/sci/ - Science & Math

>>11759019
.5

>>11759019
2/3. We're undersampling the middle box because half the time we pick it, we'll draw out a silver ball. You can explicitly write out the entire tree for this problem to confirm.

>>11759033
Or to put it a different way, each ball has equal probability of being picked. The question is essentially just asking "what percentage of the gold balls are in the two-gold box?".

>>11759027
What's the point of box on the right?

>>11759033
Nah. The odds of which gold ball you picked first are equal, so 2/3rds of the time the next ball is guaranteed gold as your first was from the 2 gold box. Then the one in 3 times you picked from the split box there's still a 1/2 chance.
So 2/3 + !/3 x 1/2 = 5/6.

>>11759019
The correct answer is 50%.

Brainlets will oppose this.

>>11759061
>there's still a 1/2 chance.
D'oh, of course ther isn't, it's 0.
So 2/3, yeah.

>>11759038
doesn't matter. we got a ball from a box and that ball was gold. we take from same box, either we got the box with 2 gold or with 1. 5050
2/3 of the img is irrelevant information. what does it matter if u can't see the boxes if I was told about the boxes.

>>11759038
to confuse with the monty hall problem.

>>11759073
>if only two events are possible, they are equally likely
Based.

>>11759093
>monty hall
Low IQ understanding.

>>11759073
So you are saying that the full gold box amd the silver/gold box are equally likely. So if we were to imagine that there are 999 gold balls in the one box, and 1 gold and one silver in the other box, you still think its a 50/50 chance you got the silver box? That your chances of getting a gold ball is completely independent of how many gold balls are in a box? You did eliminate the silver box, so I suppose you must understand that the ball you got effects your odds.
Maybe this final way of envisioning it will help you. Imagine the silver and gold box has 999 silver balls. The chances of you reaching into the silver box and getting a gold ball is extremely low. Thusly, it is more likely you are in the gold box.
However, I now wonder what is the actual probability of this problem. If you look at it as "the chance of me having any of the the three gold balls is equally likely", then the answer is obviously 2/3. But, imagine you have a literally infinite number of silver balls in the second box. It is arbitrarily certain you are in the full gold box, no?
If the boxes had no silver, the answer is definitely 2/3, but you only pull gold in silver 1/2 of the time. I.e., you are only tricked 1/2 of the time. I dont believe the answer is 1/2 but this should be factored into the problem somehow I think.
No matter what, the odds of you being in the gold box are at least greater than 1/2 and probably more like greater than 2/3.

>>11759061
>picked a gold ball from the split box
>1/2 chance there's another gold ball in the split box
you double-solved the split box

>>11759019
3 ways to pick 1st
2 ways to pick 2nd
2/3

>>11759184

wtf brailets the boxes dont matter its like putting all the balls in a hat, the probability is favorable cases / all cases so its 2/5

>>11759038
To mislead retards into answering 1/2.

>>11759227
based

>>11759184
The OP states that you HAVE pulled a gold ball already, so how often you pull gold from the gold/silver box before that doesn't matter (well, it only matters in giving you a guaranteed silver NEXT).

Are people answering anything other than .5 trolling? There no way /sci/ is that stupid.

>>11760360
>so how often you pull gold from the gold/silver box before that doesn't matter
Bayes' theorem disagrees.

>>11760360
Literally no way. You picked a gold from a box with a literally infinite number of silver balls, or you pulled a gold ball from a box with only gold balls. This clearly affects thw probability. Just bevause yyou have a gold ball doesnt mwan its equally likely you got a 100% gold ball as a < .000000000000000001% gold ball.

>>11760386
I mean seriously, just imagine you are doing this, and everytime you get a gold ball you try to get a second. 1/3 of those times you are not going to get the infinitely unlikely ball. That would allow you to break probabilities by suddenly making specific, single things far more or less likely simply by adding different choices.

>>11760380
there's some disturbing disinformation campaign going on. I think they're trying to drive people crazy
https://youtu.be/wjKQQpPVifY
like if they call u schizo enough you'll eventually believe it. idk they're probably retards

>>11759061
No idiot
There are 3 gold balls. Its more likely that you drew the gold ball out of the box with 2 gold balls than the box with 1 gold ball.

It's 0.5 you retards.
You either are going to get a golden ball next or not

>>11759033
fuck
he's right
I am an idiot
t. reformed 50 percenter

Is this some sort of in joke that I'm too much of a newfag to get? I'm starting to think it is.

>>11760465
It's just an old bait image that sheds light on how many on /sci/ can't comprehend basic math

>>11760572
>>11760465
Only the chosen with 3 gold balls shall comprehend

>>11759019
2/3.
The reason why this problem is so difficult is because of the boxes, they are a misdirection.
You can get rid of the boxes and the problem then becomes much clearer.

You have 6 balls
You randomly select a ball,
Given the ball you selected was 1,2 or 3
What is the probability that the ball was 1 or 2

>>11759019
I need to put my hand into a 2-goldballs box from the start so it's 1/3

>>11760615
ok now do it with the GG box having 1000 gold balls.
(protip: with boxes it's still 2/3)

>>11759019
not this shit again, just go read Hoel, Port, Stone's Probability Theory. Holy fuck /sci/ is full of fucking brainlets.

