You should be able to solve this

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You should be able to solve this Anonymous Sun Nov 4 09:33:46 2018 No.10116744 [Reply] [Original]

I have a container with a mixture of water and wine. The ratio of water to wine lies between 1/3 and 3. What is the probability that the ratio is less than or equal to 2?

>>	Anonymous Sun Nov 4 09:42:56 2018 No.10116765 >>10116744 Unsolvable without additional assumptions.

>>	Anonymous Sun Nov 4 09:48:16 2018 No.10116776 >>10116765 Just use the principle of indifference.

>>	Anonymous Sun Nov 4 10:41:36 2018 No.10116899 >>10116744 5

>>	Anonymous Sun Nov 4 10:48:21 2018 No.10116908 >>10116744 >What is the probability that the ratio is less than or equal to 2? What have you tried?

>>	Anonymous Sun Nov 4 10:51:26 2018 No.10116915 >>10116744 Is the water wine ratio uniformly distributed?

>>	Anonymous Sun Nov 4 10:55:52 2018 No.10116921 >>10116915 No, because that would mean the wine to water ratio is not uniformly distributed.

>>	Anonymous Sun Nov 4 10:57:23 2018 No.10116925 >>10116921 Is the ratio of wine to the whole amount of liquid uniformly distributed?

>>	Anonymous Sun Nov 4 10:58:53 2018 No.10116926 Maybe (2-1/3) / (3 - 1/3), so 0.625

>>	Anonymous Sun Nov 4 10:59:40 2018 No.10116929 >>10116744 5/8?

>>	Anonymous Sun Nov 4 11:06:22 2018 No.10116935 >>10116926 >>10116929 What is the probability that the wine to water ratio is less than 1/2?

>>	Anonymous Sun Nov 4 11:10:38 2018 No.10116938 >>10116744 Refer to >>>/sci/sqt

>>	Anonymous Sun Nov 4 11:11:34 2018 No.10116940 >>10116938 So what's the answer if this is so easy?

>>	Anonymous Sun Nov 4 11:12:45 2018 No.10116944 >>10116940 Some anons have already answered above

>>	Anonymous Sun Nov 4 11:12:58 2018 No.10116946 >>10116935 1/16

>>	Anonymous Sun Nov 4 11:13:42 2018 No.10116948 >>10116935 0.0625? I'm not really sure about the probability distribution, if someone could enlighten me i'll be glad

>>	Anonymous Sun Nov 4 11:38:15 2018 No.10116991 >>10116944 They didn't answer correctly. >>10116946 How can the probability that water/wine =< 2 be 5/8 if the probability that wine/water =< 1/2 be 1/16? If wine/water < 1/2 then water/wine > 2. So these two values must sum to 1.

>>	Anonymous Sun Nov 4 11:39:16 2018 No.10116994 >>10116948 But those probabilities must sum to 1, so your answer is wrong.

>>	Anonymous Sun Nov 4 11:56:59 2018 No.10117022 >>10116994 >variable between 1/3 and 3 >probability the variable is less than 2 >probability the variable is less than 1/2 >probabilities must sum to 1 Anon, I think one of us is retarded, and I'm pretty sure its not me.

>>	Anonymous Sun Nov 4 12:01:15 2018 No.10117031 >>10117022 >wine/water is the same variable as water/wine I'm absolutely sure it's you.

>>	Anonymous Sun Nov 4 12:43:36 2018 No.10117103 >>10116744 5/8 = .625= 62.5% chance

>>	Anonymous Sun Nov 4 12:52:06 2018 No.10117117 What probability distribution did the wine water ratio filling follow

>>	Anonymous Sun Nov 4 12:59:43 2018 No.10117138 >>10117117 (3x-1)/8 for 1/3 <= x <=3

Anonymous Sun Nov 4 13:33:55 2018 No.10117213

The answer is 5/6.

