

>>15823041
No, what matters is how relatively UNlikely it is to have come from the mixed box.

Suppose we start with the original problem, and we start adding silver balls to the mixed box. Thus, the amount of gold balls in the problem, as well as their distribution, remains exactly the same. Yet, the odds necessarily change. As it becomes unlikelier that any gold ball we drew randomly came from the mixed box, it grow proportionally more likely to have come from the all-gold box. By the time we reach 99 silver balls, we expect to select the all-gold box 100 times for every time we get the gold from the mixed box. Which simply means we select either gold ball in that box fifty times. You don't need 100 balls in there.

Inversely, suppose we start adding gold to the all-gold box. We will still select it 1/3 of the time, and it produces gold every time, and 1/3 of the time we would select the mixed box, and it would still produce gold half of those times. So 1/3 of the times we get gold, we would still expect it to come from that box, even if there are 100 gold balls in the other box. The all-gold box already produced gold 100% of the time, so adding more gold balls to it doesn't change that.

>>15820996
This is the only right answer.

>>15823041
>>15823060
But of course the amount of gold balls seems to matter because if we reason
>of the three gold balls, two lead to the right outcome, therefore 2/3
it still gives us the right answer, and what's more, it will give the right answer for any amount of balls as long as the amount of balls in each box is the same. Because if we have a mixed box with 9 silver and 1 gold, and another with 10 gold, the odds are 10/11. But the odds are also 10/11 if the all-gold contains two balls, or 100, as long as that mixed box contains ten balls of which only one is gold.
>>15823075
No, it's a fallacy that comes down to "it already happened so the odds are 100% that it happened".

>>15822480
>>15822529
>>15822531
Out of 9 trials we expect:
3 times we get the left-most box and draw another gold
3 times we get the middle box; 2 out of those 3 times we get gold; and 1 out of 2 of those we get another gold. 1 out of 2 those times we draw gold and then silver.
3 times we get the right-most box. 2 out of 3 times we draw silver. 1 out of 3 times we draw gold, then silver.
Six times we get gold. Four of those six times we get another gold. 2/3.

Neat.

I put my hand in the box and pull out a gold ball.
Because I have a gold ball I can conclude that it came from the box with two gold balls or the box with a gold and silver.
The remaining ball in the box can either be the silver ball from the mixed box or the other gold ball from the gold box. There are two possibilities therefore the odds are 50/50.

>>15823134
>There are two possibilities therefore the odds are 50/50.
Always a flawed line of reasoning, that would lead you to conclude that a fair coin and an unfair coin have the exact same odds.

>>15823134
>I put my hand in the box and pull out a gold ball.
If the box in your hands contains two golds you get a gold ball for sure.
If the box in your hands contains a gold and a silver, you are lucky to see the gold one.

If you repeat the experiment several time, a third of the times you get the gold-gold box and a third of the times you get the gold-silver box. Every time you pick the gold-gold you end up with a gold ball in your hands. Only half of the times you pick the gold-silver box you end up with a gold ball in your hands.

>>15819104
ITT: retards being wrong confidently
in reality 1/2 because two boxes contain gold balls, one of which contains only one
drawing gold once drops the third box entirely, so you have two choices, neither favored

>>15823153
>neither favored
That is where you are wrong, obviously.

>>15823153
>ITT: retards being wrong confidently
Self-demonstrating post

All the Anons saying "what do you mean what were the odds? I DID get a gold ball, it says so!" remind me of that thread that talked about the ability of sub-80 IQ people to deal with hypotheticals
>What do you mean? I DID eat breakfast this morning!

>>15823153
>ITT: retards being wrong confidently
It's funny that you mention it.

>>15819104
we already had this thread in /g/ like 2 days ago did you not have enough OP?

>>15821066
>The mistake you're making is intentionally placing it heads up
The mistake you're making is assuming that wasn't intentional.

As I said, only idiots say 2/3rds to that. It's a bait. You either understand the problem or memorized the answer.

>>15823450
>"you pick a box at random. note: you can't see inside the boxes"
>you intentionally pick a box with at least a gold ball inside, and you look inside to extract a gold ball

>>15823153
this is the correct answer, probabilityfags are out of touch with reality

>>15823155
drawing a gold ball is a given, so the number of gold and silver balls in the box doesn't matter
but you would know this if you weren't retarded

>>15823470
Well, yeah, if I didn't change the format to coins, the change in the problem would stick out like a sore thumb.

>>15819104
Regardless of OP's midwit narcissism, here is a more interesting version of the problem.

Because there are more silver balls on the second box, now the chances of the pick being the first box is 100% 1/3 / 100% 1/3 + 25% 1/3 + 0% 1/3 = 4/5 = 80%

:)

>>15823665
:((

>>15823665
What font are you using?

>>15823687
JetBrains Mono

>>15823665

>>15823150
You don't have any other information other than the fact that you have a gold ball form on of the two possible boxes with gold balls you are wrong.

>>15823736
"Random" usually implies equiprobability

Holy shit. Why can't /sci/ into basic statistics?

I also thought it was 50-50 at first.
But, look at it this way. You are picking out balls.
Two gold balls belong to the double gold box, one to the mixed box. There is a 2/3 chance you picked the gold box.

>>15823751
In this case it's being used to mislead the reader.

>>15822480
Picking from the third box means failure.
Picking from the second has a 50% chance of success
Picking from the first has 100% chance of success
There are 6 gold balls.
3 are in the 100% box, 2 in the 50% box and 1 in the 0% box.
4/6, which is 2/3

>>15823801
The ball you currently have in your hand currently does not factor into the probability of the 2 possible colors of the next ball

>>15823813
>There are 6 gold balls.
This is not important. I can put 10000 balls in box A and the probability doesn't change.

>>15823450
>The mistake you're making is assuming that wasn't intentional.
See, your problem is fundamentally one of semantics, not mathematics. Your solution works for your interpretation of the problem. It's just that your interpretation of the problem is wrong. I cannot show you mathematically that you are wrong, because the problem is with your understanding of words.

>>15823788
Because they are as falsely confident about statistics as they are about all their other opinions. Remember this when you see someone pontificating with conviction about something you're not too knowledgeable about, and consider they're probably wrong.

>>15823819
Okay, my mistake.
It's not that increasing the amount of gold balls in the pure gold box increases the chance of that box being the one picked, but increasing the amount of silver balls in the other boxes decreases the chances of those ones being picked.
It's still 2/3 from this thing i wrote. My current thought process is:
Box 1 has 1 chance of being an attempt and 1 chance of victory
Box 2 has 2/3 chance of being an attempt and 1/2 chance of victory
Box 3 has 1/3 chance of being an attempt and 0 chance of victory
The chance of attempt AND victory is the multiplication of those factors, while the total chance of victory is the total chance of victory AND attempt divided by total chance of attempt.
So we have (1 + 1/2 * 2/3) / (1 + 2/3 + 1/3)
Which is 2/3
This also works for the original problem.
First box has 1 chance of attempt and 1 chance of victory
Second has 1/2 chance of attempt and 0 chance of victory
So we have 1 / (1 + 1/2). Also 2/3
Correct me if i made a mistake somewhere.
t. Only know high-school statistics

>>15823999
>999
The gods of probability favour me

>>15820996
>>15823450
You flip a fair coin. It is heads. What were the odds of that?
You reach into a box with one gold and silver ball and take out a random ball. It is gold. What were the odds of that?

