/sci/ - Science & Math » Thread #13882631

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Boxes

Anonymous Tue 23 Nov 13:44:59 2021 No.13882631 View Reply Original Report

Quoted By: >>13882675 >>13882693 >>13883127 >>13883258 >>13884369 >>13884725

What is the correct answer to this and why is it 2/3?

Anonymous

Anonymous Tue 23 Nov 2021 13:46:53 No.13882635 Report

Quoted By: >>13882636

Either it's gold or it isn't gold. 50/50

Anonymous

Anonymous Tue 23 Nov 2021 13:47:36 No.13882636 Report

Quoted By:

>>13882635
fpbp

Anonymous

Anonymous Tue 23 Nov 2021 14:02:06 No.13882675 Report

Quoted By: >>13883194 >>13883266

>>13882631
3 gold balls, 3 ways to move ahead
G1 --> G2
G2 --> G1
G3 --> S

2/3

Anonymous

Anonymous Tue 23 Nov 2021 14:09:21 No.13882693 Report

Quoted By: >>13883269

>>13882631
When you pick the first ball, there are 3 options, G1, G2, G3
If you got G1, you'll get G2
If you got G2, you'll get G1
If you got G3, you'll get a silver ball
There's 2 out of 3 chances of getting another golden ball

Anonymous

Anonymous Tue 23 Nov 2021 17:31:58 No.13883127 Report

Quoted By:

>>13882631
Intuitively, its because there is a higher probability of observing a gold ball if box 1 is picked. If you think about picking box 1 and picking box 2 as causes for the event that you see a golden ball, doesn’t it make sense that seeing a golden ball is more indicative of the commoner cause? This is why it can’t be one half. Rigorously, this is just Bayes theorem.

Anonymous

Anonymous Tue 23 Nov 2021 17:55:33 No.13883194 Report

Quoted By: >>13883281 >>13884734

>>13882675
Is there symmetry in the system regarding the color of the bals?
What if the question were what is the probability of the second ball being the same color as the first ball?
Why restricting the color of the first ball change anything?
Congratulations, you just discovered one of the oldest accounting tricks!

Anonymous

Anonymous Tue 23 Nov 2021 18:12:48 No.13883258 Report

Quoted By: >>13883348 >>13883473

>>13882631
Use Bayes's theorem:

P(Box_1|G) = P(Box_1) P(G|Box_1) / P(G) = (1/3)(1)/((1/3)(1)+(1/3)(1/2)) = 2/3

Or use the principal of proportionality:

(1/3)(1) chance of choosing a gold ball from Box_1

(1/3)(1/2) chance of choosing a gold ball from Box_2

Chance you're in Box_1 is increased proportionally by the chance of choosing a gold ball (1/3)(1)/((1/3)(1)+(1/3)(1/2)) = 2/3

Anonymous

Anonymous Tue 23 Nov 2021 18:13:50 No.13883266 Report

Quoted By: >>13885831

>>13882675
That's not a good way of doing it. What if the number of balls in each box is not equal?

Anonymous

Anonymous Tue 23 Nov 2021 18:15:03 No.13883269 Report

Quoted By: >>13884511

>>13882693
What if there are 3 gold balls in the first box?

Anonymous

Anonymous Tue 23 Nov 2021 18:18:43 No.13883281 Report

Quoted By: >>13883389

>>13883194
That would just be the probability of choosing box 1 or box 3, which is still 2/3.

Anonymous

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Anonymous Tue 23 Nov 2021 18:35:02 No.13883348 Report

Quoted By: >>13883491

>>13883258
based 'show your work' poster

You get a smiley face sticker, everyone else deserves a frowny face

Anonymous

Anonymous Tue 23 Nov 2021 18:44:23 No.13883389 Report

Quoted By: >>13884487

>>13883281
I love these accounting tricks.

agree P(A) = 2/3

What if there were N+1 boxes with N balls in each and i-th box contains i gold balls for i in <0, N>
What is the probability the next ball is going to be the same color?

Anonymous

Anonymous Tue 23 Nov 2021 19:03:36 No.13883473 Report

Quoted By: >>13883528 >>13884311 >>13884675

>>13883258
>Bayes's theorem
A and B must be different events.

Anonymous

Anonymous Tue 23 Nov 2021 19:07:48 No.13883491 Report

Quoted By: >>13883499

>>13883348
geeks plowing forward without any concern for reality

Anonymous

Anonymous Tue 23 Nov 2021 19:09:45 No.13883499 Report

Quoted By: >>13883528

>>13883491
Wut

Anonymous

Anonymous Tue 23 Nov 2021 19:15:24 No.13883528 Report

Quoted By:

>>13883499
>>13883473

Anonymous

Anonymous Tue 23 Nov 2021 23:22:39 No.13884311 Report

Quoted By: >>13884360

>>13883473
>A and B must be different events.
That's both wrong (since P(A|A) = 1) and irrelevant since the events "you're in box_1" and "chose a gold ball" are not the same, since you can choose a gold ball from box_2.

