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Post by Eva Yojimbo on Feb 19, 2020 4:04:22 GMT
Since Arlon and I are arguing in the Profound Sayings That Are Junk thread over the Monty Hall Problem, with him accusing me of just "copying" people online who've solved it using Bayes (while seemingly being suspicious that Bayes solves it all), I thought I'd create a different problem for him and the forum. Everyone feel free to participate. PROBLEM: Say you're given a hairy bag with ten balls in it. You reach in and pull out a blue ball. You're told that one of four things is possible: a. The bag only has blue balls in them. b. The bag only has blue and red balls in equal amounts. c. The bag has two blue balls, two red balls, two green balls, two yellow balls, and two purple balls. d. The bag has one blue ball and nine variously-colored balls. Questions: 1. Is one bag more probable than the other? 2. If one bag is more probable than the others, how much more probable is it? *** NOTE: I have already solved this problem. I sent the problem and the solution to Aj_June before I posted it here. I did not want to post the solution here, even under a spoilers tag, as I know it would be easily copied. AFAIK, this problem is not copied from anyone else. I've seen versions of the "bag/ball" problem, but I invented this particular version. |
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Post by goz on Feb 19, 2020 4:30:32 GMT
The hairstyles were better in the first Star Wa…..
oh wait!
My answer is that Rebel Wilsons doesn't have 'the hairy balls'.
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Post by maya55555 on Feb 19, 2020 4:54:32 GMT
The hairstyles were better in the first Star Wa….. oh wait! My answer is that Rebel Wilsons doesn't have 'the hairy balls'. goz What is it with you and pubes? Please do tell?
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Raxivace
New Member
@raxivace
Posts: 40
Likes: 19
 
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Post by Raxivace on Feb 19, 2020 8:20:49 GMT
Since Arlon and I are arguing in the Profound Sayings That Are Junk thread over the Monty Hall Problem, with him accusing me of just "copying" people online who've solved it using Bayes (while seemingly being suspicious that Bayes solves it all), I thought I'd create a different problem for him and the forum. Everyone feel free to participate. PROBLEM: Say you're given a hairy bag with ten balls in it. You reach in and pull out a blue ball. You're told that one of four things is possible: a. The bag only has blue balls in them. b. The bag has an equal amount of blue and red balls. c. The bag has two blue balls, two red balls, two green balls, two yellow balls, and two purple balls. d. The bag has one blue ball and nine variously-colored balls. Questions: 1. Is one bag more probable than the other? 2. If one bag is more probable than the others, how much more probable is it? *** NOTE: I have already solved this problem. I sent the problem and the solution to Aj_June before I posted it here. I did not want to post the solution here, even under a spoilers tag, as I know it would be easily copied. AFAIK, this problem is not copied from anyone else. I've seen versions of the "bag/ball" problem, but I invented this particular version. Is option b meant to read as five red balls and five blue balls? Otherwise as written it seems option b applies to option c as well, since technically if there are two blue balls and two red balls then there are an equal number of blue and red balls in option c as well.
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Post by Eva Yojimbo on Feb 19, 2020 10:25:28 GMT
Since Arlon and I are arguing in the Profound Sayings That Are Junk thread over the Monty Hall Problem, with him accusing me of just "copying" people online who've solved it using Bayes (while seemingly being suspicious that Bayes solves it all), I thought I'd create a different problem for him and the forum. Everyone feel free to participate. PROBLEM: Say you're given a hairy bag with ten balls in it. You reach in and pull out a blue ball. You're told that one of four things is possible: a. The bag only has blue balls in them. b. The bag has an equal amount of blue and red balls. c. The bag has two blue balls, two red balls, two green balls, two yellow balls, and two purple balls. d. The bag has one blue ball and nine variously-colored balls. Questions: 1. Is one bag more probable than the other? 2. If one bag is more probable than the others, how much more probable is it? *** NOTE: I have already solved this problem. I sent the problem and the solution to Aj_June before I posted it here. I did not want to post the solution here, even under a spoilers tag, as I know it would be easily copied. AFAIK, this problem is not copied from anyone else. I've seen versions of the "bag/ball" problem, but I invented this particular version. Otherwise as written it seems option b applies to option c as well, since technically if there are two blue balls and two red balls then there are an equal number of blue and red balls in option c as well. Yes, but I see what you're saying. I was trying to write it in a way that used as few numbers as possible. I'll give that bit a rewrite.