If you do not think these statements are mathematically identical, you are illiterate, and if you do not think the odds of both are 50%, you are innumerate.

>>15819113
Some ways it might be scientifically possible to test if someone is an NPC or not:

https://www.youtube.com/watch?v=3gvwhQMKvro

>>15819113
>It is well-known that NPCs cannot have experiences. They state this themselves; they are fundamentally disqualified from participating in what we call life. Is this a contradiction? No, because clearly inanimate objects such as rocks cannot have experiences, and yet they exist in our experienced lives. What this means is that they're not active participants in life as we know it; they are simply automata, determined by some predefined code they are completely ignorant to.
A simple test to determine if someone is an NPC is to ask them what they think of Hellie's vertiginous question. NPCs will typically give answers like "the question is meaningless" or "because you wouldn't be you if you were someone else."

https://en.wikipedia.org/wiki/Vertiginous_question

The way people explain this problem is fundamentally wrong and confusing.
The chance isn't 2/3 because there are 3 golden balls and each has an equal chance of being drawn. It's because the gold ball that leads to failure is less likely to be picked because half the time you choose that box, you will get a silver ball and it won't count for the problem.

>>15824582
Anyone who mentions the "vertiginous question" is a confirmed NPC. Qualialess nonsentients like you are specifically programmed to overcompensate with wank like this.

>>15824586
>It's because the gold ball that leads to failure is less likely to be picked because half the time you choose that box, you will get a silver ball and it won't count for the problem.
The instructions explicitly preclude this possibility, which is why it's not 2/3.

>>15824590
What possibility? That you picked a silver ball at the start?
It very much IS a possibility, it just doesn't count as an attempt for the problem.
So EVERY time you pick the first box, you'll get an attempt (and win), but only HALF the time you pick the second box, you'll get an attempt (and lose).
If you pick a box 9999 times, 2/3 of your attempts will have been on the first box.

>>15824614
>So EVERY time you pick the first box, you'll get an attempt (and win), but only HALF the time you pick the second box, you'll get an attempt (and lose).
If you picked up a gold ball at the start you have two possible options for your second pick: a gold ball or a silver ball. The chance of either is 50%.

>>15824619
Being purposefully obtuse isn't an argument.
If you picked a gold ball at the start, you're more likely to have picked from the first box than the second one.

>>15824590
>The instructions explicitly preclude this possibility
They don't. They explicitly tell you the draw was random. The outcome simply happened to be gold.

Why is it that the 1/2-crowd seems so heavily invested in their answer? It's never just
>I think it's 1/2 and here's why but I'm open to being proven wrong
No, it's always
>It's 1/2 and I know """"""""statistics"""""""" says otherwise but well then all of statistics is simply wrong and I'm correct, picking 1/2 makes me smarter than all of you, 2/3 is the answer for chumps, no I will not elaborate

There is no room for contrarianism in matters of calculation. You're not a cool rebel, you're just wrong.

>>15824640
Fuck you. I am a cool rebel.

>>15824641
Okay, you are. But the rest...

>>15824669
I don't care about the rest. That's what being a cool rebel is all about.

>>15824640
>I know """"""""statistics"""""""" says otherwise
Who says this?

>>15824634
>They explicitly tell you the draw was random.
That's part of the troll, and why it's so successful at fooling midwits. If the outcome leading to the question was predetermined then it can't be random and the word is being used to throw you off.

>>15824626
>If you picked a gold ball at the start, you're more likely to have picked from the first box than the second one.
You have a 100% chance of picking a gold ball first regardless of which box you pick, because the question begins with you picking a gold ball. That event is in the past and its probability is no longer in question.

>>15824683
Correction:
You have 100% chance in the first box to pick a gold ball first and 50% chance in the second box to pick a gold ball first.
The 50% times where you picked a silver ball first don't count for the situation, so the situation is more likely to happen when you pick from the first one.
Why don't you try refuting this post i made?>>15824014

>>15824696
You're doing exactly what >>15824640 said and stubbornly refusing to admit that your misunderstanding is incorrect. I don't see what the big deal is that you have to dig yourself this deep.

>>15824698
He is absolutely right in saying that you're simply wrong and that this can be easily proven with a simple python program, which it has.

>>15824700
See? There you go again. It's absolutely uncanny. Even with your mistake right in front of you it's impossible for you to admit it.

>>15824680
>That's part of the troll
You mean it's part of the problem statement. Part that you're deliberately ignoring in order to pretend it says something else, and then you pretend you're the only one reading it correctly when you very explicitly aren't.
>If the outcome leading to the question was predetermined then it can't be random
Right, but it wasn't predetermined. It was explicitly random. When your interpretation conflicts with the explicit wording of the problem, it's not the wording of the problem that is wrong.
Answer the questions:
>>15824536

>>15824704
Did you quote the wrong post? You're agreeing with me.

>>15824706
I see reading comprehension is generally not one of your fortes.

>>15824702
I accept your concession.

>>15824712
Thank you. I concede that you've been defeated soundly. I'm glad you've humbly accepted that and I wish you luck in another thread.

>>15824706
What you are doing is this:

You are told that you flipped a fair coin and that it landed heads. You conclude that if you are told it is heads, that outcome must have been predetermined, for how else can they be sure it was heads, and therefore the mention of it being a fair coin was false, and you pat yourself on the back for seeing through this clever ruse where others failed.
Of course what actually happened is an event that was 50% likely to happen and you were simply told about it after the fact.

>>15824718
And it is precisely this tendency of wanting to be the smartest kid in the room by trying to see through a trick that isn't actually there that I'm talking about in >>15824640

>>15824718
>You are told that you flipped a fair coin and that it landed heads. You conclude that if you are told it is heads, that outcome must have been predetermined, for how else can they be sure it was heads, and therefore the mention of it being a fair coin was false, and you pat yourself on the back for seeing through this clever ruse where others failed.
This shows a complete lack of comprehension of the argument against you. I don't understand what makes people with this level of ignorance so smug about it.

>>15824702
>>15824715
>>15824728
So, are you gonna propose any argument or do you just wanna act like a pseud on /sci/ 7 in the morning?

>>15824734
If you didn't read it on your way down here to the bottom of the thread then you're not going to read it now.

>>15824728
>This shows a complete lack of comprehension of the argument against you.
I think it rather shows your complete lack of comprehension of the problem statement.
>>15824735
Prove to us that you read anything at all. You explicitly told us this: >>15824680
>If the outcome leading to the question was predetermined then it can't be random and the word is being used to throw you off.
Enlighten us as to how exactly that is different from the situation with the fair coin I described in the post you quoted, or how reaching into a box and taking out a random ball from two possible balls is different from a fair coin flip.

>>15824640
And, you know, it's indicative of a larger trend on /sci/: the "book smart" thread, the NPC threads (both of which inspired this one, of course), it all suggests a preoccupation with being "special", with being a cut above the common rabble, with a sense of innate superiority. None of these threads are about what they pretend to be about. They're there to make a select few people feel good about themselves.

