/sci/ - Science & Math

[Anonymous No.11933368]

No matter how I look at it, the answer I get is 50%. Yet so many people say it's 2/3rd. Am I wrong? This isn't like the Monty hall problem, it's pure chance wether you have the box with two gold balls or the box with one gold one silver ball right?

[Anonymous No.11933382]

>>11933368
Your first choice is guaranteed to be a gold ball, meaning that only 3 scenarios exist
>Pick gold ball A in the leftmost box, which also contains gold ball B
>Pick gold ball B in the leftmost box, which also contains gold ball A
>Pick the gold ball in the middle box, which also has a silver ball
Because you know that you're initially going to get a gold ball, and of the possible scenarios, 2 involve you picking the box that has 2 gold balls and 1 that doesn't, your chances of getting two gold ball draws in a row are 2/3

[Anonymous No.11933384]

>>11933368
It’s more complicated than that because you have to consider the odds you picked a gold ball to begin with. I can’t quite conceptualize the math yet, but it’s premature to say 50%

[Anonymous No.11933387]

>>11933382
Ah yeah this. You’re not looking at the odds of the boxes, you’re looking at the odds of the ball you picked. Two gold balls lie in one box, one lies in the other, so 2/3

[Anonymous No.11933410]

>>11933384
I think you're wrong. The problem states that you already picked a gold ball, so the probability of that piece doesn't matter. It is only asking for the probability of the second choice

[Anonymous No.11933413]

>>11933382

So if there was 100 Gold balls in Box A, the chance of me getting a gold ball next would be 99%?

[Anonymous No.11933561]

>>11933413
100/101 actually

[Anonymous No.11933603]

>>11933413
Increasing the numbers is a good way of thinking about the problem. Imagine box A had 1,000,000 gold balls; C had 1,000,000 silver balls; and B had 1 gold ball + 999,999 silver balls. If you pull out a gold ball, do you believe it is equally likely to have come from box B as box A?

A similar thing can be done with the Month Hall Paradox. Imagine it with a million doors, rather than just 3.

[Anonymous No.11933608]

>>11933413
>>11933561
Wrong.

(1/3)(100/100)/((1/3)(100/100)+(1/3)(1/2)) = 2/3

[Anonymous No.11933618]

>>11933410
>The problem states that you already picked a gold ball, so the probability of that piece doesn't matter.
Incorrect. This would only be true if the color of the second ball is independent from the first, but it isn't.

[Anonymous No.11933634]

>this shitty jpg
I. The correct answer, if you read the question as written in this shitty jpg, is 1/2.
II. The incorrect answer, if you hallucinate Bertrand's box into this shitty jpg, is 2/3.
III. The "correct" answer, if you ever see this shitty jpg in a standardized test, is the incorrect answer, 2/3.

Your mission, should you choose to accept it, is to beat the life out of this shitty jpg until it disappears from every last corner of the internet.

N.b. The last time this shitty jpg was posted, it was kill-switched after two probability 101 brainlets blew themselves the fuck out by answering (no,no) and (yes,yes) to the same two questions.

[Anonymous No.11933637]

>>11933410
You only made one choice, which is the ball you picked. Based off the location of the gold balls, 2 of them are in one box, one of them is in the other.

[Anonymous No.11933642]

>>11933634
>I. The correct answer, if you read the question as written in this shitty jpg, is 1/2.
Please explain.

[Anonymous No.11933645]

>>11933603
I don’t know if I agree with this line of thinking.

Let’s say you had 1 million gold balls in box A, 1 gold ball and 1 silver ball in box B.

The odds that the next ball you pick being silver is definitely not 1 in a million

[Anonymous No.11933646]

>>11933637
You chose a box and a ball. Counting only balls will give you the incorrect answer if the number of balls in the boxes differ.

[Anonymous No.11933659]

>>11933645
Correct, it's (1/3)(1/2)/((1/3)(1/2)+(1/3)(1)) = 2/3

But if box B has 1 gold and 999,999 silver then it's (1/3)(1/1000000)/((1/3)(1/1000000)+(1/3)(1)) = 1/1000001

[Anonymous No.11933677]

>>11933659
Can you explain how you’re getting these numbers? This would be more easy to comprehend if you did

[Anonymous No.11933684]

>>11933642
2/3 answers the conditional: picked,pick.
1/2 answers the unconditional: pick.

[Anonymous No.11933689]

>>11933368
2/3

[Anonymous No.11933690]

>>11933677
1/3 = chance of choosing a particular box

1 = chance of choosing gold from the all gold box

1/2 = chance of choosing gold from the box with 1 gold and 1 silver.

1/1000000 = chance of choosing gold from the box with 1 gold and 999,999 silver

The chance of the second ball being a certain color is the ratio of the chance of the first ball being a gold ball from the box whose other ball is that color to the chance of choosing a gold ball first.

[Anonymous No.11933694]

>>11933684
The question is conditional, otherwise "next ball" is meaningless.

[Anonymous No.11933731]

>>11933694
For it to be conditional, you need to ask: "what's the probability that you picked a gold ball and then you pick a gold ball?" The question as written in this shitty jpg only asks: "what's the probability that you pick a gold ball?"—which describes a single memoryless pick between two possible boxes, where one is 2/3 likely and the other is 1/3 likely.
1/2 * 2/3 + 1/2 * 1/3 = 1/3 + 1/6 = 1/2

[Anonymous No.11933732]

[Anonymous No.11933747]

>>11933732
Agreed. It’s 50%. Either you do or you don’t

[Anonymous No.11933752]

>>11933731
>For it to be conditional, you need to ask: "what's the probability that you picked a gold ball and then you pick a gold ball?"
No, that's not even a conditional. That would be the chance you initially chose the first box, which is 1/3. The verb tenses don't change anything. You have no clue what you're talking about.

>The question as written in this shitty jpg only asks: "what's the probability that you pick a gold ball?"
No it doesn't. Do you seriously think both changing the wording of the problem and ignoring its context is going to fool anyone?

[Anonymous No.11933764]

>>11933752
>No, that's not even a conditional. That would be the chance you initially chose the first box, which is 1/3.
No, 1/3 would be "what's the probability that you PICK a gold ball and then you pick a gold ball?"

