You can solve this, can't you user?

Im not sure what you did, but you fucked up

Sorry lads, not sure how to format code on this board :^)

hastebin.com/raw/erumuyexus

Sorry lads, it looks like I messed up the code, it should be if "ball == gold", not if "ball_choice == gold" (ball_choice is just the index). I need some type safety, anyways corrected answer is 2/3 :^)

If you already have a gold ball in your hand and you have to draw from the same box, there's a fifty-fifty chance that the box you're limited to is the one that has not one, but two balls. If this was a sporting event, you'd be hard-pressed to find a bookie to take the bet in either direction. I don't math, so maybe I'm wrong.

Yeah you shouldn't use python for that reason. Functional languages are better for math.

2-1, in favor of two gold balls.

Now, the reason that it's 2-1 in favor of the two gold balls is because we start out with six balls, eliminating the two silvers in the silver box, as we pulled a gold one out. That leaves two gold and one silver unseen. Therefore, the odds are 2-1 that the other ball is gold.

thats not the final box, it's the second box

It's 50/50.
Because you have a gold ball, that means you either: Got the silver+gold box, or the gold+gold box.
If it was the silver+gold, then you must pull out a silver next.
If it was the gold+gold than you must pull out out a gold next.
There is a 50/50 chance of it being gold+gold. So therefore it is a 50/50 chance you will pull out a gold next.

>If you already have a gold ball in your hand and you have to draw from the same box, there's a fifty-fifty chance that the box you're limited to is the one that has not one, but two balls.
False. If you have a gold ball in your hand it is twice as likely you picked the box with two gold balls in it than the box with one gold ball.

NVM this guy is right.

False. See

it's a 50% chance to draw a gold ball in the first place: 1/3 for the double gold box plus (1/3) / 2 for the mixed box (1/3 for the box and half of that for the golden ball).

It's a 50% chance to draw another golden ball after you have made your choice and already gotten a golden ball. The double silver box doesn't factor in, because it doesn't satisfy the initial condition of being able to draw the first golden ball. The double golden ball will net another golden ball. The mixed box will never yield a golden ball, as you already have the one from it in your hand.

You pick boxes, not balls.

You are a biologist traveling in the rainforest. You are bitten by a poisonous snake. Luckily, you know that the antidote for this poison is secreted by the female of a certain species of frog native to this rainforest. You remember that females and males of this species look exactly the same, and can only be distinguished by the distinctive croaking of the male. You also remember that the population is split evenly between females and males. Amazingly, you spot a frog of this species in front of you. At the same time you hear the distinctive croak of a male of the species behind you. You turn around and see two frogs where the croak came from. You are starting to fade out and only have enough time to run to the frog in front of you and lick it or to the frogs behind you and lick them. Which choice will maximize your chance of survival?

You could have pulled either of the two gold balls in the first box. You must have pulled the gold ball out of the two balls in the gold/silver box. With two gold balls unseen, and only one silver ball unseen, the odds are 2-1 in favor of the gold only box.

>It's a 50% chance to draw another golden ball after you have made your choice and already gotten a golden ball.
No. See

You aren't taking the odds from the beginning, just from the point where you already have one gold ball in your hand. Previous factors are inconsequential.

Yes, see
>You pick boxes, not balls.

>just from the point where you already have one gold ball in your hand
At which point you are more likely to have picked one box over another

This guy got it

>You aren't taking the odds from the beginning, just from the point where you already have one gold ball in your hand.
That's exactly what I'm doing.

>Previous factors are inconsequential.
What is the chance of collecting cash from the lottery given you have a winning ticket? Oh I guess it's very small since having the winning ticket came before you collected the cash!

But that post is wrong. you can simplify the problem to two boxes with a golden ball and a silver ball respectively and just ask someone to pick a box at random.

The second ball doesn't matter.

And holding a gold ball means its more likely you picked the first box than the second

You pick a box and then you pick a ball. Since you picked a gold ball it is more likely you chose the box with two gold balls in it.

Nope, see:

...which is a factor that no longer matters. You're left with one ball that can either be gold or silver. there are only two possible outcomes from that point and only one available ball to pick. It's 50/50.