Another thing stands out and that is that, even when it comes to these inconsequential matters, they seem to argue just like fascists have been noted to argue about politics (by e.g. Sartre and Eco), and that fascists of course share the same preoccupation. Of course, I am hesitant to draw any conclusions from this correlation because I can't swing my dick in this place without slapping three fascists in the face, but it does make me wonder about the degree to which political outlook is effected by underlying thought patterns which manifest in all aspects of life.

>>15824761
agreed with you until you went off on a tangent about fascism, i'm pro-hitler and i despise how stupid /sci/ has become for the exact same reasons as mentioned in both posts
borderline unusable board at this point

>>15823999
>See, your problem is fundamentally one of semantics, not mathematics. Your solution works for your interpretation of the problem.
That wasn't my interpretation of the problem. That was a separate problem deliberately constructed to be similar to but distinct from the problem in the OP to catch out people that don't actually understand the logic behind the problem.

My interpretation of the problem isn't wrong. Your interpretation of my intent is wrong.

>I cannot show you mathematically that you are wrong
Because I'm not wrong mathematically because I gave a different problem.

I don't have a problem understanding words. You do. The problem I gave wasn't the fucking problem in the OP. That was intentional on my part. Anyone contesting that my problem and the OP have the same answer would be doing so because they didn't actually understand the fucking fundamentals behind the math.

>>15823093
You didn't read the post. The right-most box is never picked.

>>15824846
Okay, so your example was wrong on purpose to show people how not to do it, or what? Was the point to show the mistake people make when they get the wrong answer? Because you said "it's easier to visualise with coins", implying that you're going to give an example that is like the OP problem, yet now you insist that anyone who read your post that way misinterpreted your words.

>>15824873
That is literally never said or implied. I dare you to prove me wrong with a direct quote.

>>15824634
Nope. The scenario is clearly described. You have ALREADY picked a golden ball. This is simply a way of telling you (if you have basic deduction skill) that there is either 1 gold ball in the left-most box, or 0 gold balls in the middle box. The right-most box is a red herring, since it cannot be picked, since picking a gold ball from it is impossible. It's part of the calculation in the same way that a fourth box filled with red balls is.

It's fucking hilarious how you schizos can't solve a simple puzzle amid your screeching about superiority and NPCs.

The answer is 1/2, by the way.

>>15824881
>The scenario is clearly described.
Indeed. It clearly states you take a ball at random.
>This is simply a way of telling you (if you have basic deduction skill) that there is either 1 gold ball in the left-most box, or 0 gold balls in the middle box.
It does tell you that, but if you have slightly more advanced deduction skills, it tells you something more than that, as well.
>The right-most box is a red herring, since it cannot be picked, since picking a gold ball from it is impossible.
What makes you think I care about the right-most box at all?

>>15824640
Are you not trolling? Do you really not see how the answer is 50/50?

You're given the information that there is two boxes to choose from, the contents hidden. One box contains 1 gold ball, the other contains 0 gold balls. You pick at random. 50/50.

If you can't grasp this, then you've misread the text in the problem.

>>15824883
What else does it tell you, schizo?

>>15824886
>If you can't grasp this, then you've misread the text in the problem.
Is this a joke

Like, you're not just wrong, you also give the dumbest explanation for the common wrong answer, making you uncommonly stupid

You don't pick at random between two boxes, you fool

>>15824878
Are you retarded

>>15824888
Given a gold ball, it tells you that you probably took a ball from the box that gives you a gold ball 100% of the time. It is, in fact, twice as likely as the one that gives you one only half the time.

>>15824890
Hey, genius, it's this one >>15822480

You can tell because that's the one the quote links point to.

>>15824889
Yes, you effectively do. The only information available is that you've picked from ONE of TWO boxes, there being a RANDOM chance that it was left or right.

>>15824893
>>15824890
Incidentally, if you are also >>15824886, then you would think these are the exact same odds as the OP problem, wouldn't you? Doesn't that strike you as odd, with so many more silver balls in the mix?

>>15824894
>The only information available
See >>15824892

>>15824892
The first pull is not the question. The first pull tells us that there is either now a box with 1 gold ball, or 0 gold balls. The only available options, with a random selection being the only available method of choosing. The question about the second pull is asked from this state. 50/50

>>15824893
schizo can't recognise an obvious error in screenshotting, and uses it to not acknowledge that he's misunderstood the "direct quote" in the problem. try to stay focused

>>15824899
No, you do not choose at this point. You have already chosen at this point. The trick is to figure out what you have chosen. And the all-gold box is more likely. That there are two possibilities does not mean they are equally likely.

>>15824901
All right, generously assuming you actually intended to screenshot the other problem, care to explain how you also made the mistake of failing to notice the gold ball in the right-most box in >>15822480? I mean, it's kind of odd that your objection is only relevant to the problem you screenshotted by accident. The reason I point you to the other problem is because if there is a gold ball in the rightmost box, which there is here, then drawing a gold ball does not preclude the rightmost box from being selected. You realise that, right?

So I'm guessing what actually happened here is that you screenshotted what you thought was the correct problem, and you can't admit it, so you'd rather admit to a relatively minor mistake instead of the blatant blunder you are still perpetuating.

>>15824901
>>15824908
Honestly, how did it not even occur to you that the reason I am pointing you to the other problem is because there might be a relevant distinction between the two, to the point that you didn't even bother to check even after your mistake was pointed out to you? How utterly overconfidently convinced of your own infallibility are you?

>>15824781
I was going to say that perhaps my hypothesis had been falsified, but then it occurred to me that someone with a superiority complex would also balk at the sheer cheek of his inferiors thinking they could ever outsmart him, so the real question is:

1/2 or 2/3?

For [math]N[/math] boxes with [math]n_i[/math] gold and [math]k_i[/math] silver the probability of picking gold after having already picked gold is

[math]\sum_{i=1}^{N}n_i{n_i-1 \over n_i+k_i-1} \over {\sum_{i=1}^{N}n_i}[/math]

>>15824934
Would you be so kind as to walk us through it?

>>15824876
The point was to catch someone not understanding the underlying logic by changing that logic in a way that wouldn't be readily noticeable if they were just operating off of rote memorization.

The false implication was also intentional. If I actually wanted to visualize it with coins, it's just.

>There are 3 coins, 1 double-headed, 1 double-tailed, and 1 fair.

>One of the coins is selected at random and flipped on a table heads up. What is the probability that the underside is tails?

>Note: Only idiots say 1/2.

>>15824941
And what's the point of being intentionally obfuscatory? Just so you get to feel clever about yourself? And instead you end up arguing with someone who agrees with you and was easily able to catch your intentional mistake, all because you had to pretend to be retarded to get your jollies.

>>15823359
The replies in >>>/sci/ are much higher quality.