[Anonymous No.11933774]

>>11933764
That’s a different problem.

The original problem specifically states “next pick from the same box”, which is not a memoryless pick.

It’s the equivalent of saying you picked the first 5 numbers of the lottery correctly, what are the odds you win the lotto? At that point it’s not 1 in a trillion, it’s 1/55

[Anonymous No.11933775]

>>11933764
Nope, tense doesn't tell you that a problem is conditional. The chance you won the lottery is the same as the chance of winning the lottery.

[Anonymous No.11933784]

>>11933775
Tense had nothing to do with it. I’m the definition of the problem it’s eliminating outcomes.

Given you’re 5 for 5 for winning the lotto, and you just need a 6th number, the odds of you winning the lotto becomes 1 in 55 because there are only 55 outcomes for that ticket. Any outcome where only 4 or less numbers are correct are removed from the problem.

[Anonymous No.11933786]

What if im king midas

[Anonymous No.11933788]

>>11933784
>I’m the definition
I meant in the definition

[Anonymous No.11933789]

>>11933774
I know it's a different problem, that's my point.
The set up to the question says we PICKED a gold ball, which gives us two box states of 1/3 and 2/3. A single choice between 1/3 and 2/3 gives us 1/2, as per arithmetic above.

[Anonymous No.11933793]

>>11933775
>The chance you won the lottery is the same as the chance of winning the lottery.
Lmao this is where you retards blew yourselves the fuck out last time and had to delete your own thread.

[Anonymous No.11933820]

You have 1 choice and selection of 3 balls, 2 of the 3 balls are gold.

2/3.

[Anonymous No.11933846]

>>11933775
>>11933784
Lol both of your verbal IQs are so low that you're now literally arguing against yourselves trying to defend the same stupid point.

The chance that you won the lottery and can afford to buy a new car is high, because you already WON it.
The chance that you win the lottery and can afford to buy a new car is low, because you haven't WON it yet.

[Anonymous No.11933862]

37,5?

[Anonymous No.11933867]

>>11933784
>Tense had nothing to do with it.
Them picked vs. pick has nothing to do with it.

>I’m the definition of the problem it’s eliminating outcomes.
Which problem?

>Given you’re 5 for 5 for winning the lotto, and you just need a 6th number, the odds of you winning the lotto becomes 1 in 55 because there are only 55 outcomes for that ticket.
"Given X" is a condition. The probability of X and Y" is not a conditional.

[Anonymous No.11933873]

>>11933789
>The set up to the question says we PICKED a gold ball, which gives us two box states of 1/3 and 2/3. A single choice between 1/3 and 2/3 gives us 1/2, as per arithmetic above.
Gibberish. The problem tells us there's a 2/3 chance we choose from the first box and a 1/3 chance we chose from the second. so the answer is 2/3.

[Anonymous No.11933874]

>>11933645
>The odds that the next ball you pick being silver is definitely not 1 in a million
>>11933659
>Correct, it's (1/3)(1/2)/((1/3)(1/2)+(1/3)(1)) = 2/3
I think it is 1/3, not 2/3
Increasing the number of gold balls in the first box while leaving the ratio of silver to gold unchanged has absolutely ZERO effect
half of your second boxes will be discarded (due to picking a silver ball), so you will have twice as many first boxes as second boxes in your trials.

[Anonymous No.11933879]

>>11933793
???

>>11933820
Correct answer, wrong reasoning. See >>11933646

[Anonymous No.11933883]

>>11933775
>The chance you won the lottery is the same as the chance of winning the lottery.
this is true, but in this particular case you are given the additional information that you have in fact won the lottery already.

[Anonymous No.11933891]

>>11933846
>The chance that you won the lottery and can afford to buy a new car is high, because you already WON it.
Nowhere was it stated that you already won it. Asking for the chance you won the lottery doesn't mean you win it. Learn English.

[Anonymous No.11933895]

>>11933874
>I think it is 1/3, not 2/3
Why?

>Increasing the number of gold balls in the first box while leaving the ratio of silver to gold unchanged has absolutely ZERO effect
Yes, which is why counting balls as if they are all equally likely can give the wrong answer.

[Anonymous No.11933897]

>>11933883
Which case?

[Anonymous No.11933903]

>>11933891
>Nowhere was it stated that you already won it.
dude it literally says in the OP that you pick a box and take a ball and that the resulting ball is gold
you know the universe you are in is one where your first ball was gold
you are finding the probability that your next ball is also gold; you are NOT finding the probability that your first ball was gold, because you already know your first pick was a gold ball.

>>11933897
The OP case (and by extension the analogical case of already having won the lottery).

[Anonymous No.11933908]

>>11933903
>dude it literally says in the OP
Are you incapable of reading? We were not talking about OP's problem.

[Anonymous No.11933909]

>>11933895
>>I think it is 1/3, not 2/3
>Why?
read the rest of the post

>>11933895
>Yes, which is why counting balls as if they are all equally likely can give the wrong answer.
not really.
All the gold balls are equally likely.
It is just that there are more gold balls in the first box, so it is more likely you picked one of the gold balls in the first box.

[Anonymous No.11933911]

>>11933908
link the problem statement of the problem you are talking about, then.
I see no post that clearly states the lottery problem in a way that is not a halfassed analogy to the OP post.

[Anonymous No.11933916]

>>11933879
Brainlet

[Anonymous No.11933927]

>>11933909
>read the rest of the post
I did, none of it disagreed with anything I said. If the first box is twice as likely as the second then that's 2/3, not 1/3.

>not really.
Then tell me what the answer if the second box has 2 gold and 2 silver? If we only count balls then we have

First box: G1 -> G2
First box: G2 -> G1
Second box: G1 -> G2
Second box: G1 -> S1
Second box: G1 -> S2
Second box: G2 -> G1
Second box: G2 -> S1
Second box: G2 -> S2

Which would give an answer of 4/8 not 2/3. So clearly this method fails.

[Anonymous No.11933931]

>>11933911
>link the problem statement of the problem you are talking about, then.
Read the thread: >>11933775

>>11933916
Not an argument. Try again.