Anonymous

Anonymous Tue 23 Nov 2021 23:39:21 No.13884360 Report

Quoted By: >>13884469

>>13884311
I think here "different" means "independent"

Anonymous

Anonymous Tue 23 Nov 2021 23:41:34 No.13884369 Report

Quoted By:

>>13882631
its not

glow niggers changed statistics about 12 years ago, we all felt the shift

but some of you change your opinions so fast...

Anonymous

Anonymous Wed 24 Nov 2021 00:24:02 No.13884469 Report

Quoted By:

>>13884360
Still wrong, the events don't have to be independent. They're not being independent is the whole point of Bayes Theorem.

Anonymous

Anonymous Wed 24 Nov 2021 00:32:25 No.13884487 Report

Quoted By: >>13885129

>>13883389
Trivial. It's just

Sum from k=0 to N of ((N-k)(N-1-k)+k(k-1))/((N+1)N(N-1)) = 2/3

Anonymous

Anonymous Wed 24 Nov 2021 00:38:52 No.13884511 Report

Quoted By: >>13884721 >>13886564

>>13883269
g1 and g2 turn into pick1 and pick2
nothing really changes, it's still 2/3

Anonymous

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Anonymous Wed 24 Nov 2021 01:49:05 No.13884675 Report

Quoted By:

>>13883473
Smiley face poster here. I don't believe you, and you didn't show any work. I'm so disappointed in you that I'm going to have to give you a stormy cloud sticker.

Anonymous

Anonymous Wed 24 Nov 2021 02:04:55 No.13884721 Report

Quoted By: >>13885670

>>13884511
It destroys your explanation.

Anonymous

Anonymous Wed 24 Nov 2021 02:05:37 No.13884725 Report

Quoted By:

>>13882631
0.33%

Anonymous

Anonymous Wed 24 Nov 2021 02:08:28 No.13884734 Report

Quoted By:

>>13883194
yes, if you pull a silver ball the probably you pulled from box 1 is zero, the entire arrangement is perfectly symmetric and logical, you just arent even trying to do the problem

Anonymous

Anonymous Wed 24 Nov 2021 04:30:41 No.13885129 Report

Quoted By: >>13885159

>>13884487
nonsense, what are you calculating?
Problem:
second ball the same color as the first one once we know the first ball is gold

once we get the first ball only N boxes <1,N> are in play with N-1 balls in each
The probability for getting the right ball for k-th box is (k-1)/(N-1)

sum from k=1 to N (k/1)/(N-1)=1/2
and doesn't depend on N

also fpbp

stop confusing people with accounting tricks

Anonymous

Anonymous Wed 24 Nov 2021 04:39:18 No.13885144 Report

Quoted By: >>13885165 >>13885177 >>13885178 >>13885662

Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests.

On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. As the guests are not aware of the total of the revised bill, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself, and proceeds to do so.
https://en.wikipedia.org/wiki/Missing_dollar_riddle
As each guest got $1 back, each guest only paid $9, bringing the total paid to $27. The bellhop kept $2, which when added to the $27, comes to $29. So if the guests originally handed over $30, what happened to the remaining $1?

Anonymous

Anonymous Wed 24 Nov 2021 04:46:15 No.13885159 Report

Quoted By: >>13885214

>>13885129
>second ball the same color as the first one once we know the first ball is gold
You just said same color, you didn't say the first ball is gold.

>sum from k=1 to N (k/1)/(N-1)=1/2
This would only be the solution if it's equally likely you chose a gold ball from any of the boxes with a gold ball. But of course we know that's false since the chance of choosing a gold ball from a box with k gold balls is k/N.

There are (N+1)N/2 gold balls so the chance you're in a box with k gold balls after choosing a gold ball is 2k/((N+1)N) this is the factor your sum is missing.

Therefore the solution is sum from k=1 to N of 2k(k-1)/((N+1)N(N-1)) = 2/3

>stop confusing people with accounting tricks
It's called math, you should learn it before trying to solve math problems.

Anonymous

Anonymous Wed 24 Nov 2021 04:47:31 No.13885165 Report

Quoted By: >>13885761

>>13885144
If you get paid 30 and give 3 back you are paid 27. The employee takes two leaving 25 gained on the rooms. I don't understand, is this a puzzle?