Being indifferent over ratios doesn't work because the problem becomes variant under redescription. If the ratio of water to wine lies between 1/3 and 3, then the ratio of wine to water ALSO lies in that range. The only difference is that, in the second case, you need to find the probability of the ratio being greater than 0.5. Identical problems, different results.

>>	Anonymous Sun Nov 4 13:51:02 2018 No.10117262 >>10117103 And what is the chance the ratio of wine to water is less than 1/2?

>>	Anonymous Sun Nov 4 13:52:17 2018 No.10117267 >>10117138 guaranteed case: 1 = integral 1/3 to 3 in c * (3x-1)/8 dx c=3/4 your case: integral 1/3 to 2 in 3/4 * (3x-1)/8 dx ~.39

>>	Anonymous Sun Nov 4 14:07:37 2018 No.10117320 >>10116991 >hurr whats the answer >they didn't get it right :) please kys

Anonymous Sun Nov 4 14:26:43 2018 No.10117372

>>10117213
This guy is right. Look at the total proportion of water/wine. r = 1/3 would be 75% wine, 25% water, and r = 3 is 25% wine, 75% water. So the amount of water is somewhere between 25% and 75%. Assume a uniform distribution of probability between those two extremes. A value of r = 2 would be 66.66... % water, and the range of 25% - 66.66... % water is 5/6 of the uniform range of possibilities.

>>	Anonymous Sun Nov 4 14:40:45 2018 No.10117400 >>10116744 How you going to find out?

>>	Anonymous Sun Nov 4 18:41:19 2018 No.10117863 >>10116744 8 disjoint events of equal likelihood ( 1/3<x<2/3, 2/3<x<1, 1<x<4/3 etc. ) 5 of them satisfy the stipulations, so the answer is just 5/8

>>	Anonymous Sun Nov 4 18:53:28 2018 No.10117893 >>10116921 >because that would mean the wine to water ratio is not uniformly distributed. And that's not allowed because? Anyways, this question is unsolvable without a distribution

>>	Anonymous Sun Nov 4 18:54:30 2018 No.10117896 >>10117863 >of equal likelihood You don't know that, retard

>>	Anonymous Sun Nov 4 18:57:56 2018 No.10117901 >>10117893 If you can assume the water to wine ratio is uniformly distributed then by symmetry you should also be able to assume the wine to water ratio is uniformly distributed.

>>	Anonymous Sun Nov 4 18:58:58 2018 No.10117902 >>10117863 And what is the probability that the wine to water ratio is less than 1/2?

>>	Anonymous Sun Nov 4 19:01:59 2018 No.10117907 >>10117901 Did you say somewhere that the wine to water ratio is not uniformly distributed? I asked if the water to wine ratio is uniformly distributed, and you said no because that would mean the wine to water ratio is also uniformly distributed

Anonymous Sun Nov 4 19:03:56 2018 No.10117908

>>10117907
>Did you say somewhere that the wine to water ratio is not uniformly distributed?
Yes.

>I asked if the water to wine ratio is uniformly distributed, and you said no because that would mean the wine to water ratio is also uniformly distributed
No, I said that would mean it's *not* uniformly distributed.

>>	Anonymous Sun Nov 4 19:07:10 2018 No.10117913 >>10117908 >Yes. Where? >No, I said that would mean it's not uniformly distributed. Why would it mean that? Are you saying that if water to wine ratio is uniformly distributed then wine to water is not uniformly distributed?

>>	Anonymous Sun Nov 4 19:11:28 2018 No.10117926 >>10117902 3/8

Anonymous Sun Nov 4 19:12:21 2018 No.10117927

>>10117913
>Where?
Right here >>10116921

>Why would it mean that?
Because the inverse of x does not change linearly with x. Use your brain.

>Are you saying that if water to wine ratio is uniformly distributed then wine to water is not uniformly distributed?
I'm not saying it, I already said it.