[Anonymous No.11933933]

>>11933927
>I did, none of it disagreed with anything I said. If the first box is twice as likely as the second then that's 2/3, not 1/3.
2/3 the next ball is a gold ball
1/3 the next ball is a silver ball
one of the two anons quoted in >>11933874 might have mixed the two up

[Anonymous No.11933934]

>>11933368
3 gold balls each gold ball has 1/3rd probability to be the ball you pulled so the chance that it's from box A is 2/3rds.

[Anonymous No.11933939]

>>11933933
The second person you quoted is me and I was calculating the chance the next ball is gold. You responded by saying it's 1/3.

[Anonymous No.11933943]

>>11933873
No, it eliminates the box containing two silver balls, leaving us with a box containing one gold ball—which is 2/3 likely—and a box containing one silver ball—which is 1/3 likely. The single unconditional choice between those two boxes is 1/2 * 2/3 + 1/2 * 1/3 = 1/3 + 1/6 = 1/2.

[Anonymous No.11933947]

>>11933927
>>not really.
>Then tell me what the answer if the second box has 2 gold and 2 silver?
haha, shit
I might have brainfarted with my whole thing about ratio of gold to silver, then.
it only applies if there is [1 gold 1 silver] in the second box

>>11933931
>>11933775
>The chance you won the lottery is the same as the chance of winning the lottery.
I can accept this statement as true.
It is a different situation from the OP post, though, because in the OP post you already know your first pick was gold.
Your lottery statement is completely off-topic and has nothing to do with conditional probabilities.

[Anonymous No.11933951]

>>11933891
>Nowhere was it stated that you already won it.
>won
"Won" refers to something that already happened. The past tense literally means something already happened in the past, you absolute buffoon.

[Anonymous No.11933955]

>>11933939
>The second person you quoted is me and I was calculating the chance the next ball is gold. You responded by saying it's 1/3.
Both the post you quoted and I were talking about the chance of the next ball being silver (I agree with gold being 2/3).
This is the post you quoted: >>11933645
>I don’t know if I agree with this line of thinking.
>Let’s say you had 1 million gold balls in box A, 1 gold ball and 1 silver ball in box B.
>The odds that the next ball you pick being silver is definitely not 1 in a million
this is your repsonse: >>11933659
>Correct, it's (1/3)(1/2)/((1/3)(1/2)+(1/3)(1)) = 2/3

[Anonymous No.11933960]

>>11933891
>Asking for the chance you won the lottery doesn't mean you win it.
this is true. On the other hand,
asking for the chance that you won the lottery if one of your tickets was a winning ticket
is equivalent to saying you won the lottery.

[Anonymous No.11933965]

Praise Jebus we's already > 3/16 of the way to the bump limit of this excruciatingly shitty jpg.

[Anonymous No.11933966]

>>11933943
>No, it eliminates the box containing two silver balls,
And it also eliminates choosing silver from the second box. Nice logic, retard.

>The single unconditional choice between those two boxes
This is utter nonsense. How is choosing between the boxes answering the probability your next ball will be gold? You already have the chance you're in the first box, 2/3.

[Anonymous No.11933968]

continuing on this line of reasoning >>11933960
saying that you picked a gold ball and asking for the chance that the next ball you pick is also gold
...is equivalent to saying that you have already picked a gold ball.

[Anonymous No.11933973]

>>11933966
>And it also eliminates choosing silver from the second box. Nice logic, retard.
Wow no shit man, where do think 1/3 and 2/3 came from?

[Anonymous No.11933976]

>>11933965
I know you are both OP and the anon sperging out about verb tenses
and that you make this thread several times a week

I hope you get banned

[Anonymous No.11933980]

>>11933968
Finally, someone ITT who knows how read English. You're a rare bird here, amigo.

[Anonymous No.11933988]

>>11933976
Nope, absolutely not. I hate this shitty jpg and hope the jpg itself gets banned.

I hope you get banned for false reporting, but only after you add a few more posts to this thread to help kill the shitty jpg.

[Anonymous No.11933994]

>>11933988
it is clearly a png

[Anonymous No.11934005]

>>11933966
>You already have the chance you're in the first box, 2/3.
That's picked,pick—a present pick conditional on a past pick.

[Anonymous No.11934011]

>>11933994
Touché. I admit my error. The last few times it was a jpg.

I, unlike some people in this thread, am always happy to be wrong and learn from my mistakes.

[Anonymous No.11934032]

>>11933947
>I might have brainfarted with my whole thing about ratio of gold to silver, then.
No, you're correct that keeping the ratios the same doesn't change the answer. However you need to realize that the choice between boxes is also relevant.

[Anonymous No.11934064]

>>11933951
>"Won" refers to something that already happened.
Yes, i.e. what is the probability you won the lottery = what is the probability you winning the lottery already happened. This does not imply it already happened. You can try to remove context and obfuscate all you want, it won't help you.

[Anonymous No.11934071]

>>11933960
>On the other hand,
>asking for the chance that you won the lottery if one of your tickets was a winning ticket
>is equivalent to saying you won the lottery.
Yes, so what?

[Anonymous No.11934077]

>>11933684
Omg not the pick picked picket pick sperg

[Anonymous No.11934079]

>>11933973
It probably came from stone other person's post, since you're incapable of answering a simple probability question without devolving into gibberish.

[Anonymous No.11934083]

>>11934005
Gibberish. The chance you're in the first box is 2/3, that's the answer. Verb tenses don't change that.

[Anonymous No.11934084]

>>11933410
There was a video I watched about how statistics change as soon as you "know" a piece of information.

[Anonymous No.11934092]

>>11934064
>what is the probability you won the lottery
> = what is the probability you winning the lottery already happened
>This does not imply it already happened
Lmfao. Oh boy is this delicious.

[Anonymous No.11934099]

import random
gold = 0
silver = 0
for i in range(1000000):
boxes = [[1,1],[1,0],[0,0]]
box = random.choice(boxes) # choose a random box
ball1 = random.choice(box) # choose a random ball
box.remove(ball1) # remove from the box
if ball1 == 0:
next # Skip if we didn't pick gold
ball2 = random.choice(box) # choose another random ball
if ball2 == 0: # add to the count
silver += 1
else:
gold += 1
print "Probability Gold = %g" % (float(gold)/float(gold+silver))
> Probability Gold = 0.500088

[Anonymous No.11934102]

>>11934077
>>11934079
>stone other person's post
Rtft you fucking retard stoner.
>>11934083
Nope, 2/3 is picked,pick; 1/2 is pick; 1/3 is pick,pick.

