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/sci/ - Science & Math

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File: 32 KB, 320x269, unnamed.jpg [View same] [iqdb] [saucenao] [google]
9650317 No.9650317 [Reply] [Original]

This picture is still relevant as long as some people say 1/2.
P(A)=1/3, P(B) =1/3, P(C) =1/3
P(D|A)=1, P(D|B)=1/2, P(D|C)=0
Put the numbers into Bayes theorem and get 2/3.

>> No.9650329

>>9650317
well simply plugging in just shows you have no intuition on the matter; what good is that? you have to feel it that there really are 2 ways of picking the gold ball in the first box and only 1 way of picking the gold ball in the second box so you really do have a 2/3 chance that the next ball is gold since out of 3 possible outcomes, 2 have the gold ball waiting next.

>> No.9650369

>>9650329
Simply assuming that I'm simply plugging it shows that you're the one lacking something.
Using that formula just might be better for arguing on 4chan. Your argument, while true, won't help many of the people who say 1/2.

>> No.9650961

If the first ball was gold you know its not the box with two silver balls.

That means the remaining balls are two gold and one silver, which gives you a 2/3rd chance of drawing gold again.

I'm a mathlet, so I did that with pure Graecian logic

>> No.9650998

>>9650317
https://www.onlinegdb.com/SJ7-knDFz

>> No.9651020

>>9650317
>9 paths
>one is gold
from now on there are two paths
>one of them is gold
1/2, faggots

>> No.9651303
File: 14 KB, 728x441, bertrandBox.png [View same] [iqdb] [saucenao] [google]
9651303

2/3

>> No.9651504

>>9650961
I used logic too at first before remembering Bayes theorem. I learnt it very long ago and haven't thought about it since but I was curious about how people would try to argue against it.

>> No.9651597

The question as asked is exactly equivalent to this one:
>You have two boxes. You have already chosen your box. One of these boxes has sufficient properties to be a winning box. The other cannot possibly be a winning box. What is the probability that your box is a winner?
Phrased this way, it's clear that the answer can only be 1/2.

>> No.9652675

>>9651597
>is exactly equivalent
nope, since the answer is different

>> No.9652703

>>9650317
I tested this myself and figured out why

>> No.9652706
File: 3 KB, 125x118, bertrandBox_diagram.jpg [View same] [iqdb] [saucenao] [google]
9652706

2/3

>> No.9652744

>>9652675
>>9652706
You have already chosen a box. You have already drawn a gold ball. You have already narrowed everything down to one of two possibilities. It is completely irrelevant what the probability of doing this was. That's already happened. It is in the past. You are allowing the phrasing, which asks about the colour of the next ball, to confuse you. You can ignore all of that. You either have the left-hand box, or you have the centre box.

>> No.9652749

>>9652744
>You have already drawn a gold ball
three gold balls to choose from
two of them lead to gold
one of them leads to silver
2/3

>> No.9652777

>>9650317
3 possible ways to pick gold ball 1st

1. Pick gold ball 1 in box 1

2. Pick gold ball 2 in box 1

3. Pick gold ball 1 in box 2

Option 1 and 2 lead to another gold ball while 3 doesn't

P = 2/3

>> No.9652790

>>9652749
Let's change the question a bit. Suppose you don't choose a box. Suppose you know their contents already, and you number the balls 1-6, left to right. You choose a random number in [1,3], guaranteeing a gold ball. You now ask: What is the probability that the gold ball I just selected shares a box with another gold ball?

This is clearly 2/3.

But that is not the question. In the question, you have chosen a box, not a ball. You got lucky at least once and perhaps twice- first by choosing a box that contains at least one gold ball, and potentially (if you chose gold+grey) again by picking out the gold ball first. It's all immaterial now, because it already happened. We now just need to guess which of two boxes we have.