>>	Anonymous Sun Nov 4 19:17:41 2018 No.10117931 >>10117926 But according to the logic of your argument, there are 16 disjoint events of equal likelihood (1/3<y<1/2, 1/2<y<2/3, 2/3<y<5/6 etc.) 1 of them satisfies the stipulation that y<1/2 so the answer is 1/16, not 3/8.

Anonymous Sun Nov 4 19:18:52 2018 No.10117933 [DELETED]

>>10117927
>Right here >>10116921
That's for water to wine ratio. I asked if water to wine ratio is uniformly distributed, and you said no because that would imply wine to water ratio is not uniformly distributed. So I asked if you said that wine to water is not uniformly distributed. Because if you never said that wine to water must be uniformly distributed, then there was no way to deduce that water to wine is not uniformly distributed. So did you say that wine to water is uniformly distributed here >>10116921? Because in >>10116921 you seem to suggest that wine to water rario being not uniformly distributed is some sort of contradiction to something you said earlier

Anonymous Sun Nov 4 19:21:38 2018 No.10117937

>10117927
>Right here >>10116921
That's for water to wine ratio. I asked if water to wine ratio is uniformly distributed, and you said no because that would imply wine to water ratio is not uniformly distributed. So I asked if you said that wine to water is uniformly distributed. Because if you never said that wine to water must be uniformly distributed, then there was no way to deduce that water to wine is not uniformly distributed. So did you say that wine to water is uniformly distributed here >>10116921? Because in >>10116921 you seem to suggest that wine to water ratio being not uniformly distributed is some sort of contradiction to something you said earlier

Anonymous Sun Nov 4 19:23:33 2018 No.10117940

>>10117933
>That's for water to wine ratio.
It's for both. If one is uniform then the other is not. Therefore neither are uniform since by symmetry wine is interchangeable with water.

>Because if you never said that wine to water must be uniformly distributed, then there was no way to deduce that water to wine is not uniformly distributed.
I just explained the way to deduce it.

>So did you say that wine to water is uniformly distributed here >>10116921 (You)?
No.

>Because in >>10116921 (You) you seem to suggest that wine to water rario being not uniformly distributed is some sort of contradiction to something you said earlier
One of the ratios being non-uniformly distributed contradicts the assumption that the other should be uniformly distributed, since wine and water are interchangeable.

Anonymous Sun Nov 4 19:29:23 2018 No.10117950

>>10117940
>It's for both. If one is uniform then the other is not. Therefore neither are uniform since by symmetry wine is interchangeable with water.
You didn't say they were interchangeable. It could've been the case that one ratio was uniformly distributed while the other was not. There was no reason to assume they were interchangeable
>One of the ratios being non-uniformly distributed contradicts the assumption that the other should be uniformly distributed, since wine and water are interchangeable.
Firstly, there was no assumption that either ratios were uniformly distributed. There was no information about the distribution of either ratios at all. So this is an assumption added by you on the spot. Secondly, this point contradicts your first point. If we do assume that "the other" is uniformly distributed, then your first point: "Therefore neither are uniform" is a contradiction of this assumption that you made

>>	Anonymous Sun Nov 4 19:32:25 2018 No.10117954 >>10117931 Wrong

Anonymous Sun Nov 4 19:37:29 2018 No.10117960

>>10117950
>You didn't say they were interchangeable.
Why would I have to? Use your brain.

>It could've been the case that one ratio was uniformly distributed while the other was not.
It could be the case that the ratio is distributed solely on 2. That would be a dumb assumption to make though in answering the question.

>There was no reason to assume they were interchangeable
Of course there is: there is no reason to assume they are not interchangeable.

>Firstly, there was no assumption that either ratios were uniformly distributed.
Do you not understand how a proof by contradiction works?

>So this is an assumption added by you on the spot.
No, it's not. I don't assume that either are uniformly distributed because that leads to a contradiction.

>If we do assume that "the other" is uniformly distributed, then your first point: "Therefore neither are uniform" is a contradiction of this assumption that you made
Again, do you not understand how a proof by contradiction works? This is hilarious. An assumption for the purpose of invalidating that assumption via contradiction is not the same thing as an assumption made in order to answer the question.