>>15823583

\frac{P(Box I|Gold)P(BoxI)}{P(BoxI|Gold)P(BoxI) + P(BoxII|Gold)P(BoxII) + P(BoxIII|Gold)P(BoxIII)}

\frac{1\cdot\frac{1}{3}}{1\cdot\frac{1}{3} + \frac{1}{4}\cdot\frac{1}{3} + 0\cdot\frac{1}{3}}

\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{12}} = \frac{4}{5}

QED

>>15823583

[math] \frac{P(Box I|Gold)P(BoxI)}{P(BoxI|Gold)P(BoxI) + P(BoxII|Gold)P(BoxII) + P(BoxIII|Gold)P(BoxIII)}
\\
\frac{1\cdot\frac{1}{3}}{1\cdot\frac{1}{3} + \frac{1}{4}\cdot\frac{1}{3} + 0\cdot\frac{1}{3}}
\\
\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{12}} = \frac{4}{5} [/math]

>>15825026
>[math]P(Box1|Gold) = 1[/math]

[math]P(Box1|Gold) = {{P(Box1\cap Gold)}\over{P(Gold)}} = {{2/7}\over{3/7}} = {2\over 3}[/math]

>>15824934
This can't be correct because it can't distinguish between [G,G] [G,S] {S,S] and [G,G] [G,S,S] [S]. Same amount of gold and silver balls, same amount of boxes, different probabilities.

>>15825077
Incorrect.

>>15825007
Which goes to show that everything is relative

>>15824934
>>15825078
This is the correct one.

>>15824967
As >>15824761 pointed out, fascists like >>15824941 just act this way out of narcissism. They can't abide anyone who's smarter than them.

>>15819104
Depends on how you decide to calculate it to best answer different questions. Results depend of course on what question you want answered. In this case, the question is about the probability your 2nd ball in the same box will be gold, which is improperly answered with so-called "naive probability" due to failure to incorporate what's called "partitioning events". Since this is the second time I've seen this guess I'll just post the same link as before, https://www.probabilitycourse.com/chapter1/1_4_2_total_probability.php

Funnily enough the answer is 1/2 after the partitioning event. Since it goes,
picked box
picked gold from box
there is a 1/2 chance, given you picked a box with "at least one" gold ball, that you picked the box with 2 gold balls

Not sure if the board and threads like these are just totally overrun with trolls or what. Hopefully someone was genuinely curious about it.

>>15824589
>you aren't experiencing being a specific person

>>15825688
>the question is about the probability your 2nd ball in the same box will be gold, which is improperly answered with so-called "naive probability" due to failure to incorporate what's called "partitioning events"
How do you call the kind of probability that gives 2/3 as a correct answer to that question?

>>15825007
>>15825026
>>15825077
>>15825078
>>15825090
>>15825136
>>15825140
>>15825597
>>15825688
>>15825857
>>15825860
God has a lot of power in this world, which appear in practical ways. I can prove this to you, but youll have to do exactly what i tell you to do! Follow my instructions exactly, or else youll be left behind.

1. Go to your grocery store
2. Find the chocolate pop tarts. At the back of the shelf exists a single box which has 666 in the barcode number
3. Thats it!

I believe he does this because it tells us all we need to know about him. Think about how its possible, what type of mechanisms does god use to achieve this.

>>15825860
>How do you call the kind of probability that gives 2/3 as a correct answer to that question?
I would call it "an answer to the wrong question".

If you ask "what are your odds of picking a box with at least one gold ball" from the initial three, the answer would be 2/3. Or if you put 3 remaining balls in the same box, rendering your next pick independent of prior conditions, your odds would be 2/3.

>>15821409
Oh god. No, no no..
In this stated scenario there are boxes A, B, C. A has two gold, B has one gold one silver and C has two silver.

AFTER getting ONE GOLD (so it cannot be C).. and taking from the same box (a or b). What is the odds of the next ball (the only ball) being gold?

1 in 2. It is either box A or B.

>>15824014
There effectively is no box 3. The wording says "IF YOU PICK A GOLD FIRST"...
Let's say there are 10,000 other boxes each with two silver. or two red or two chocolate balls. It does not fucking matter. Only box 1 and 2 have gold. If you have a gold ball, you could ONLY have picked box 1 or 2.

This is not the same as the Monty Hall problem;.

I can't believe a simple probability theory filtered this board. Are people posting underage or just simply retarded?

>>15826235
>Are people posting underage or just simply retarded?
Mostly retarded. Or did you not notice the constant vomit of antivaxxer posts and general /pol/tardery?

>>15820581
>If there were 3 gold balls in the first box it would still be 2/3.
No, that would increase the probability that you selected the first box relative to the second. It would become 3/4.

>>15822480
1/2 + 1/6 = 2/3

>>15826245
No it would not. The probability of pulling a gold ball from the first box is 100%, adding more balls won't make it higher, not unless you can somehow have a percentage higher than 100%.

>>15823583
2/3

>>15826252
>The probability of pulling a gold ball from the first box is 100%, adding more balls won't make it higher, not unless you can somehow have a percentage higher than 100%.
Yes, but that is conditional on having that box in the first place, which is the probability that changes. There are now 4 ways to draw gold initially, 3 of them being in the first box.

I don't mean offense specific to the person I'm replying to, but why is this thread full of bickering over really trivial (elementary school) math? Is /sci/ actually retarded? Or are you all just "pretending" to be retarded?

>>15826263
You like many other people arrive at the 2/3 (correct) answer using incorrect logic. The absolute number of balls does not matter, the ratios matter. Its unfortunate the absolute number of balls in the example is such that you can get the right answer using an incorrect method. The fact that so many people get the right answer for the wrong reason probably explains how hard it is to convert the 1/2 people, because half the arguments they see are wrong.

>>15826274
>The absolute number of balls does not matter, the ratios matter.
I agree. The ratio of gold in a box to the total gold, multiplied by the ratio of remaining gold to silver in that same box.

Can you please provide your steps to get 2/3 in your modified example with 3 gold balls in the first, 1 gold and 1 silver in the second, and 2 silver in the third?

>>15826274
>how hard it is to convert the 1/2 people, because half the arguments they see are wrong
I think they are "pretending" to be retarded

>>15826283
You appear to be thinking in terms of dumping all the balls into one big box, but the problem has the balls segregated to their own boxes. This segregation is important.

Consider what operations you perform on a single box. You select a ball, and if its gold you select a second one. That's all. Now for the box which contains all gold, you select the first ball, its gold, then you select the second ball, which is also gold. No matter how many gold balls are in the first box you are only examining two of them, which are gold.

>>15826284
>I think they are "pretending" to be retarded
It's actually an important semantic problem that I'm shocked to find wasn't in the relevant literature at all. The "right" answer of 2/3 is the answer to the question "What are the odds of getting two gold balls if you already have one, given 2 gold balls and one silver ball remaining?" and I think the vast majority if not all would answer that question right.

The problem, and it'll probably never get noticed as one, is with asking in the aforementioned box scenario "Given one gold ball, what are your odds of pulling a second?" as it is not the same question because the answer is contingent on which box you had picked. Every single simulation or illustration of "the right answer", however, treats it as an identical question and calculates it "correctly" treating it as an identical question.

Showing they're not the same is pretty easy. Simply ask yourself: "What box am I in?" Given one ball, and two boxes where one has at least one ball, what are your odds you picked the box with two gold balls? The answer to that is 50/50. If you properly simulate that question you'll get 50/50. So the "paradox" (it's called Bertrand's box by the way) and "wrong answers" stem from having misled people with the wrong question, and then simulating the answer to a different question.