[Anonymous No.11934103]

>>11933368
0%.

You pick a box at random, but it's mentioned that the FINAL box has one gold and one silver. You already picked the gold.

Fucking morons. Fuck.

[Anonymous No.11934115]

>>11934092
What is the probability you were a fag when you made that post? This means you are a fag. QED.

[Anonymous No.11934125]

>>11934099
>ball2 = random.choice(box) # choose another random ball
Wrong.

[Anonymous No.11934129]

>>11934102
Nope, verb tenses are irrelevant. Try again, retard.

[Anonymous No.11934145]

>>11934115
No, that means you either were or weren't a fag, and that we already know the result because it already happened in the past you drooling ESL 101 abortion.

[Anonymous No.11934159]

>>11934129
Of course they are.
The chance you pick a gold ball from the original three boxes and then pick another gold ball is 1/3.
The chance you picked a gold ball from the original three boxes and then pick another gold ball is 2/3.
The chance you pick a gold ball from the current two boxes is 1/2.

[Anonymous No.11934162]

>>11933731
>For it to be conditional, you need to ask: "what's the probability that you picked a gold ball and then you pick a gold ball?"
this is not conditional, unless you have more information.
Luckily, as the question is written in OP, you actually have more information. Thus the way you probably want to phrase it is
>What's the probability that you picked a gold ball and then you pick a gold ball, given that the first ball you pick is a gold ball?
as it so happens, this is how it is phrased in the OP.

[Anonymous No.11934171]

christ almighty, I swear conditional probability is the penultimate brainlet filter.

[Anonymous No.11934178]

>>11934145
If I already know the result what is the point of asking retard? What's the "known result?" Are you mentally ill?

[Anonymous No.11934183]

>>11934162
>What's the probability that you picked a gold ball and then you pick a gold ball, given that the first ball you pick is a gold ball?
I wouldn't complain if the question was phrased like this. The subordinate clause you added is completely redundant, but redundancy doesn't change the question, it just makes it more verbose and awkward.

[Anonymous No.11934184]

>>11934145
You realize that there are plenty of things that have already occurred or not occurred but that are not known right? Fucking retard. There is no difference in asking for the probability of a past event.

[Anonymous No.11934189]

>>11934159
>The chance you pick a gold ball from the original three boxes and then pick another gold ball is 1/3.
yes

>The chance you picked a gold ball from the original three boxes and then pick another gold ball is 2/3.
yes, as long as what you are saying is "the chance of picking a gold ball (from the same box) given that you have already picked a gold ball"

>The chance you pick a gold ball from the current two boxes is 1/2.
no? are you saying that the chance of your first ball taken from a randomly chosen box out of A and B is gold?
I believe the chance of that is not 1/2, but 3/4.

[Anonymous No.11934190]

>>11934171

[Anonymous No.11934198]

>>11934190
Sorry posted a high res of OP >>11934171

[Anonymous No.11934201]

>>11934190
from which box? do you pick a new box at random?
I assume you also do not put the ball you took back?

[Anonymous No.11934202]

>>11934178
>what is the point of asking
You're the one asking, retard. You tell me.
In the context of conditional probability, it's used to tie a new result to a previous result. As explained here>>11933846

[Anonymous No.11934204]

>>11934159
>The chance you picked a gold ball from the original three boxes and then pick another gold ball is 2/3.
No, it's 1/3.

The probability you won the lottery is 1? Amazing, go buy a Ferrari.

>The chance you pick a gold ball from the current two boxes is 1/2.
This is gibberish. There are three boxes. If you are going to use the information that you chose a gold ball then its a conditional probability and the answer is 2/3. You are simultaneously treating the problem as conditional and unconditional and getting a nonsensical answer.

[Anonymous No.11934206]

>>11934198
this is not the OP problem. This one does not specify that it is the same box.

[Anonymous No.11934212]

>>11934171
Maybe, but the antepenultimate brainlet filter is conflating penultimate and ultimate.

[Anonymous No.11934220]

>>11934202
>You're the one asking, retard.
Yes, and you're the one misinterpreting what I'm asking.

>You tell me.
I did.

>In the context of conditional probability, it's used to tie a new result to a previous result.
It's not. Show me one source saying this.

>As explained here>>11933846 #
That's wrong, as I already explained.

[Anonymous No.11934223]

>>11934212
well played

[Anonymous No.11934229]

>>11934189
No, given a choice between two boxes such that box A=2/3 and box B=1/3, your expected value is 1/2.

[Anonymous No.11934233]

You pick up each box, you select the heaviest box. You have a 100% chance to select 2 gold balls. You did not look inside the boxes.

[Anonymous No.11934240]

>>11934220
>It's not. Show me one source saying this.
conditional probabilities are simply a generalization of unconditional probabilities.
you can condition on basically any event you want to, regardless of if it has happened or not.
your result will simply be the probability conditional on that that/those events have happened.

[Anonymous No.11934248]

>>11934220
>Show me one source saying this
Literally everyone ITT who is answering 2/3. They're answering 2/3 because they think the question asks for picked,pick.
>>11934204
>The probability you won the lottery is 1
No, the probability that you won the lottery and can afford to buy a new car is very close to 1.
But the probability that you win the lottery and can afford to buy a new car is very close to 0.

[Anonymous No.11934250]

>>11934229
>No, given a choice between two boxes such that box A=2/3 and box B=1/3, your expected value is 1/2.
what do you mean? I am not sure how this relates to the post you quoted.
the post you quoted also contains three separate statements. It is not clear at all which one you are talking about.

[Anonymous No.11934255]

>>11934240
So no source. You lose.

[Anonymous No.11934263]

>>11934248
>they think the question asks for picked,pick.
not exactly.
They are (rightly) interpreting the statement to be about the probability that your next pick is gold if your first pick is gold

[Anonymous No.11934269]

>>11934248
>Literally everyone ITT who is answering 2/3.
Not true and not a source. You lose.