>>	Anonymous Sun Nov 4 19:38:30 2018 No.10117962 >>10117954 How?

>>	Anonymous Sun Nov 4 19:45:16 2018 No.10117973 5/8

>>	Anonymous Sun Nov 4 19:48:33 2018 No.10117978 >>10117973 >>10116935

Anonymous Sun Nov 4 19:48:51 2018 No.10117980

>>10117960
>Why would I have to? Use your brain.
There's no way to deduce that they are interchangeable
>It could be the case that the ratio is distributed solely on 2. That would be a dumb assumption to make though in answering the question.
I'm not assuming the distribution or whether or not the 2 liquids are intercheaboe, you are
>Of course there is: there is no reason to assume they are not interchangeable
Then there's no reason to assume either way, yet you assume one way over the other
>Again, do you not understand how a proof by contradiction works? This is hilarious. An assumption for the purpose of invalidating that assumption via contradiction is not the same thing as an assumption made in order to answer the question.
You not not invalidating the assumption. You assumed that "that the other should be uniformly distributed" to show that one of the ratios cannot be non-uniform. Here's what you said: "One of the ratios being non-uniformly distributed contradicts the assumption that the other should be uniformly distributed, since wine and water are interchangeable."
As you can see, you did not invalidate your assumption by showing a contradiction. You made conclusions based on them

Anonymous Sun Nov 4 19:53:15 2018 No.10117992

>>10117960
>Of course there is: there is no reason to assume they are not interchangeable
By the way, this is also circular reasoning. I can say "there is reason to assume that they are not interchangeable: there is no reason to assume that they are interchangeable"

>>	Anonymous Sun Nov 4 19:55:17 2018 No.10118000 >>10117978 1/4?

Anonymous Sun Nov 4 20:00:23 2018 No.10118007

>>10117980
>There's no way to deduce that they are interchangeable
By the principle of indifference they are interchangeable. It's the simplest assumption to make, preserving symmetry.

>I'm not assuming the distribution or whether or not the 2 liquids are intercheaboe, you are
Then what is the point of saying it could be the case?

>Then there's no reason to assume either way, yet you assume one way over the other
Are you incapable of reading? I just gave you a reason to assume one way over the other.

>You not not invalidating the assumption. You assumed that "that the other should be uniformly distributed" to show that one of the ratios cannot be non-uniform. Here's what you said: "One of the ratios being non-uniformly distributed contradicts the assumption that the other should be uniformly distributed, since wine and water are interchangeable."
The fact that wine and water are interchangeable means that if one of the ratios is uniformly distributed, the other is too. But that is mathematically impossible, so the assumption that one is uniformly distributed is invalid. What is so hard to get about this?

>As you can see, you did not invalidate your assumption by showing a contradiction.
No, that's exactly what I did.

Anonymous Sun Nov 4 20:00:47 2018 No.10118008

>>10117980
>You made conclusions based on them
To expand on this: you assumed that "the other should be uniformly distributed". Then showed that non-uniformity of one ratio contradicts this initial assumption. However, there is no contradiction. It is possible for 1 ratio to be uniform while the other is not. But since you assumed that water and wine are interchangeable, you argued that this cannot be the case. So you're using your assumption that water and wine are intercheageable to make conclusions

>>	Anonymous Sun Nov 4 20:01:25 2018 No.10118009 >>10117992 >I can say "there is reason to assume that they are not interchangeable: there is no reason to assume that they are interchangeable" No, you can't, because there is in fact reason to assume they are interchangeable.

Anonymous Sun Nov 4 20:03:56 2018 No.10118014

>>10118008
> It is possible for 1 ratio to be uniform while the other is not.
No, it's not, because they're interchangeable. They differ by name and nothing else.

>So you're using your assumption that water and wine are intercheageable to make conclusions
Yes, specifically to make a proof by contradiction.