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Post by Winter_King on Feb 19, 2020 10:44:39 GMT
Hairy blue balls? Sounds painful.
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Post by general313 on Feb 19, 2020 17:51:46 GMT
Since Arlon and I are arguing in the Profound Sayings That Are Junk thread over the Monty Hall Problem, with him accusing me of just "copying" people online who've solved it using Bayes (while seemingly being suspicious that Bayes solves it all), I thought I'd create a different problem for him and the forum. Everyone feel free to participate. PROBLEM: Say you're given a hairy bag with ten balls in it. You reach in and pull out a blue ball. You're told that one of four things is possible: a. The bag only has blue balls in them. b. The bag only has blue and red balls in equal amounts. c. The bag has two blue balls, two red balls, two green balls, two yellow balls, and two purple balls. d. The bag has one blue ball and nine variously-colored balls. Questions: 1. Is one bag more probable than the other? 2. If one bag is more probable than the others, how much more probable is it? *** NOTE: I have already solved this problem. I sent the problem and the solution to Aj_June before I posted it here. I did not want to post the solution here, even under a spoilers tag, as I know it would be easily copied. AFAIK, this problem is not copied from anyone else. I've seen versions of the "bag/ball" problem, but I invented this particular version. 1. What is the probability that what I'm told is true? 2. If I'd never seen a ball of any color before in my entire life it might be reasonable to assume that a. is more probable. On the other hand, if the room I'm in has thousands of red and blue balls, but no balls of any other color, then I might go with b.
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Post by Eva Yojimbo on Feb 20, 2020 1:14:20 GMT
Since Arlon and I are arguing in the Profound Sayings That Are Junk thread over the Monty Hall Problem, with him accusing me of just "copying" people online who've solved it using Bayes (while seemingly being suspicious that Bayes solves it all), I thought I'd create a different problem for him and the forum. Everyone feel free to participate. PROBLEM: Say you're given a hairy bag with ten balls in it. You reach in and pull out a blue ball. You're told that one of four things is possible: a. The bag only has blue balls in them. b. The bag only has blue and red balls in equal amounts. c. The bag has two blue balls, two red balls, two green balls, two yellow balls, and two purple balls. d. The bag has one blue ball and nine variously-colored balls. Questions: 1. Is one bag more probable than the other? 2. If one bag is more probable than the others, how much more probable is it? *** NOTE: I have already solved this problem. I sent the problem and the solution to Aj_June before I posted it here. I did not want to post the solution here, even under a spoilers tag, as I know it would be easily copied. AFAIK, this problem is not copied from anyone else. I've seen versions of the "bag/ball" problem, but I invented this particular version. 1. What is the probability that what I'm told is true? 2. If I'd never seen a ball of any color before in my entire life it might be reasonable to assume that a. is more probable. On the other hand, if the room I'm in has thousands of red and blue balls, but no balls of any other color, then I might go with b. 1. You have no other information to go on, so what you're told is what you have to base your probabilities on. 2. Even assuming that (which I didn't specify) I'm not sure why you'd go with B.
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Post by Eva Yojimbo on Feb 20, 2020 1:57:23 GMT
Just thought I'd say phludowin solved the problem in a PM to me. THIS IS SOLVABLE, PEOPLE! |
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Post by kls on Feb 20, 2020 2:17:31 GMT
Just thought I'd say phludowin solved the problem in a PM to me. THIS IS SOLVABLE, PEOPLE! Will you share the answer soon?