>> No.9652806

>>9652790
>you have chosen a box, not a ball
but that's history and doesn't matter

>> No.9652807

>>9651597
>arguing about proven math
Stfu baddi

>> No.9652853

>>9652806
The box is still relevant, because it's what you're currently considering ("did I choose GG or GS?").

>>9652807
It's a word problem. Word problems can always be interpreted incorrectly. Your proof can be as rigorous as you like; if your starting model was constructed from a misunderstanding, it doesn't solve the problem.

>> No.9652866

>>9652853
>you're currently considering
nope, i could have my head cut off
and the odds would still be 2/3

>> No.9652876

>>9652853
There are 4 balls in the selection. One is taken from the pool. 2 out of three balls are gold

Those are the odds from the word problem

>> No.9652926

>>9652853
> what i picked is what I'm considering
The word problem specifically mentions you cannot determine a difference between the boxes; no.

>> No.9652977
File: 1.25 MB, 1080x1417, 1422468099173.png [View same] [iqdb] [saucenao] [google]
9652977

You people are retarded fucking brainlets, it's obviously 1/2.
For fucks sake, it says
>'the next ball IN THE SAME BOX.'
You're presumably not replacing the fucking gold ball after drawing it the first time.

>> No.9652980

>>9652977
g8 b8 m8

>> No.9653270

>>9652977
No shit, where did you get the impression that putting the ball back was ever being considered in the first place? The question can be rephrased as:
>what is the probability that the box you picked is the one with two gold balls in it
to which the answer is 2/3

>> No.9654871

>>9651020
Yes, but you're forgetting that you could've picked either gold ball from box 1. Of the three gold balls, two are paired with another gold ball. Essentially, the fact that you aren't guaranteed to get a gold from box 2 is the hangup.

>> No.9655966

>>9652977
This man is right. It's the logically equivalent to this question:

>An Urn contains two white marbles and one black marble. A marble is drawn from the Urn without replacement and put aside without my seeing it. Then a second marble is drawn, and it is white.
What is the probability that the unknown removed marble is white, and what is the probability that it is black?

>> No.9656013

Surely you people are pretending to be retarded? You picked a gold ball so box 3 is eliminated. There are 3 balls left, but only 2 in play as you picked a gold, so may as well eliminate a gold from either box as you must draw from same box. It's 1/2

>> No.9656030

>>9656013
>You picked a gold ball
>>9652749

>> No.9656033

>>9650317
When you claim the first ball to be golden you are elliminating the third box. Now it doesnt matter in which order you draw balls from the first 2 boxes, the probability of each of draws being golden is 3/4. Simple logic!

>> No.9656043

>>9651303
The last two are identical cases, so your mistake is counting the same situation twice. The question is asking about any gold ball, not a specific gold ball.

>> No.9656050

>>9656043
>your mistake
prove it

>> No.9656053

>>9652790
>We now just need to guess which of two boxes we have.
Thankfully, you can make that an educated guess based on how likely it was for you to get a golden ball from any given box.

>> No.9656056

>>9655966
Wait, aren't you twice as likely to get a white one if your first one was black?

>> No.9656083

>>9650317
Bayes theorem confirms it because you're giving it the wrong input.
Whoever says 2/3 bases it on assumption he's got both of the remaining boxes to take the next ball from, while the task clearly says you're taking it from the SAME box. So essentially you cut the number of outcomes not only by taking out a gold ball probability-theory-style, but also by inevitably choosing a single box while doing so, which becomes a starting condition for the next trial.
You chose a box = you're stuck with either another gold ball inside (if that was box 1), or a silver one (box 2). So 1/2.

>> No.9656090

>>9656083
>Whoever says 2/3 bases it on assumption he's got both of the remaining boxes to take the next ball from
Wrong

>> No.9656091 [DELETED] 

>>9656083
so 50/50 either it is or isn't
your fields medal is in the mail

>> No.9656093

>>9656083
so 50/50 either it is or isn't
your fields medal is in the mail
or isn't