>No, the probability that you won the lottery and can afford to buy a new car is very close to 1.
Nope, it's very close to 0. The probability you can afford a new car given you won the lottery is close to 1. Learn the basic terminology of conditional probability instead of making up your own arbitrary rules.

[Anonymous No.11934273]

>>11934250
Was answering your last question.
>no? are you saying that the chance of your first ball taken from a randomly chosen box out of A and B is gold?

[Anonymous No.11934277]

>>11933368
P(2nd ball gold | 1st ball gold) = P(2nd ball AND 1st ball gold) / P(1st ball gold)

= (1/3) / (1/2)

= 2/3

[Anonymous No.11934280]

>>11934255
any book that defines conditional probability
myers & walpole, for instance.

>>11934273
>The chance you pick a gold ball from the current two boxes
is not clear to me what you are saying about that one. Have you already picked a gold ball? Are you picking your first ball? Which two boxes?

[Anonymous No.11934282]

>>11934171
True.

[Anonymous No.11934285]

>>11934269
>You lose
The probability that an ESL dropout used this phrase in two consecutive posts and then follows it with some other illiterate nonsense should be pretty close to 1.

>Nope, it's very close to 0. The probability you can afford a new car given you won the lottery is close to 1. Learn the basic terminology of conditional probability instead of making up your own arbitrary rules.
Yep, just as expected.

[Anonymous No.11934287]

>>11934280
>any book that defines conditional probability
Wrong.

>myers & walpole, for instance.
What page?

[Anonymous No.11934289]

>>11934285
0 argument, thanks for admitting you lost.

[Anonymous No.11934291]

>>11934255
>>11934220
>>In the context of conditional probability, it's used to tie a new result to a previous result.
>It's not. Show me one source saying this.
by even asking this question, you are just showing everybody in this thread that you have either
>never read a book on probability
>not understood after reading a book on probability
but I will humour you despite the fact that you are almost certainly trolling

[Anonymous No.11934307]

>>11934287
>What page?
check the table of contents for the section on conditional probability

[Anonymous No.11934312]

>>11934289
"You lose"
There, now I win according to your own proprietary definition of an argument. Btfo.

[Anonymous No.11934314]

>>11934291
Nowhere does this say the past tense indicates a conditional. Try again, retard.

[Anonymous No.11934317]

>>11934307
I'm not going to read an entire section for something I know isn't there. Give the page number or fuck off.

[Anonymous No.11934319]

>>11934314
>Nowhere does this say the past tense indicates a conditional.
it says that it does if we know for a fact an event has already occurred
I do not know why you are so obsessed about tenses.

[Anonymous No.11934322]

>>11934312
See >>11934289

[Anonymous No.11934327]

>>11934317
>I'm not going to read an entire section for something I know isn't there. Give the page number or fuck off.
I already told you the page number.
it should be mentioned in the first paragraph of the section or something
using additional information to modify your probabilities (degree of belief) is extremely basic and pretty much the whole purpose of conditional probability

[Anonymous No.11934329]

>>11934319
>it says that it does if we know for a fact an event has already occurred
If we know an event has already occurred then it's already a conditional. Simply being passed in the past tense doesn't mean we know it occured. Wow you're dumb. It even gives an example of a die already having been rolled and then asks for the probability of A given B. So A is not a condition even though it's in the past.

[Anonymous No.11934331]

>>11934322
See>>11934312

[Anonymous No.11934333]

>>11934327
>I already told you the page number.
Where?

>using additional information to modify your probabilities (degree of belief) is extremely basic and pretty much the whole purpose of conditional probability
And thinking that anything phrased in the past tense is a conditional is extremely wrong.

[Anonymous No.11934335]

>>11934314
>Nowhere does this say the past tense indicates a conditional.
Lmao it's a math book, not an ESL book you absolute horse's ass. Textbook authors tend to assume that their readers will have a basic understanding of the language they're writing in, unless they're writing language textbooks.

[Anonymous No.11934352]

>>11934329
>If we know an event has already occurred then it's already a conditional.
great, I think we are on the same page then.
We know our first pick was a gold ball, since that is clearly stated in the OP image.
Because of this, we have to condition on this information.

>Simply being passed in the past tense doesn't mean we know it occured.
I do not understand what you are saying here.
It is not about tense at all, it is about whether you have the information or not so that you can restrict your statespace.

>It even gives an example of a die already having been rolled and then asks for the probability of A given B. So A is not a condition even though it's in the past.
This is correct.
The information you condition on does not necessarily have anything to do with tenses.
It has everything to do with whether it is information you have.

>>11934333
>Where?
the page number listed in the table of contents for conditional probability.
The page is very likely that exact page.

>>11934333
>And thinking that anything phrased in the past tense is a conditional is extremely wrong.
I have never said this (though another anon might have)
often, but not always, a past tense indicates that something has happened which might give you extra information, though.
But it is perfectly possible for a past tense to not give you any information which can reduce your state space.
It is also perfectly possible for a present or future tense to construct a hypothetical situation in which you have been granted information you can use to reduce your state space (and thus update your probabilities, conditional on this information you have been granted).

[Anonymous No.11934361]

>It is also perfectly possible for a present or future tense to construct a hypothetical situation in which you have been granted information you can use to reduce your state space (and thus update your probabilities, conditional on this information you have been granted).
... and, often (as well as in the OP image), the so called "question" is querying about this hypothetical constructed state, in which you have been generously granted additional information to calculate your degrees of belief with.

[Anonymous No.11934419]

>>11933659
> Correct, it's (1/3)(1/2)/((1/3)(1/2)+(1/3)(1)) = 2/3

isn't it (1/6) /(1/6) + 1/3 which is 4/3, according to your equation?

[Anonymous No.11934503]

>>11934335
>Lmao it's a math book, not an ESL book you absolute horse's ass.
Is this really the best excuse you could come up with for your idiotic lie? LOL, you're pathetic.