>>11760659
>Hoel, Port, Stone's Probability Theory
it says 2/5, so there's that

>>11760669
first I was dogmatically convinced it was 1/2 and nothing would change my mind because duh. then I realized my ignorance and understood the fault in my reasoning, and accepted the truth of 2/3. now youre telling me it's 2 fucking 5ths
I'm going to bed

>>11760693
>taking anything in a Yak inseminator hentai pic site seriously

I allways knew this board was full of retards.
2/3?? You are not even sophomores fuck you

>>11759019
>post a question
>samefag the correct answer
>sit back

>>11759019
50%, either happens or it doesn't. This goes for all "probability" by the way.

>>11759019
>You should be able to solve this, right?
Yup. I ran a simulation 2 million times, and I got:

gold count: 666038
silver count: 334032

Here is the source code that I used. (Paste it into a html file with script tags around it.)


const G = 0; // "gold" is encoded as 0
const S = 1; // "silver" is encoded as 1
let box = [ [G,G], [G,S], [S,S] ]; // the contents of the boxes
let count = [0, 0]; // the counts for how many G and S balls were the second ball
for (let i = 0; i < 2_000_000; i++)
{
let x = Math.floor(Math.random() * 3); // random box number (0 to 2)
let y = Math.floor(Math.random() * 2); // random ball number (0 or 1)
//
// box[x] is a random box
// box[x][y] is a random ball from within box[x]
// count[G] is how many gold balls we have counted so far
// count[S] is how many silver balls we have counted so far
//
if (box[x][y] == G) // if the randomly-selected ball is gold
{
let secondball = box[x][1-y]; // the second ball in the selected box
count[secondball]++; // increment the counter for the second ball
}
}
document.write("gold count: ", count[G], "<br>");
document.write("silver count: ", count[S], "<br>");
document.write("total: ", count[G] + count[S]);


here we go again.
the question is about which box you picked and you already have a golden ball in your hand.
since you have a golden ball in you hand then you are certain it's not the 2 silver box so you are either left with a box with 1 gold or one silver

>>11759019
It's 2/3rds because the chance of getting a gold ball in the GG box is two times and the GS box one time.

>>11762739
Indeed, and it's twice as likely you got that ball from the box with two gold as it is you got it from the box with one gold. 2/3.

>>11759019
There are 6 balls you could pick first, and you have a 1/6 chance of picking each one:

If you pick gold ball #1 from box 1, then the other ball in the box is also gold.
If you pick gold ball #2 from box 1, then the other ball in the box is also gold.
If you pick the gold ball from box 2, then the other ball in the box is silver.
If you pick the silver ball from box 2, then the experiment ends with no result.
If you pick silver ball #1 from box 3, then the experiment ends with no result.
If you pick silver ball #2 from box 3, then the experiment ends with no result.

If you look only at the experiments that yield a result, then you will get a gold ball 2/3 of the time.

>>11759038
>What's the point of box on the right?

The box on the right is not important. Read:
>>11762769
and you'll see that picking any ball from the right box causes the experiment to end with no result, so it has no effect on the answer.

Therefore, the answer would be the same if you got rid of the right box. It would also be the same if you added 100 more boxes each with 2 silver balls.

50/50
6 possible outcomes and you have a 1/3 chance of removing the middle gold in pick one.

>>11759027
>>11759064
>>11760380
>>11760410
>>11762689
These.

>>11762810
That's the probability of picking a gold ball first, not the probability of picking a second gold ball.

>>11762810
>6 possible outcomes
????
But there's only 4 balls.

>>11762831
Still 50/50

Do you have a gold ball from box A, or from box B?

>>11759019
Holy shit I actually just derived the correct solution and all further correct solutions for this problem.
Of these three boxes, you have two gold, one silver and gold, and two silver. 1/3 of the time you get 2 gold balls, 1/6 of the time you get a gold and silver, 1/6 you get a silver and gold, and 1/3 of the time you get a double silver.
So, your chanves of getting a good result is 1/3. Your chsnce of a false positive is 1/6. That means, of all first gold times, you gecond gold twice as many times. Because, 1/3 ÷ 1/6 is two. I.e., for every 1 false positive gold, you get two correct golds. Or, in other words, it is a two thirds chancw you get a second gold ball. HOWEVER, if you add a second silver ball to the halfsie box, my math says you then have a 3/4 of getting a gold ball the second time you pull a ball out. This is logical, as it becomes less likely to get the gold ball in a larger and larger silver box while the double gold ball boxes probability remains the same. Also, my math, since it is a ratio, stays consistent no matter how many silver-full boxes you add.
I feel very accomplished right now.

>>11762955
I normally don't respond but congratulations in figuring out a 5th grade math problem that has had it's solution posted 50 times a thread, 2 threads per day for what 10 years running

You should feel bad

>>11759019
P(gold2|gold1)=P(gonld1 and gold2)/P(gold1)=(1/3)/(3/6)=2/3
/thread

>>11762955
hahahahahahahahha

>>11762996
>gonld1

Fail.

>>11762689
Ah, yes. By that line of reasoning, I should win the lottery every two days on average. Either I win or I don't.

>>11763153
The probability of the machine picking your numbers is not 50%.

The probability of picking up a second gold ball is 50%.

>>11762973
You are less than nothing. No amount of acting superior to me will ever fulfill you. You are cursed to live your life.

>>11759227
ThIs is what I thought too.

>>11760410
Only two of the five balls left are gold, you've already pulled one.

> muh balls

>>11759019
First try: 50%
Second try: 40%

Answer is 40% probability

>>11765870
Adding to this, the probability of picking two gold balls in a row is 20%

>>11759019