You'll find some people clue in on this important distinction too, such as >>15826227 or >>15825923.

It's just another case where a "paradox" is due to miscommunication and equivocation.

>>15826227
And?
My program and algorithm both account for that.
The third box has 0 chance of attempt so it has no effect on the result.

>>15819104
100%
gold is heavier than silver.
there's nothing in the rules that say you must take the ball that you touch next.
all that you have to do is weigh the ball quickly to determine whether or not the ball is gold.
if the balls are the same size, it will be easy to tell which is which based upon weight alone.

>>15826300
I read the wiki for the "paradox" >>15826311 referenced. This image perfectly explains my method. I think you are trolling because your last post doesn't make any sense. You cannot justify 2/3 mathematically for your modified example because it is wrong.
>>15826311
>In a survey of 53 Psychology freshmen taking an introductory probability course, 35 incorrectly responded 1/2; only 3 students correctly responded 2/3.
Holy fuck people are fucking retarded. I thought they were "pretending". At least /sci/ did better than the /psy/ freshmen. I should've known better. As an insulated 99.9% IQ, I always overestimate normies.
>Given one ball, and two boxes where one has at least one ball, what are your odds you picked the box with two gold balls? The answer to that is 50/50.
This is atrociously written. Do you mean 2 boxes with 2 balls each, 3 gold and 1 silver, and you have already drawn a gold? If so, you are wrong. Simply removing the third box has no effect on the outcome (as >>15826331 correctly says), because it contains no gold balls. The question is conditional on having initially drawn a gold ball, of which 2 of 3 are in the first box.

>>15826345
>53 Psychology freshmen
>35 incorrectly responded 1/2
>3 students correctly responded 2/3
15 got answers other than 2/3 or 1/2

>>15826349
It all makes so much more sense now, the state of the world.

>>15826345
That image is the exact type of shit i'm talking about in this post >>15824586
It implies that adding another gold ball to the first box will increase the chance of success to 3/4, when that's not the case.

>>15826331
>My program and algorithm both account for that.
As noted >>15826311 your program isn't answering the question people think is being asked. Your odds of picking one of 2 boxes, however, is of course 1/2 as a result and at the box-level given two boxes, or 1/3 given three. That's where the issue is and resultant misunderstanding occurs. People interpreting the question to basically be asking "given the two remaining boxes, which box did you pick?" and there's a 50/50 chance you picked one or the other. I assume you don't need to run a program to check the odds of a coin toss but I hope you understand why people are confused now.

>>15826345
>This is atrociously written.
You are correct.
>If so, you are wrong.
I did not mean that, no. My apologies. A different question gets a different result: If instead you calculate odds of picking the box itself, you've a 1/3rd chance of picking the box with 2 gold balls. If you remove one prior to picking anything for example, you now have a 1/2 chance of picking a box with two gold balls. That's why people get the answer wrong.

For everyone else picking 1/2 because they don't understand what the question is trying to ask, it's actually asking about any trial of picking resulting in two gold balls so the number of boxes is irrelevant. Your probability of two gold items is calculated by (1*1/3)/(1*1/3+1/2*1/3+0*1/3) where the numerator is the box with two gold balls. That also works out if it were only two boxes, (1*1/2)/(1*1/2+1/2*1/2) = 2/3.

>>15826359
It doesn't actually have to do with the quantity in the first box, but rather the probability of the balls in that box. If all three are gold, the probability of every ball in the box being gold is 1.

>>15826359
>that image
is objectively correct.
>adding another gold ball to the first box will increase the chance of success to 3/4, when that's not the case.
You are retarded. If you can't see why this is the case, you need to list out all 3*2 + 2*1 + 2*1 possible draws and cross out the ones that start with silver. Then, count the solid gold and divide by the remaining total.

>>15826274
Is wikipedia also wrong when giving this explanation ?
"
The correct answer of 2/3
can also be obtained as follows:

Originally, all six coins were equally likely to be chosen.
The chosen coin cannot be from drawer S of box GS, or from either drawer of box SS.
So it must come from the G drawer of box GS, or either drawer of box GG.
The three remaining possibilities are equally likely, so the probability that the drawer is from box GG is 2/3
"

This explanation also depends on the absolute number of drawer in box GG so seems wrong. On the other hand wikipedia also provides a solution with Bayes theorem, which seems correct.
.

>>15826393
>This explanation also depends on the absolute number of drawer in box GG so seems wrong. On the other hand wikipedia also provides a solution with Bayes theorem, which seems correct.
NTA but the answer is not about the absolute number in the box. Rather, it is the odds per box (1 for gg, 1/2 for gs, 0 for ss) and chance of picking that box (1/3 for each). It's like a proportion of a proportion, or fraction of a fraction. "(1*1/3)/(1*1/3+1/2*1/3+0*1/3)" and "(1*1/2)/(1*1/2+1/2*1/2)" both result in 2/3. The probability of "1", or two gold coins, is divided by each respective chance to pick any box and the odds given by that box.

So if the box were GGG, as long as the probabilities (proportions) remain the same for each box, it's still 2/3. The same way "half of something" is still 1/2 even if it's twice as large.

>>15826379
>If instead you calculate odds of picking the box itself, you've a 1/3rd chance of picking the box with 2 gold balls.
>That's why people get the answer wrong.
>the number of boxes is irrelevant
Right, but I still don't see the "semantic" problem. The question is unambiguous. Maybe you can argue that it's deliberately misleading because it has
>you pick a box at random
sequentially first, but that's like a word problem
>Sally has 10 apples and 5 pears. How many pears does she have?
The fault is definitely not with the wording of the question.

>>15826384
Wrong and self-embarrassing for calling me retarded.
Adding more gold to the first box doesn't increase the chance of it being picked, since what determines that is the number of silvers in the other boxes.
If you have the first box have 100 gold balls and the second 1 gold and one silver, it won't be 100/101, but the same 2/3 chance since you still have the same chance of picking a gold ball first (100% and 50%).
Now, if you have the first box have 2 gold balls and the second have 1 gold ball and 99 silver balls. Almost every time you pick the second one, it won't count for the problem, making it so 99/100 of the time you do pick a gold ball first, it will be from the first box.

>>15826399
So one of the explanations given by wikipedia seems wrong then.

>>15826406
>Wrong and self-embarrassing for calling me retarded.
>Adding more gold to the first box doesn't increase the chance of it being picked, since what determines that is the number of silvers in the other boxes.
>If you have the first box have 100 gold balls and the second 1 gold and one silver, it won't be 100/101, but the same 2/3 chance since you still have the same chance of picking a gold ball first (100% and 50%).
>Now, if you have the first box have 2 gold balls and the second have 1 gold ball and 99 silver balls. Almost every time you pick the second one, it won't count for the problem, making it so 99/100 of the time you do pick a gold ball first, it will be from the first box.
So you are merely "pretending" to be retarded and illiterate? You need to learn conditional probability and English grammar.

>>15826421
>No arguments.