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Post by Eva Yojimbo on Feb 20, 2020 2:20:22 GMT
Just thought I'd say phludowin solved the problem in a PM to me. THIS IS SOLVABLE, PEOPLE! Will you share the answer soon? I'll probably wait until the OP shows the exact time of the posting. I want to do that because, as I said, I solved this in a PM I sent to Aj before I posted it here and I want proof, which means waiting for the exact timestamps to appear. I also want to give people a chance at solving it, so I might wait an extra day or so.
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Post by kls on Feb 20, 2020 2:30:48 GMT
Will you share the answer soon? I'll probably wait until the OP shows the exact time of the posting. I want to do that because, as I said, I solved this in a PM I sent to Aj before I posted it here and I want proof, which means waiting for the exact timestamps to appear. I also want to give people a chance at solving it, so I might wait an extra day or so. I sent a pm. Sorry if it is ridiculously off. I think I should be sleeping.
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Post by phludowin on Feb 20, 2020 7:04:16 GMT
Just thought I'd say phludowin solved the problem in a PM to me. THIS IS SOLVABLE, PEOPLE! True, but you did not supply a piece of information I requested also via PM: You need the priors for the four bags. This is something general313 was hinting at. So for those who want to solve the problem, here's information about the priors. The a priori probability for each bag is 0.25
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Post by Eva Yojimbo on Feb 20, 2020 11:04:31 GMT
Just thought I'd say phludowin solved the problem in a PM to me. THIS IS SOLVABLE, PEOPLE! True, but you did not supply a piece of information I requested also via PM: You need the priors for the four bags. This is something general313 was hinting at. So for those who want to solve the problem, here's information about the priors. The a priori probability for each bag is 0.25 I didn't want to spell this out. I actually worded the problem carefully to force people to make the (hopefully correct) assumption about the priors. You made the correct assumption, but were unsure... maybe you thought I was trying to trick you or something. Now, why would I do that? 
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Post by Eva Yojimbo on Feb 20, 2020 14:38:01 GMT
Still waiting for Arlon10, the guy who perfectly understands probability/Bayes and how useless they are, to have a go at this. |
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Post by general313 on Feb 20, 2020 17:20:05 GMT
Still waiting for Arlon10 , the guy who perfectly understands probability/Bayes and how useless they are, to have a go at this. I PM'ed you my solution, including probability calculations.
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Post by phludowin on Feb 20, 2020 23:13:09 GMT
True, but you did not supply a piece of information I requested also via PM: You need the priors for the four bags. This is something general313 was hinting at. So for those who want to solve the problem, here's information about the priors. The a priori probability for each bag is 0.25 I didn't want to spell this out. I actually worded the problem carefully to force people to make the (hopefully correct) assumption about the priors. You made the correct assumption, but were unsure... maybe you thought I was trying to trick you or something. Now, why would I do that? Because it's a common mistake to misestimate the priors when (mis)applying the Bayes formula. When talking about harmless stuff like balls in bags, or wet sidewalks, errors are not dangerous. But when it comes to evaluate the odds that you have a certain type of cancer, when a test turns out positive, then the matter becomes more serious. And it becomes downright dangerous when you calculate the probability that someone committed murder, based on small evidence. Let's say you find various pieces of evidence at the crime scene that point to a suspect, and for each of these pieces, the odds of finding them there, under the condition that he committed the crime, are higher than finding them there if he didn't commit the crime. Now, how big are the odds the suspect is the murderer? True story: A lawyer proposed 0.5 as a priori probability, because "he either did it or he didn't". Using the Bayes formula with this parameter would have disastrous consequences. That's why you can't insist too much on pointing out correct priors when using Bayes. Not mentioning them can lead to dangerous conclusions.