[Anonymous No.11934527]

>>11934352
>I do not understand what you are saying here.
>It is not about tense at all, it is about whether you have the information or not so that you can restrict your statespace.
Then don't respond to posts in the middle of discussions you don't understand the context of.

>the page number listed in the table of contents for conditional probability.
Do you even know what you're supposed to be showing?

[Anonymous No.11934532]

>>11934503
Keep serving me up that delicious cope, retard.

[Anonymous No.11934533]

>>11934419
You're missing parentheses.

[Anonymous No.11934536]

Also
>>11934329
>Simply being passed in the past tense doesn't mean we know it occured
Jesus fucking christ you're stupid. If you deny the concept of a logical antecedent, you deny the whole concept of conditional probability.
The fuck good will a page number do you if you deny the whole textbook lmao.

[Anonymous No.11934554]

>>11934527
you are the one who keeps going on about tenses, when conditional probability is not about them.

[Anonymous No.11934563]

>>11934532
Keep trying and failing miserably to provide a source for your obviously false claim and then protecting your failure onto others.

[Anonymous No.11934570]

>>11934536
Where did I deny the concept of a logical antecedent you blithering moron? Simply being phrased in the past tense doesn't mean we know it already occurred.

[Anonymous No.11934573]

>>11934563
strawman deluxe

[Anonymous No.11934579]

>>11934554
He's an idiot.
But you can't differentiate between conditional and unconditional probability without using the correct tense to imply the logical antecedent, as I explained here>>11934159
>The chance you PICK a gold ball from the original three boxes and then pick another gold ball is 1/3.
>The chance you PICKED a gold ball from the original three boxes and then pick another gold ball is 2/3.

[Anonymous No.11934580]

>>11934554
Please explain how me telling a moron that tense are irrelevant to conditional probability is me going on about tenses. Please explain how agreeing with me is a retort. Please explain why you continue to post in a discussion you have no grasp of.

[Anonymous No.11934584]

>>11934573
>still no source
You lose.

[Anonymous No.11934588]

>>11934570
>Simply being phrased in the past tense doesn't mean we know it already occurred.
stop obsessing about verb tenses and start reading what the words say.
we are being told about it happening means we know it happened.
We are told we pick a gold ball, so we know we picked a gold ball.

it does not matter which tense the information is served in.

>>11934579
yes, but we are not in the first situation.
we know our first pick is a gold ball as per the OP image.

[Anonymous No.11934601]

>>11933382
ITT:
fpbp
141 replies
Jesus...

[Anonymous No.11934602]

>>11934563
>>11934570
Idiot, conditional probability literally means that you're taking a past result as a logical antecedent to a new result.

[Anonymous No.11934604]

>>11934579
>>The chance you PICK a gold ball from the original three boxes and then pick another gold ball is 1/3.
This is correct if we have no additional information.
Fortunately we have additional information, namely that the first ball we pick is a gold ball.

Notice that there is no past tense here, yet the probabilities involved are still conditional.

[Anonymous No.11934608]

>>11934579
The second sentence is wrong. Past tense is neither necessary nor sufficient for a conditional. Example: the chance you roll a 3 given you roll an odd number.

[Anonymous No.11934620]

>>11934588
>we are not in the first situation
I know, we were having a separate discussion about how (pick,pick)=1/3; (picked,pick)=2/3; and (pick)=1/2.

The other jackass can't even differentiate between (pick,pick)=1/3 and (picked,pick)=2/3.

[Anonymous No.11934622]

>>11934588
>stop obsessing about verb tenses and start reading what the words say.
Stop responding to my posts, retard. You're not even disagreeing with anything I've said.

[Anonymous No.11934635]

>>11934602
>Idiot, conditional probability literally means that you're taking a past result as a logical antecedent to a new result.
Wrong. The condition can be a hypothetical future result. The idiot in arguing with thinks that anything in the past tense is a conditional and anything in the present tense is not. So for example he thinks that "the probability you won the lottery" = the probability you won the lottery given you won it. He also bizarrely claims that the question in the OP is unconditional because it is in present tense.

[Anonymous No.11934645]

>>11934622
I think I am disagreeing with the way you are saying the things, and also the fact that you are saying them when they are not relevant here?

>>11934620
>I know, we were having a separate discussion about how (pick,pick)=1/3; (picked,pick)=2/3; and (pick)=1/2.
this is incredibly ambigous and bad notation/language, and anybody that calls you out for it has every reason to.
If your response to criticism is not to clearly state what you mean with one or both of
>proper notation
>full sentences stating which information is available and which event you are specifying the probability of
then you have yourself to blame

[Anonymous No.11934647]

>>11934604
>the first ball we pick is a gold ball
This is a statement, not a question.
A question must either reference that pick—in which case the past tense is required—or reset that pick—in which case the present tense is required. If you ask "what's the probability that you pick a gold ball and then pick a gold ball?" then 1/3 is the only correct answer.

[Anonymous No.11934652]

>>11934645
>is not to clearly state
Stated many times in clear, full sentences. Read the fucking thread.

[Anonymous No.11934657]

>>11934635
>anything in the past tense is a conditional and anything in the present tense is not
No, you fucking ESL dipshit, I've described the exact sentence structure again and again. If you persist in arguing against your own stupid hallucinations, I can't help you.

[Anonymous No.11934661]

>>11934645
>(pick,pick)=1/3
is this the probability of:
>picking a random box
>taking one ball
>taking another ball
>both balls being gold balls?
yes, this is 1/3

>(picked,pick)=2/3
is this the OP image? i.e.:
>pick a box
>take a gold ball from it
>probability of the next ball being gold?
yes, the probability is 2/3

>(pick)=1/2.
is this the probability of:
>picking a random box
>picking a ball from it
>the ball being a gold ball?
yes, the probability is 1/3.

wow using clear language sure was difficult

[Anonymous No.11934666]

>>11934652
you are not using a tripcode so I can not tell which posts are yours.

[Anonymous No.11934672]

>>11934647
>This is a statement, not a question.
the OP image contains this statement
the OP image references this statement when it asks for the probability of the next ball also being gold


>If you ask "what's the probability that you pick a gold ball and then pick a gold ball?" then 1/3 is the only correct answer.
the OP image says your first pick is a gold ball and then asks for the probability your next pick is also a gold ball.
you already know your first pick is a gold ball.