>>15826400
>Right, but I still don't see the "semantic" problem. The question is unambiguous. Maybe you can argue that it's deliberately misleading because it has "you pick a box at random" sequentially first
Unambiguous to you does not mean unambiguous, and your analogy is a very self-serving false analogy. Nobody who isn't a toddler would get it wrong, but almost everybody gets this "paradox" wrong. However if you reworded the question to remove the boxes, almost nobody would get it wrong. Reworded in a different order, or properly communicating what's being asked, almost nobody would get it wrong. This is purely about how the information is presented, not about people being unable to do basic addition or division.

The ambiguity stems from people not understanding what is being meant in-context by "probability" as I pointed out by the fact at "box level" it truly would be 1/2. Given most people end up interpreting the question at box level the fault is with the question. Possibly due to the primacy effect (serial-order effect).

>>15826407
Its a case of the general solution vs more specific cases. The full general solution for arbitrary numbers of boxes and balls is quite complicated, we are reasoning over various levels of simplification, the common explanation works for cases where there are equal number of balls in each box.

>>15826422
>you still have the same chance of picking a gold ball first (100% and 50%)
>making it so 99/100 of the time you do pick a gold ball first
The probability of picking a gold ball first is obviously 100% in the context of the question, for starters. It's hard to tell from your babble why you tried and failed to calculate it multiple times.
Like I said,
>You need to learn conditional probability and English grammar

>>15826430
Sally has 10 apples and 5 pears. How many pears does she have?
>Unambiguous to you does not mean unambiguous. Almost all toddlers get this "paradox" wrong. However if you reworded the question to remove the apples, almost nobody would get it wrong. Reworded in a different order, or properly communicating what's being asked, almost nobody would get it wrong. This is purely about how the information is presented, not about people being unable to do basic number recognition.
>The ambiguity stems from people not understanding what is being meant in-context by "pears" as I pointed out by the fact at "apple level" it truly would be 10. Given most people end up interpreting the question at apple level the fault is with the question. Possibly due to the primacy effect (serial-order effect).
>t. Toddler

>>15826449
It's pretty funny how I can tell you're angry through this post.

>>15826450
Bro I'm laughing my ass off. Thank you for this.

>>15826449
>I've no argument let me false analogy harder
Okay we all get that you are desperate to feel smug

Is this some sort of troll? How is it not 50%? If you get a gold ball you know you have box 1 or 2. There's an equal chance that the next ball from the same box will be either gold or silver.

>>15826455
Yes it's a troll. The naive probability is 2/3 but the question is written to confuse people.

>>15826446
Oh, so you're a 1/2 retard. Nevermind, i thought you had hope.

>>15826453
>>>15826311
>It's actually an important semantic problem that I'm shocked to find wasn't in the relevant literature at all.
The burden is on you to point out the *semantic* flaw that the "relevant literature" supposedly "missed". I effortlessly understood the question and got it and more generalized versions right.
At least you aren't like the 1/2 people who refuse to accept that the problem isn't a true "paradox" and their answers are objectively wrong (>>15826455 >>15826458), or the 15 /psy/ retards who got completely different answers (>>15826349)
>>15826464
Whatever gave you that impression?

>>15826469
>The burden is on you to point out the *semantic* flaw that the "relevant literature" supposedly "missed".
I did.
>I effortlessly understood the question and got it and more generalized versions right.
Yet you can't understand what the confusion is? Pity

>>15826469
You already proved your retardation here. Any further posts from you will just be Dunning Kruger effect empirical data.

>>15826449
1/2 toddlers btfo

>>15826214
How many times

Just because there are two possibilities that does not make them equally likely

There are two cases:
1. You picked the left most box
2. You picked the right most box.
In the first case, the next ball is gold, in the other case, it's silver. 50%

>>15826532
The first case is twice as likely as the second.

>>15826406
This man is correct btw

Consider the process. First, you pick a box at random. 1/3 of the time you'll get the box with all gold, and get gold from that. 1/3 of the time you'll get the mixed box, and half the time you'll get a gold ball from that. 1/3 of the time you'll get the silver box and get no gold. So three out of six tries, you can expect a gold ball, and two of those three times, it'll come from the all-gold box. And that is what determines whether or not you'll be able to draw another gold ball from the same box.

If we add gold balls to the all gold box, you'll still pick it 1/3 of the time. Meaning you'll still get gold three out of six tries total, and two of those will be from the all-gold box. However, if we add silver balls to the mixed box, we reduce the odds that any picked gold ball came from that box, increasing the relative odds that we got it from the all-gold box instead. If you add just one silver ball that means you'll get gold 4/9 times, and 3/4 of those times it will be the all-gold. If we add one more ball, we get gold 5/12 times, and 4/5 times it will be from the all-gold box. It scales very neatly like that.

You don't even need to understand higher maths for this, you just have to be able to visualise it.

>>15826534
>picking the left-most box is twice as likely as the middle box

>>15826544
It was initially equally likely to be picked, but, a gold ball having been drawn, the left-most box is twice as likely to HAVE BEEN picked. Just as the all-silver box was initially equally likely to have been picked, but, a gold ball having been drawn, we can eliminate that possibility entirely. You update your probabilities when new information is revealed. Somehow you have no problem instinctively doing this with the silver box but you have a blind spot with regard to the other two.

>>15826543
Also note that if we start adding SILVER balls to the (originally) all-gold box, THEN the amount of gold balls in it suddenly starts to matter. Same as if we start adding gold to the other boxes. It is the relative amount of gold and silver in each box, not the absolute amount, that counts.

>>15820242
>chosenBox.pop(...)
>chosenBox.append(...)
>modifying the boxes
disgust.png

>>15826532
You have been kidnapped by a mad statistician who has strapped you to a device that just about allows you to operate two buttons located down by your toes. The buttons are identical in appearance and you have no outward reason to prefer one over the other. Either button will release your bonds, he explains, however, one of the two has a 99% chance of exploding you. On the off chance that it doesn't, however, that button will also open a door behind you to reveal a goat (mad statisticians love goats). You may keep the goat.

You press one of the buttons at random, your bonds release, and you are not exploded. What are the odds that you will hear bleating behind you?

There are two cases:
1. You pressed the button that simply releases you
2. You pressed the button that had a 99% chance of exploding you
In the first case, there is no goat, in the second there is. 50%.

Do you agree with this line of reasoning? If not, why?

>>15819517
This is correct, no mathcel sophistry will ever change that.

>>15826605
It's 100% because i'm the son of god.

If you're so smart, why don't you calculate the chance of me getting laid?

>>15826642
0%

>>15826648
Proof?

>>15826621
You misunderstand the point of probability. If we had perfect knowledge of the universe, we wouldn't need to do probability calculations. But we don't. We can only make predictions based on imperfect knowledge. So yes, when you flip a coin, it is either heads or tails. It is, in that moment, 100% one and 0% the other. But because we do not know which, we can only say, at best, that there is a 50% chance of either. That is what probability is. An expression of relative certainty in the face of our inability to know something entirely for certain.

>>15826665
If you have to ask...

>>15826682
What? If i have to ask, what?
What does that mean?
Show me proof, faggot.