>You pick box at random
>Random meaning equal distribution over time
>This means you pick one box more than the other

F-

Afraid not

en.wikipedia.org/wiki/Bertrand's_box_paradox

>you can simplify the problem to two boxes with a golden ball and a silver ball respectively and just ask someone to pick a box at random.
No, that would be a completely different problem. If you are too stubborn to get it, I suggest you take two coins, flip them, and count how many times both are heads out of the times at least one is heads. You'll find it's 2/3, not 1/2.

You pick a random box and take a gold ball out if it. Given that you pulled a gold ball of the box you chose, its more likely to be one box than the others. Of the 3 original boxes, the SS box has a 0/3 chance of being the box you picked because it has no gold balls. The GS box has a 1/3 chance of being the box you picked, because of the 3 gold balls you might be holding, the GS box has 1. the GG box has a 2/3 chance of being the box you picked, because it contains 2 of the 3 gold balls you might be holding in your hand

Its unintuitive, but true

Probability is simply a measure of what knowledge you have at a certain time. Picking a gold ball tells you that you probably chose from the box with two gold balls when you chose randomly. If you don't think the information you have can change the probability that something occurred, then you would think that having the winning lottery ticket does not change your probability of collecting the jackpot to (almost) 1 from what was previously a very small probability.

Newfag here. How do I sage this crap? I've seen this exact thread before.

Sage goes in all fields.

And answer this if you think you know everything.

Dont open the thread

According to the way the question is phrased here, only the odds of the second ball are in question. The paradox you presented covers the overall odds of collecting two objects of the same color from a possible three combinations. The way you interpreted it makes sense if you use your interpretation of the question. If you take it as it's stated, there's only a 50/50 chance.

More proof that OP is a faggot.

The question is clear, there is only one correct interpretation and you are not making it

>According to the way the question is phrased here, only the odds of the second ball are in question.
The odds of the second ball are completely determined by the probability that you chose the box with two golds. It's the same exact problem.

The only way to identify the needed frog is by it's croak? Only the two behind you made a noise, so if you can lick them both behind you, I'd say there's a 100% chance that you'd survive if you grabbed the two behind you. Did you mean to phrase it that way?

>The only way to identify the needed frog is by it's croak?
Can you not read? The antidote is only secreted by females. The croak is distinct to males.

>I suggest you take two coins, flip them, and count how many times both are heads out of the times at least one is heads. You'll find it's 2/3, not 1/2.

Actually I'm simulating this right now and it's exactly 50%

Just so we're understanding your example here:
>Flip two coins
>If one OR the other coin is heads, count it as one head
>If BOTH are heads, count it as both heads

You're saying this should result 2/3 both head vs 1/3 one head?

the question is clearly stated as: "What is the probability that the next ball you take from the same box will also be gold?"

It's not asking for the combined probability, only the probability of the second ball, and it can only be one of two choices.

I can read just fine. No problem with comprehension, either. Maybe you'd better reread what you wrote.

>and it can only be one of two choices.
Yes, and one is more likely than the other

Females secrete the antidote:
>Luckily, you know that the antidote for this poison is secreted by the female of a certain species of frog native to this rainforest.

The croak is distinct to males:
>You remember that females and males of this species look exactly the same, and can only be distinguished by the distinctive croaking of the male.

Next time someone tells you to read, do it.

Lets be clear - the question is only asking the result of the equivalent of one coin toss.

You win this one, faggot.
Your question still sucks and I was the only one to respond. You've trolled successfully.

No, it's not. The wikipedia article explains it perfectly and is exactly the same as the problem asked.

You wouldn't get the right answer even if you read it correctly.

You are referring to the overall odds. As stated, this question isn't asking for the overall odds of two choices, only the odds of the second choice. 50/50

The wiki article would apply if OP had phrased the question right.

Maybe not, but I've had sex with a real girl.

OPs question is phrased perfectly, you are just failing to comprehend it correctly. You are answering the question you think its asking, not the actual question

Hey fucker, I want an answer.

No, I'm taking the literal meaning. You're inferring that the answer is the paradox you presented. I may not maths, but I English very well.

I cooked up a picture because who doesn't like pictures?