[Anonymous No.11934718]

>>11934645
>think I am disagreeing with the way you are saying the things
I don't care.

>and also the fact that you are saying them when they are not relevant here?
They are relevant to the person in having a discussion with, which you are oblivious to.

[Anonymous No.11934729]

>>11934657
>No, you fucking ESL dipshit, I've described the exact sentence structure again and again.
You've described the same arbitrary and false interpretation you claimed was standard but which you can't provide a single source for. The probability of X and Y is not even a conditional.

[Anonymous No.11934843]

>>11934729
>The probability of X and Y is not even a conditional.
Wow, and an apple is not even a lizard.
The fact that you can imagine stupid shit no one said and then argue against it doesn't mean the other person "loses," it means you're either a schizo or you can't read.

[Anonymous No.11934848]

>>11934672
>you already know your first pick is a gold ball
This gets you to a 1/3 chance of a box with one silver ball and a 2/3 chance of a box with one gold ball. I think we agree up to here.

Now, if the question is "what's the probability that you picked a gold ball and then pick a gold ball?" then the answer is 2/3.
But if the question is "what's the probability that you pick a gold ball and then pick a gold ball?" then the answer has to be 1/3, because if you deny the difference then there's no way to ask for the unconditional.
And if the question is simply "what's the probability that you pick a gold ball?" then the answer is a random choice between 1/3 and 2/3, which has an expected value of 1/2.

[Anonymous No.11934866]

>>11934206
are you blind that's the same things lol

[Anonymous No.11934886]

And we are now mercifully > 31/60 of the way to the bump limit of this shitty jpg. May it be acid washed from every corner the internet forever and ever, amen.

[Anonymous No.11934893]

>>11934886
>jpg
Sorry, png. It's a fucking png this time.

[Anonymous No.11934895]

>>11934848
>Now, if the question is "what's the probability that you picked a gold ball and then pick a gold ball?" then the answer is 2/3.
>But if the question is "what's the probability that you pick a gold ball and then pick a gold ball?" then the answer has to be 1/3, because if you deny the difference then there's no way to ask for the unconditional.
>And if the question is simply "what's the probability that you pick a gold ball?" then the answer is a random choice between 1/3 and 2/3, which has an expected value of 1/2.
are you describing situations in which you have not been told about reaching in and picking a gold ball, and instead the only information you have is one of these three above situations (+ that there are the three boxes)?
if so I agree.

On the other hand, I can not conceive of any way to construct a situation as in the OP (up to and including saying your first pick is a gold ball), and then ask
>"what's the probability that you pick a gold ball and then pick a gold ball?",
and intend for the answer to be 1/3 because "haha I was asking about the unconditional one"
In order to ask for the unconditional one, you would either have to ask before providing more information, OR you would have to explicitly state "in absense of information about the colour of the first ball, ..."

>>11934866
it is not the same thing
your image says "a box", not "the same box".
but you knew that.

[Anonymous No.11934897]

>>11934895
nvm I'm retarded I didn't read it.
not my image though

[Anonymous No.11934905]

>>11934843
>The fact that you can imagine stupid shit no one said
>The chance you PICKED a gold ball from the original three boxes and then pick another gold ball is 2/3.
Your stupidity is amazing.

[Anonymous No.11934917]

>>11934895
>and intend for the answer to be 1/3 because "haha I was asking about the unconditional one"
As I said in my first post>>11933634 the "correct" answer if you're taking a test and see (pick,pick) is to assume the author of the test made a mistake and to give the incorrect answer 2/3, even though the correct answer is 1/3. Understanding that people express themselves poorly doesn't change the fact that the sentence (pick,pick) as written can only describe an unconditional reset to the original three full boxes.

[Anonymous No.11934920]

>>11934905
>The chance you PICKED a gold ball from the original three boxes and then pick another gold ball is 2/3.
>The probability of X and Y is not even a conditional.
>this is the same thing
You're not even trying anymore, are you?

[Anonymous No.11934923]

>>11934917
the author would likely never use the term "(pick, pick)".
OPs image is perfectly fine. It tells you your first pick is gold, and asks the probability that the next pick also is gold.

[Anonymous No.11934988]

>>11934923
>the author would likely never use the term "(pick, pick)"
Of course not, I'm using it as shorthand to refer to the full sentence structure I've already written out over and over again in this thread. If an author decided to randomly use that term, the resulting question would be even shittier than the OP png. However, the "correct" answer would almost certainly still be the incorrect answer, 2/3.

>OPs image is perfectly fine
Oh God no, it's literally the shittiest, most poorly-conceived recurring image on /sci/.
>It tells you your first pick is gold
As I said>>11934848
>This gets you to a 1/3 chance of a box with one silver ball and a 2/3 chance of a box with one gold ball. I think we agree up to here...

[Anonymous No.11935111]

>>11934920
Those are the same thing, retarded troll.

[Anonymous No.11935182]

>>11935111
not him but no the probability of e.g. roll a 1 and roll a 6 on the same dice is not conditional and not the same as rolling a 6 if rolling a 1 first changes the dice which is conditional

[Anonymous No.11935350]

>>11933368

Imagine there were 100 gold balls in the left box instead of 2 and 99 silver balls in the middle box. All you know is you put your hand in a box and took out a gold ball. Then you're much more likely to have taken it from the left box. That basically is where your mistake is - in the original set up you're twice as likely to have taken the ball from the left box.

[Anonymous No.11935679]

>>11935182
Where did I say anything different?

[Anonymous No.11935700]

>>11935182
No, two dependent events occurring simultaneously is not a conditional. The probability of X given condition Y is a conditional. The probability of X and Y occurring is not conditional and in fact must be different from the first probability if P(Y)<1.

[Anonymous No.11936365]

>>11935700
>No,
>The probability of X and Y occurring is not conditional
that’s what i said don’t at me

[Anonymous No.11936600]

3 gold balls
You picked 1 gold ball
2 of the 3 gold balls are in gold box, 1 of the 3 gold balls are in mixed box
2/3

[Anonymous No.11936612]

>>11936600
It's this fucking simple and a science/math board still gets stumped?