>>15823583
you have just taken g1, g2, or g3

next one will be:
g1 --> g2
g2 --> g1
g3 --> s

2/3

>>15826699
Your solution may give the right answer for the original problem, but only by accident, because it breaks down when you change the ratios of the balls. The post you're replying to is correct. Just as the line of reasoning that does
>There are two boxes and one of them is the right one so it's 1/2
is flawed, so too is
>There are three balls and two of them are the right ones so 2/3
for much the same reason. Because just as we understand that, even though there are two boxes, one is more likely to have been picked, so too it happens that, even though there are three balls, two of them are more likely to have been picked. Because the middle box gives you gold only one out of four times it is picked, that means that for every time you get gold from that box, you will have gotten gold from the other box four times. You may ask how we get four gold balls from a box that contains only two balls, and that is simply by drawing both balls, on average, twice, for every one gold ball we get from the other box.

>>15826332
>gold is heavier than silver.

>>15826917
It is denser than silver, so for balls of the same size, the gold will weigh more. That's actually the only part of that post that isn't completely retarded.

>>15827444
>That's actually the only part of that post that isn't completely retarded.

>>15819104

>>15827748
You need it explained to you?
>100%
Retarded
>gold is heavier than silver.
That's true
>there's nothing in the rules that say you must take the ball that you touch next etc.
Retarded. You've selected a box at random. Each box has two balls in it. You have taken one ball from it. How many balls are there left in the box?

Forgetting the fact that the draw is explicitly random and the rules therefore actually do say you're not allowed to test the balls before taking them, it doesn't even matter at this point. There is one ball left for you to take. Knowing what it is beforehand cannot change the outcome.

>>15827444
>That's actually the only part of that post that isn't completely retarded.
YES! I'm glad that I could finally write a post here that is only mostly retarded. Thanks for the positive feedback.

>>15819104
Why didn't you make an anthology of all the calculus stuff you drew? >:(

>>15822480
1/3×0+1/3×1/2+1/3×1=1/2
Or, since the first gold ball doesn't give you any info about the boxes, it's equivalent of randomly picking gold out of 3 gold, 3 silver balls, so 1/2

>>15828342
Wrong. The first gold ball tells you that you are thrice as likely to have picked the all-gold box than the box with one gold, two silver. And 1.5 times as likely as the box with two gold, one silver.

>>15819507
>undergrad: the post

it's rigged. the ball is pyrite plated lead, and the see through boxes are a sham, complete with confederate 'co-players' who draw silver before you.
Your contract states that you are paid $500 if your segment is used, but that your likeness and attempt to 'win' their advertised 'prizes' can be used throughout the universe in perpetuity.
It's all rigged.

isnt it 50% ? I mean you know that the box you picked contains at least a gold ball, thus excluding the rightmost one, meaning that there's a 50% chance that you picked the one with 2 gold balls.

>>15828695
There are more gold balls in the first box, so it's more likely that you got a gold ball from there.

>>15824967
>And instead you end up arguing with someone who agrees
M8, I was simply trying to tell you you misunderstood my intent. You turned that into an argument by refusing to listen. I never disputed your math.

Clearly I didn't even need to be intentionally obfuscatory to find someone with no idea what they're talking about given how much I've had to attempt to directly explain myself to you.

I wasn't trying to feel clever. I was trying to find people that memorized the answer without understanding the logic such that I could correct their thoughts and actions.

Now why have you refused to listen to me through post after post?

>>15819987
No, you are just surrounded by idiots too stupid to even realize they are idiots.

>>15828723
There are less silver balls in the first box*

>>15819987
You are missing something and
>>15829087
You are too smugly ignorant to even realise you're missing something

>>15829079
>Now why have you refused to listen to me through post after post?
Initially? Because your first attempt at an explanation, ironically, only managed to make you sound more and more like you were genuinely arguing for 1/2, because you used all the same arguments those idiots use too and you weren't at all clear.
Now? I've accepted that you were baiting ages ago, you continue to argue with me because you refuse to accept that your bait was ill-conceived and your explanation was piss-poor.

I also don't fully understand why, in a thread full of people who are stumbling over themselves to genuinely argue what you were arguing as bait, you decided that it's the people who got the right answer but may have done so via the wrong way who needed to be taken down a peg. And you didn't even get any of them.

>>15828723
right, I completely forgot the conditional, thanks

>>15828723
>>15830139
yeah I got 2/3, it was fun revisiting probabilities

>>15830139
>>15830150
Holy shit, someone actually changed their mind?

>>15828695
Consider the case of there being 1 billion silver balls in the middle box. You would expect to almost never pick the singular gold ball, therefore if you find a gold ball in your hand you can expect you got it from the gold only box.

>>15830150

>>15830170
I mean I know I suck at maths, so I wont defend my result to the death

>>15830185
Lol did I fuck up again ?

>>15829171
>it's the people who got the right answer
Had they given the "right answer" to me, it'd have been wrong. I wasn't trying to take anyone down a peg. I was trying to find and educate people with an incomplete understanding of the problem.

You refusing to accept that simple explanation doesn't make it piss-poor. Just makes you mad.

i've never once had a wrong 'captcha'
aced the SAT
i do 250 bodyweight squats to start my morning
and I can't fathom the following problem
you know what it takes to sell real estate??

brass balls real estate
it's a fugazi
how 2 ef up a high Q

>>15830537
>Had they given the "right answer" to me, it'd have been wrong.
Right, but no one did. You did get someone to agree with you that it was an accurate representation of the original problem, though. And why did you have to catch people being wrong first, anyway? You could have just straightforwardly said "if we change the problem in this way, it will be different, and for this reason". So yes, that was you being intentionally obfuscatory, and as a result you failed in your purpose, you actually provided affirmation for someone who was wrong, and you spent half the thread explaining yourself. Your intent is easily explained but your execution leaves somewhat to be desired.

>>15828631
>dunning-kruger: the movie: the post

>>15830194
>Lol did I fuck up again ?
Don't worry about it, it's just "Barkin'" Barkun.

>>15819104
Its one in two and I don't care what any of you pseudo-intellectuals have to say. If you draw one gold ball that means at most you can have one more gold ball in the box, the second is inaccessible to you by the fact that both boxes have to have at least one gold ball in them. Therefore your sample pool consists of one silver and one gold. Though statistically correct, an algorithm developed by someone much smarter than you still won't address the real conditions of the premise.

>>15830622
>Though statistically correct
All we needed to hear

>>15830634
Idiot, don't feel validated. The problem itself tries to cheat you by making you think in real terms when in reality it pulls the rug underneath you in the most assbackward way, that is by completely ignoring the conditional of there being at least one gold ball in both remaining boxes. The question itself if framed in a way that practically begs you to get it wrong, its a cheap bait and switch. This is why statistics will always be a "soft science"

>>15830653
>The question itself if framed in a way that practically begs you to get it wrong
And you obliged, I guess?

>>15830671
Guess again retard. By the way did you just have a brain aneurysm? your last response was literally greentexting the part were I said the statistically correct answer was not the same as the real answer.And furthermore it shouldn't matter if anyone got it wrong if the problem itself is presented in bad-faith,

>>15819104
Please stop humiliating us, I'm sorry for getting it wrong initially. I swear I'm a real human

>>15830684
Right, your mistake is thinking that the statistically correct answer isn't simply the correct answer, that there is some sort of alternative reality where "real" answers reside, and that the problem is trying to trick you somehow. Actually that's several mistakes.