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Post by Arlon10 on Feb 20, 2020 23:20:34 GMT
Still waiting for Arlon10 , the guy who perfectly understands probability/Bayes and how useless they are, to have a go at this. I'm still waiting for you to decide what exactly you want to know. Are the three "other" bags considered separately or collectively? The thirteen people here, usually less than four at a time, are not my teacher and never will be. If you are too stupid to understand that, and it appears you are, you are in for more disappointment than this. You don't make the rules. Your grades are meaningless. You are not a teacher here or in real life. It is amazing how having internet access makes people think they are teachers. A very good question is what in real life does picking things out of bags prepare a person to do? It's not even geology. I see you already lost the taxicab problem. You know that one makes no sense, right? Yes. the math follows a formula, but those "given" conditions that you never justify do need to be justified. You gave up on that, I disregard this. Here is the "new" information for your scenario, no one does or should care how such a failure as you entertains himself. The internet is full of people like you who are failing real life. That's why the political news is so absurd. The worst part though is how you think you're the teachers. You are not. You are the grunts who follow orders you can't understand and expect others to follow your orders. Wait, national debt skyrocketing? Not to worry, you have confidence in your absurd guesses.
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Post by Eva Yojimbo on Feb 21, 2020 2:19:51 GMT
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Post by Eva Yojimbo on Feb 21, 2020 2:38:34 GMT
I didn't want to spell this out. I actually worded the problem carefully to force people to make the (hopefully correct) assumption about the priors. You made the correct assumption, but were unsure... maybe you thought I was trying to trick you or something. Now, why would I do that? Because it's a common mistake to misestimate the priors when (mis)applying the Bayes formula. When talking about harmless stuff like balls in bags, or wet sidewalks, errors are not dangerous. But when it comes to evaluate the odds that you have a certain type of cancer, when a test turns out positive, then the matter becomes more serious. And it becomes downright dangerous when you calculate the probability that someone committed murder, based on small evidence. Let's say you find various pieces of evidence at the crime scene that point to a suspect, and for each of these pieces, the odds of finding them there, under the condition that he committed the crime, are higher than finding them there if he didn't commit the crime. Now, how big are the odds the suspect is the murderer? True story: A lawyer proposed 0.5 as a priori probability, because "he either did it or he didn't". Using the Bayes formula with this parameter would have disastrous consequences. That's why you can't insist too much on pointing out correct priors when using Bayes. Not mentioning them can lead to dangerous conclusions. You can't really "misestimate" priors. The problem is that you're applying a frequentist view of probabilities onto Bayes, and that's precisely what Bayes is trying to get away from. In Bayes, priors are based on whatever knowledge you have. Even if that knowledge is highly speculative and imperfect, even if there are many (or, indeed, more) unknown and imprecise quantities than known and precise quantitites, even if whatever your prior is based on is something you haven't kept track of at all (like the reliability of your memory). Of course the issue can be serious with stuff like cancer, which is why we tend to tend to do lots of extensive research on how many people get certain cancers, and how accurate certain screenings are for diagnoses, and/or how effective certain treatments are. I'm not sure why you think this is incompatible with Bayes, though. Research is just a method of updating our very imprecise priors with something more precise. As for your murder example, your prior would be the probability that anyone actually commits a murder. Then every piece of evidence would modify that (very low) prior the way Bayes suggests: "given so-and-so did it, what's the probability of finding X evidence? Given so-and-so didn't do it, what's the probability of finding X evidence?" The stupidity of the "it's 50/50, he either did it or he didn't" notion is pretty easy to see through: "if you walk off a building it's 50/50 if you'll fall; you either will or you won't." That thinking is only true if we had no prior information about how gravity works, or about how often people commit murder. In fact, investigators use priors all the time; it's why in murder cases friends and family are investigated first, because the prior someone committed murder given they knew the person is higher than if they were a stranger. I'm certainly not suggesting that we shouldn't try to be precise about priors, I'm merely saying that we aren't paralyzed when we're not. My coin-flip thought experiment also showed this: we have no idea how much more common fair coins are compared to trick coins, but keep flipping the coin and getting heads and you'll still be convinced it's a trick one eventually. Same kind of thinking applies to any situation where our priors are fuzzy, but the evidence keeps piling up.
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