>>	Anonymous Sun Nov 4 20:08:22 2018 No.10118023 File: 37 KB, 800x800, Water to Wine 1:3 - 3:1.png [View same] [iqdb] [saucenao] [google] It's 50%, pic related

>>	Anonymous Sun Nov 4 20:09:25 2018 No.10118026 >>10118023 Oops, That's less than 1:1. Give me a moment

>>	Anonymous Sun Nov 4 20:13:24 2018 No.10118034 >>10118009 >>10118014 It's not a good principle and produces paradoxes, so why would you use it? What is the reason to believe in this principle?

Anonymous Sun Nov 4 20:25:16 2018 No.10118056

>>10118034
>It's not a good principle and produces paradoxes
No it doesn't. Hint: the ratios are not interchangeable if water and wine aren't.

>so why would you use it?
Because in order to answer most questions you need to make assumptions. But you should assume the least information necessary in order to not bias your answer. This is a fundamental principle in logic and science (Occam's razor).

>>	Anonymous Sun Nov 4 20:27:12 2018 No.10118061 >>10118056 *Hint: the principle of indifference does not apply to the ratios themselves if wine and water are interchangeable.

>>	Anonymous Sun Nov 4 20:30:52 2018 No.10118072 >>10118056 >>10118061 Probability 1/3 to 1 = 0.5 Probability 1 to 3 = 0.5

>>	Anonymous Sun Nov 4 20:31:37 2018 No.10118076 >>10118072 Why?

>>	Anonymous Sun Nov 4 20:33:33 2018 No.10118081 >>10118076 1/3 to 1 converted to the other liquids ratio is 1 to 3 and they must be equal

>>	Anonymous Sun Nov 4 20:34:40 2018 No.10118083 File: 37 KB, 528x482, Screen Shot 2018-11-04 at 8.33.02 PM.png [View same] [iqdb] [saucenao] [google] The answer is 5/8 t. cs

>>	Anonymous Sun Nov 4 20:38:35 2018 No.10118086 >>10118083 What about wine to water < 1/2?

>>	Anonymous Sun Nov 4 20:40:10 2018 No.10118089 >>10118081 Why must they be equal?

>>	Anonymous Sun Nov 4 20:41:55 2018 No.10118095 >>10118089 1/3 to 1 wine to water is the same as 1 to 3 water to wine

>>	Anonymous Sun Nov 4 20:49:05 2018 No.10118109 >>10118095 Good.

>>	Anonymous Mon Nov 5 01:21:38 2018 No.10118678 >>10118000 >>10117978 Ah shit nm My reading comprehension is shitty It's the same probability then

>>	Anonymous Mon Nov 5 04:33:41 2018 No.10118880 >>10116744 2/9 You can't convince me otherwise.

>>	Anonymous Mon Nov 5 08:20:13 2018 No.10119061 >>10118880 It has to be greater than 1/2 since the chance that the ratio is less than 1 is 1/2 (water and wine have the same restrictions thus by symmetry the chance that they are at least equal is 1/2). Try again.

Anonymous Mon Nov 5 14:47:30 2018 No.10119667

>>10118880
there are 18 possible ratios

wine to water = 1/3 2/3 3/3 4/3 5/3 6/3 7/3 8/3 9/3

water to wine = 1/3 2/3 3/3 4/3 5/3 6/3 7/3 8/3 9/3

In total there are 18 possible ratios. of those 18 6 represent a ratio of water to wine less than or equal to 6/3

therefore the probability of water to wine less than or equal to 2 is 6/18 or 1/3

if you want the probability of both water to wine and wine to water less than 2 then it's 12/18 or 2/3

>>	Anonymous Mon Nov 5 14:51:13 2018 No.10119681 >>10116744 1 if it is, 0 if it isn't

>>	Anonymous Mon Nov 5 14:53:02 2018 No.10119687 >>10119681 What if you don't know if it is or isn't?

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