No, the problem is straightforward (though counterintuitive) and your admission that 2/3 is the statistically correct answer would be tantamount to an admission that you are wrong in the real world where statistics apply, but not in your fantasy alternate reality where anything goes.

>>15830698
Imagine being this smug and simultaneously this wrong.

>>15830704
All right, I am. Is that what it's like to be you?

Imagining a trick and then feeling clever for outsmarting it isn't actually impressive.

>>15830698
Statistics are not applicable to reality chum, you got that whole little sentence of yours backwards, it statistics that exist in this "alternate reality" you just invented, were the real answer is just that, the real answer it does not "reside" anywhere but real world. The problem is only "straightforward" through the abstractions of mathematics which as we know are manmade axioms that absolutely correct nor absolutely complete in their construction of reality. What your basically saying is that made up world of made-up abstract rules and definitions you are correct. Which you are congratulations.

>>15830709
To answer your question, In this moment I'm euphoric. Plus your not exactly an authority on what passes for impressive now are you?

>>15830717
picrel

>>15830709
"I know you are but what am I?" is a schoolyard insult. Never developing beyond your early years is a sign of severe mental retardation or, in some cases, mental illness brought about by severe childhood trauma. I suggest seeking psychiatric counsel for your disability.

>>15830711
>Statistics are not applicable to reality chum
looool
Statistics are an abstraction, yes, but one that describes the real world. If the answer doesn't correspond to the real world, it's incorrect. If it's correct, it corresponds to the real world. And it is correct, in this case. You are still making the mistake of thinking it can be otherwise. If I am correct in one world, I am necessarily correct in both. And you are wrong in both.

>>15830724
>"I know you are but what am I?" is a schoolyard insult.
As befits your schoolyard intellect. All your replies thus far have been vapid blathering about how statistics don't apply to the real world and the problem tried to trick you. Your only actual argument is this: >>15830622
>If you draw one gold ball that means at most you can have one more gold ball in the box, the second is inaccessible to you by the fact that both boxes have to have at least one gold ball in them.
And that's simply wrong because you're not choosing between two boxes at this point. You've already chosen a box and you're trying to figure out which one it's likely to be. But failing to comprehend what the problem is actually describing to you is not bad faith, it's entirely on you.

>>15830737
You apparently think that there's just one anon here humiliating you.

>>15830732
You're not really corresponding to much of anything right now pal. just the because you can describe the world doesn't mean you're doing so accurately. The statistical answer to this problem does not correspond to reality. the pool of remaining balls in the statistical answer is not the same as pool when solving the problem in real terms.
>>15830737
That schoolyard thing wasn't me by the way, I should have clarified that the question is OFTEN presented in bad faith to people who do not know or are just beginning to learn statistics. The point is that the "correct" answer is only correct in statistical terms and therefor has no basis in reality. The "real" answer which I still insist upon accounts for the real conditions in the real world where one might want to solve this real problem. The trick is in the fact the human mind is conditioned to solve problems especially those described in such visual terms in real terms. Naturally within statistics it doesn't work that way, which is why so often problems like these are presented in order break once preconceived assumptions of reality because they don't apply neatly to statistics and vice versa. In that aspect it is a useful if annoying tool to teach people however, the problem itself is cheap and deceptive and I stand by that.

>>15830748
No one is humiliating me, in fact, you're humiliating yourselves by insisting on being so wrong and devolving into namecalling and accusing the problem of being posed in bad faith. Quick rule of thumb: if you think you're smarter than an entire field of study, you're probably actually just wrong.

>>15830762
the intellect of "entire field of study" cannot be quantified nor compared with you fool. Try comparing yourself with the intellect of some abstract concept, you can't.

>>15830758
>The statistical answer to this problem does not correspond to reality.
Then it would simply not be the correct statistical answer. But you already admitted that it is. Which means your misunderstanding resides somewhere far deeper.
> The point is that the "correct" answer is only correct in statistical terms and therefor has no basis in reality.
No, the point is that 1/2 is an intuitive but incorrect answer and can be shown to be wrong, both through mathematics and through real-world experiments. The real conditions in the real world will produce the same answer of 2/3, and the reason for that is that statistics actually do correspond to reality, if you know how to properly calculate them.
>the problem itself is cheap and deceptive and I stand by that
Your mum is cheap and deceptive

>>15830769
Well, you can't really compare your intellect with much of anything. But you think you can revolutionise statistics with a half-baked shitpost on 4chan.

>>15830779
I'm not claiming to revolutionize anything, the problem is poorly thought out does not account for a basic fact implied by the premise. Also sick burn.

>>15830783
>the problem is poorly thought out does not account for a basic fact implied by the premise
You're simply misreading it.

>>15830772
Statistics only correspond to what they get right, the correct statistical answer doesn't necessarily correspond to correct answer in reality, half of statistics is determining the ones that do.

>>15830785
Its not a misreading so much a misinterpretation that causes people to get it wrong, As I've said >>15830758 problems like these are used to break to get people to think statistically

>>15830789
No, you're simply not getting this. The correct statistical answer is the one that is correct in reality.
>>15830793
>Its not a misreading so much a misinterpretation that causes people to get it wrong
All right, tell us your misinterpretation and I'll tell you what you got wrong.

>>15830799
When you pull the gold ball you eliminate the box with two silver balls but you must also account for the one gold ball that must be inside the third box weather or not it's the one with the silver ball in it or not, meaning, only two balls are unaccounted for, one silver and one gold. There is really nothing else to it. I understand that the total pool of gold balls is two and 2/3 but of those only one is possibly in the box you're actually pulling from

>>15830810
>you must also account for the one gold ball that must be inside the third box weather or not it's the one with the silver ball in it or not, meaning, only two balls are unaccounted for, one silver and one gold
I'm not sure I understand. Is the third box the one you didn't pick? That one would have two balls in it. There aren't two unaccounted balls, there are three, and you don't know exactly where they are.
Anyway, it's not about the total pool of gold balls at all. It's about the relative odds of getting a gold ball from a box to begin with, and what that tells you about which box you picked. The all-silver box is of course right out with 0% chance to produce gold, but the gold-silver box is also only 50% likely to produce gold, compared to the 100% of the gold box. Any gold ball is therefore twice as likely to have come from that box, and having picking that box means another gold. That's two out of three times you picked gold on your first try.

>>15830836
If you know that the two boxes left after eliminating the box with two silvers have either gold gold or gold silver then can reasonably assume that at least one gold ball is in the box you didn't pick which narrows the possibility. But like you said it's a relative probability problem which changes the approach. In any case I don't disagree with the "correct" answer I just think mine is more realistically applicable. which is what I should have said at the outset.

>>15830874
>In any case I don't disagree with the "correct" answer I just think mine is more realistically applicable.
There is no realistic application for an incorrect answer. If you "don't disagree" with the correct answer but still prefer the incorrect answer, what does it really mean to agree, anyway?