You're still considering the other boxes in the overall equation. The question is clearly phrased as only wanting the odds of the second ball. Regardless of how many balls or combinations you started with, the odds of the last ball being silver or gold is 50/50

There is no paradox. You chose a box, and are then given information about the box you chose. The information you are given means that the box you chose is more likely to be one than the others

>The question is clearly phrased as only wanting the odds of the second ball
This is identical to asking which box you chose. If the next ball is gold you chose box A, if the next ball is silver you chose box B

>What is the probability that the next ball you take from the same box will also be gold
So according to you "same box" does not refer to anything, and "next ball" does not refer to the gold ball you picked out of that box. Because you are so good at English.

at the point where the question picks up in the overall equation, you have one box with one ball that is either gold or silver, and you have to choose that one. 50/50

Where's a lawyer when you need one? I can't explain the question any better. You're inferring a complex equation when all that's being asked about is the second ball.

You think I'm just bad at math, but you're reading into the question too deeply.

Sure you did buddy, sure you did. "Real girls" get so horny around illiteracy.

If you were the one that included the wiki link, it literally says "paradox" in the article. I was just pulling from your source. Blame yourself.

>at the point where the question picks up in the overall equation, you have one box with one ball that is either gold or silver, and you have to choose that one. 50/50
The box with the gold ball is twice as likely. You are just assuming it's 50/50 without thinking about what information you have.

Right. Two choices.

Don'y be jel

At the point the question is asked, you have already picked a box. You are given information about that box, namely that it contains at least one gold ball. This information affects the odds that the box you picked is box a or box b or box c

So I just rand the whole thing in a simulator. Wanna guess the result? It's 50%.

Or I did a really stupid mistake, if so, please point me towards it so I can fix it.

>Right. Two choices.
The choice was made at the start of the question. Its asking what the odds are that you made a specific choice given the information you have been given. You are not making a new choice at the point the question is asked

You're still factoring in the second and third boxes. They no longer apply, as that stage is in the past. What remains is the same possibility of a silver or a gold ball coming next. 50/50

You're still inferring information that isn't there.

# of times the second ball was gold:
33472

# of times the second ball was not gold:
16646

Yup, clearly the same...

>You are still factoring in all the information you are given to calculate a probability
Oh wow, what a mistake.

There are 3 boxes. The first box contains a thousand gold balls. The second contains 999 silver balls and 1 gold ball. The third box contains a thousand gold balls. You randomly pick a box, reach in and pull out a gold ball. What are the odds that you are holding the first box?

You're ignoring information that is there. It's funny because you're fine with reducing the chance you took from the box with two silver from 1/3 to 0, but you won't modulate the other probabilities. You're being hypocritical.

Sorry that should be the third box contains 1000 silver balls, my bad

It's not asking for the odds from three boxes anymore. Essentially, once you've removed a gold ball from one box, the third is eliminated. The second is immediately eliminated by default since you can't choose from it anyway, so it doesn't matter what's in it, so the odds of picking a gold ball out of one box with only one choice and two possible outcomes is 50/50.

Sorry, percentage was wrong, here is the code for yourself to try: jsfiddle.net/0kz9ox9j/1/

Don't misquote me.

I got something different.

That changes the problem entirely.

Its asking the odds of your original choice out of the 3 boxes having been the first box

...

Look at this, you can literally run the experiment yourself and look at the evidence.

Its exactly the same problem

You may be good at math, but the question was poorly phrased. If you interpret it the way you did, you're right. If interpreted literally, I am.

How so, sports fan?

You mean like this?

All I did was make the numbers bigger and more obvious, the core problem is identical. You are being asked what the odds are that you randomly chose a specific box, given that you pulled a gold ball out of that box.

Whats the answer to my question by the way?

>It's not asking for the odds from three boxes anymore.
It's always been from three boxes. That is the context of the question, which it clearly refers to. Why would you ignore what the question refers to?

>Essentially, once you've removed a gold ball from one box, the third is eliminated.
So you ARE taking into account what happened before the question. Hypocrite.

Don't misinterpret the problem, or my paraphrase.

Just number the balls. Then magically, it isn't possible to achieve the 50/50 answer.

The question is phrased fine. You are not interpreting the question literally, you are ignoring most of the sentence.