[Anonymous No.11936613]

>>11933382
That's retarded.
You've picked up a gold ball.
The second ball will either be gold or not.
It's fifty-fifty y common sense, fuck of with your fake science jew.

[Anonymous No.11936623]

There’s three gold balls you could have picked 2 of them are in a box with both gold so 2/3 times if you picked a gold ball the other will be gold.

[Anonymous No.11936684]

>>11934988
I don't know what OP image you're reading but it doesn't seem to be the same as the one I'm seeing. There is no ambiguity. The only possible answer is 2/3.

[Anonymous No.11936718]

>>11936365
No, you said:

>rolling a 6 if rolling a 1 first changes the dice which is conditional

in response to me saying

>The probability of X and Y is not even a conditional.

So either your response is wrong or irrelevant to what I said.

[Anonymous No.11936725]

>>11936600
And if there were 2 silver balls in the mixed box instead of 1 wouldn't you say the exact same thing? Because that would be wrong. In that case it would be 1/(1+1/3) = 3/4

[Anonymous No.11936784]

>>11936725
What? Don't put words in my mouth, you transgender niggerfaggot.

[Anonymous No.11936802]

>>11936784
he isn't, what you say in >>11936600
doesn't change if the middle box has more than 1 silver ball, your explanation relies only on the fact that there are 3 golds.
Yet, if middle box has 2 silvers the odds change from 2/3 to 3/4 - which proves that your explanation is wrong, even if by chance it gave the right answer.

[Anonymous No.11936897]

>>11936802
This is correct

[Anonymous No.11936952]

>>11933368
if you remove the concept of the boxes you have 2/3 balls being gold left. But the question explicitly stated the SAME box. Meaning the box is relevant and at that point you could either get the silver from the same box or the gold from the same box making it effectively 1/2. Unless there's something I don't understand 1/2 makes sense

[Anonymous No.11936974]

[Anonymous No.11936976]

>>11936952
>if you remove the concept of the boxes you have 2/3 balls being gold left.
It has nothing to do with ignoring boxes.

Chance of choosing a gold ball from the all gold box = (1/3)(1)

Chance of choosing a gold ball from the mixed box = (1/3)(1/2)

Since it's twice as likely you are in the first box, it's 2/3.

[Anonymous No.11937300]

>>11936976
this post finally convinced me to change my view from 1/2 to 2/3

[Anonymous No.11937938]

>>11936976
It doesn't work like that.
You pick one box at random. Then you pick a ball at random.
That first ball is always a gold one.
You don,t get to pick the box with two gold balls teice as many times as the one woth one gold ball.
It's a scripted event.

[Anonymous No.11937941]

>>11937300
Good job.

[Anonymous No.11937948]

>>11937938
>Then you pick a ball at random.
>That first ball is always a gold one.
It doesn't work like that. Just because you happened to pick a gold ball in this instance doesn't mean it will always be a gold ball. Others, it would not be random!

>You don,t get to pick the box with two gold balls teice as many times as the one woth one gold ball.
Where did I say you do? I said the probability of choosing either box is 1/3. We want to know the probability we chose the box with two gold balls with the additional information that our first ball was gold. That's increases to 2/3 because it eliminates the possibility we chose from the all silver box and the possibility we chose the silver ball from the mixed box. Understand?

[Anonymous No.11937953]

>>11936976
To make it clearer than in my previous reply: the first ball is 100% of the time gold.
That can't happen naturally, you literally can't run that experiment irl because you'll fuck it up by putting out the silver one in some cases.
So strictly theoretically, you always pull out a gold ball from either the first or second box.
It doesn't matter which gold ball you pulled out from the first box.

[Anonymous No.11937966]

>>11937953
>the first ball is 100% of the time gold.
No, since we chose randomly the first ball is gold only 50% of the time. Why are you contradicting what the wisdom says?

>That can't happen naturally, you literally can't run that experiment irl because you'll fuck it up by putting out the silver one in some cases.
Yes, what you're saying can't happen naturally. Luckily that's not what the question is saying. It is completely natural and possible for you to choose a box and ball randomly and come up with a gold ball. I suggest you try it yourself if you don't believe me.

[Anonymous No.11937995]

>>11937966
>at random.
>It's a gold ball.
But the 2/3 only works if you repeat the experiment enouch times, but then you're gotta randomly get silver balls too.
God I'm so happy I quit math a long time ago, this shit is worse than drugs.

[Anonymous No.11938014]

>>11937995
>But the 2/3 only works if you repeat the experiment enouch times
No, probability is a measure of your knowledge, not of frequency.

>but then you're gotta randomly get silver balls too.
So what? You can just ignore those cases as irrelevant to the question.

>God I'm so happy I quit math a long time ago
It shows.

[Anonymous No.11938213]

>>11936718
rolling 1 changes the dice then prob rolling 6 after rolling 1 is conditional on rolling 1 dummy. you other X and Y thing is irrelevant

[Anonymous No.11938217]

>>11933368

[Anonymous No.11938249]

>>11938213
>rolling 1 changes the dice then prob rolling 6 after rolling 1 is conditional on rolling 1 dummy.
The probability of rolling 6 given you rolled a 1 is not what was asked. So that's irrelevant. We're talking about the probability of two events occurring, not the probability of an event occurring given another event.

>you other X and Y thing is irrelevant
Then why did you respond to it?

[Anonymous No.11938280]

>>11938217
>prohibitively long
it is microsofts thriftstore java
it is a foregone conclusion that it will be verbose

[Anonymous No.11938304]

>>11938249
>not the probability of an event occurring given another event
this whole thing and op is about events given events
i responses to your X and Y because it’s irrelevant and not on topic

[Anonymous No.11938392]

>>11938304
>this whole thing and op
You didn't respond to OP, you responded to my post. If you cared to read the posts I was responding to instead of making a fool of yourself by butting in to a conversation you didn't understand, you would see how it relates to the OP.

[Anonymous No.11939422]

>>11938392
>two dependent events occurring simultaneously is not a conditional
ok went back and read again you’re still wrong and off topic and now i also agree with the schizo you can’t read english since this was your response to my response
happy now fool?