Anonymous

Anonymous Wed 24 Nov 2021 04:52:24 No.13885177 Report

Quoted By:

>>13885144
>The bellhop kept $2, which when subtracted to the $27, comes to $25
Fixed
Tricky jew

Anonymous

Anonymous Wed 24 Nov 2021 04:52:25 No.13885178 Report

Quoted By:

>>13885144
>The bellhop kept $2, which when added to the $27, comes to $29.
This is a meaningless summation. The $2 should be subtracted from, not added to, the $27 they paid to get the amount that went to the manager: $25.

Anonymous

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Anonymous Wed 24 Nov 2021 05:09:42 No.13885214 Report

Quoted By: >>13885227

>>13885159
quick check in python proves you are right

Anonymous

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Anonymous Wed 24 Nov 2021 05:18:10 No.13885227 Report

Quoted By: >>13886548

>>13885214
>he needed to simulate it in python instead of using his brain

Anonymous

Anonymous Wed 24 Nov 2021 07:37:42 No.13885662 Report

Quoted By:

>>13885144
>As each guest got $1 back each guest only paid $9
No, they paid $25 and then got $1 extra each which totals to $28.

Anonymous

Anonymous Wed 24 Nov 2021 07:41:07 No.13885670 Report

Quoted By: >>13886169

>>13884721
how exactly?
protip: it doesn't

Anonymous

Anonymous Wed 24 Nov 2021 08:40:00 No.13885761 Report

Quoted By:

>>13885165
You'd be surprised how easily this confuses people. I think it threw me off for a minute the first time I heard it.

Anonymous

Anonymous Wed 24 Nov 2021 09:34:11 No.13885831 Report

Quoted By: >>13886171

>>13883266
We KNOW what the number of balls in each box is. This affects the odds.

Anonymous

Anonymous Wed 24 Nov 2021 11:29:29 No.13886064 Report

Quoted By: >>13886182

I think the definition is favorable outcomes / possible outcomes so it's 1/2 : 50%

Anonymous

Anonymous Wed 24 Nov 2021 12:32:33 No.13886169 Report

Quoted By: >>13886564

>>13885670
When you pick the first ball, there are 4 options, G1, G2, G3, G4
If you got G1, you'll get G2 or G3
If you got G2, you'll get G1 or G3
If you got G3, you'll get G1 or G2
If you got G4, you'll get a silver ball
There's 3 out of 4 chances of getting another golden ball

Anonymous

Anonymous Wed 24 Nov 2021 12:33:41 No.13886171 Report

Quoted By:

>>13885831
Yes, which is why your explanation isn't correct.

Anonymous

Anonymous Wed 24 Nov 2021 12:38:21 No.13886182 Report

Quoted By:

>>13886064
>favorable outcomes / possible outcomes
What is an "outcome?" Half of the boxes with gold balls have another gold ball. But 2/3 of the gold balls are in a box with anther gold ball. So which is an "outcome." It's amazing how many people think arbitrarily listing events let's them calculate a probability. That only works if each outcome is equally likely given the information you have.

Anonymous

Anonymous Wed 24 Nov 2021 16:01:36 No.13886548 Report

Quoted By: >>13886832

>>13885227
Instead of accepting the concession with grace let's make fun of the defeated. this way future conflicts will be more fun.

Anonymous

Anonymous Wed 24 Nov 2021 16:04:58 No.13886557 Report

Quoted By:

python code simulating 1,000,000 attempts for those who still have doubts if 2/3 is the right answer

https://pastebin.com/mPziC6ir

Anonymous

Anonymous Wed 24 Nov 2021 16:07:46 No.13886564 Report

Quoted By: >>13886841

>>13886169
lrn2read >>13884511

Anonymous

Anonymous Wed 24 Nov 2021 18:05:03 No.13886832 Report

Quoted By: >>13887005 >>13887526

>>13886548
Die, CSfag

Anonymous

Anonymous Wed 24 Nov 2021 18:08:18 No.13886841 Report

Quoted By:

>>13886564
When you pick the first ball, there are 3 options, pick1, pick2, G3
If you got pick1, you'll get pick2
If you got pick2, you'll get pick1
If you got G3, you'll get a silver ball
There's 2 out of 3 chances of getting another golden ball

This is nonsensical.

Anonymous

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Anonymous Wed 24 Nov 2021 19:01:11 No.13887005 Report

Quoted By: >>13887526

>>13886832

Anonymous

Anonymous Wed 24 Nov 2021 22:15:06 No.13887526 Report

Quoted By:

>>13887005
See >>13886832

Anonymous

Anonymous Wed 24 Nov 2021 23:44:39 No.13887750 Report

Quoted By: >>13887875

it's 50%

Anonymous

Anonymous Thu 25 Nov 2021 00:45:54 No.13887875 Report

Quoted By:

>>13887750
Proof?

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