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Ytlaya posted:The only exception are paradoxes related to the concept of infinity, which don't really bother me much for some reason. All the infinity paradoxes evaporate when you think of infinity as a direction, not a number. "One car goes Left, and another car goes Left twice as fast, and yet they are both still going Left!"
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Sep 2, 2016 15:30
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| # ¿ Apr 28, 2024 00:28 |
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Bob has two children. The younger one is a girl. What are the odds that the older one is a boy? About 50% Bill has two children. One is a girl. What are the odds that the other one is a boy? 67%. Yes.
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Sep 3, 2016 14:20
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His dick extends forever in the dickwise direction, so a wind going that way provides spatially unlimited suction.hth.
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Sep 3, 2016 15:05
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There are 4 equally likely outcomes when you have 2 kids: Boy Boy Boy Girl Girl Boy Girl Girl In Bob's case, we know B G G G Are the only two possibilities. In Bill's case, B G G B G G Are three equally likely possibilities.
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Sep 3, 2016 15:53
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GAINING WEIGHT... posted:
Yes. What are the odds that the last coin flip is heads? What are the odds that one of the hundred coin flips is heads?
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Sep 3, 2016 18:39
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GAINING WEIGHT... posted:That second question isn't quite the same though. Asking: "if I flip a coin 100 times, what is the probability that any is heads?" is not the same as "if I flip a coin 100 times and 99, in any order, are tails, what is the probability that the other one is heads?" In the second instance, for 99 of the flips, the probability of heads is now 0, which changes the overall total a bit. It is the same. For 99 of the flips, the probability of heads is now 0, which does not change the probability of the other flip. "If I flip a coin 100 times, and 99, in any order, are tails, what is the probability that #1 is heads Or #2 is heads Or #3 is heads Or #4 is heads Or #5 is heads Or . . . "
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Sep 4, 2016 04:04
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Phyzzle posted:"If I flip a coin 100 times, and 99, in any order, are tails, what is the probability that #1 is heads Or #2 is heads Or #3 is heads Or #4 is heads Or #5 is heads Or . . . " GAINING WEIGHT... posted:To put a finer point on my above reasoning with the 100 coins example, your treating of "no heads" as one option is mistaken. It's actually 100 options: the coin we didn't know about is the first, and it was tails; the coin we didn't know about was the second, and it was tails; etc. See the 'Or' in the statement about one heads result? You're statement about no heads has semicolons, but they don't represent 'Or', do they? They represent 'And'. A bunch of 'And's strung together to make one unlikely case, instead of a bunch of cases connected by 'Or's to make one much more likely case.
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Sep 4, 2016 15:18
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GAINING WEIGHT... posted:Of course they mean or? Oh! Well taking another look, the problem must be this: quote:To put a finer point on my above reasoning with the 100 coins example, your treating of "no heads" as one option is mistaken. It's actually 100 options: the coin we didn't know about is the first, and it was tails; the coin we didn't know about was the second, and it was tails; etc. So the "it" in the sentence refers to coin we don't know about? Then you're assuming that probability of it being tails is 1/2, so that the sum is 100/200 for all coins. But assuming the 1/2 begs the question.
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Sep 4, 2016 21:00
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GAINING WEIGHT... posted:I'm sorry, I don't follow. Why would the probability of a coin being tails being 1/2 be begging the question? We're assuming fair coin right? A fair coin doesn't always have a 1/2 probability of being tails, any more than a 'fair' child must always have a 1/2 probability of being male. So, when you say that 100/200 = 1/2 must be the right probability, because the treating of "no heads" as one option is a mistake, because it's actually many options, because 1/2 is obviously the right probability, that's begging the question.
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Sep 5, 2016 01:08
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You can also just flip a pair of coins. H H you win H T or T H you lose T T you toss the result If H T and T H are really a *nested* pair with a 50% probability, you should come out even with a lot of flips. Would you play that one in a casino?
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Sep 5, 2016 02:07
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A man flips two coins. One comes up H, but the other one rolls under a desk. The other one has a 50% chance of being T. A man flips two coins, and they both roll under a desk. His wife looks under the desk and says, "It's dark, but I can see one of them, and it's H". The other one now has a 67% chance of being T. For the man. Since he doesn't know which coin came up H, there are three equal possibilities for him: TT, TH, and HT. But since his wife is looking directly at one specific coin rather than hearing a report of "at least one H", the other coin still has a 50% chance of being T. But only for her. Something seems amiss here . . .
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Sep 5, 2016 17:01
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wateroverfire posted:When his wife tells him "I can see one of them, and it's H.", TT is eliminated and the possibilities are only TH or HT. Or HH.
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Sep 5, 2016 17:18
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VitalSigns posted:It's twice as likely for there to be HT/TH than TT. But if it's TT she's twice as likely to see a tails so they cancel out. Her husband knows she only saw one coin so he has the same information she does. Ah, I see. Because the wife is not an accurate Heads detector, but is randomly sampling one of the coins, then that probability goes in.
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Sep 5, 2016 19:33
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Dzhay posted:"I'm really bad at maths" isn't a paradox. The paradox is that anyone is good at maths. Seriously, that's called Quine's Paradox or something. That manipulating little symbols by human-made rules and syntax can match the behavior of nature so well.
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Sep 6, 2016 14:50
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Nah, the concept of paradox was already destroyed thoroughly enough that they added the third definition here: http://www.merriam-webster.com/dictionary/paradox : a statement that seems to say two opposite things but that may be true I mean, "The Twin Paradox" in Relativity has been around since the 1920's, but it never actually indicated a contradiction.
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Sep 6, 2016 15:37
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twodot posted:This is an English problem and not a math problem. Yeah, or an 'information' problem. There are some subtleties of information that seem difficult to hold onto. "I examined both coins, and I'm willing to tell you for sure that at least one came up H." "I found one coin [that randomly bounced to where I can see it], and it was H, so now I can tell you for sure that at least one came up H." The conclusions are the same, but there is information lurking in the premises that you can use on that set of two coins.
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Sep 6, 2016 17:47
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wateroverfire posted:Hear me out, man, and follow the logic below to the end. It's this step here. P(Coin you showed is Coin 2) is not 50%. If VitalSigns looked at Coin 1, and sees that it's not tails, he moves on to Coin 2. He only shows you Coin 2 in the case of HT, and this does not have a 50% chance of happening.
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Sep 7, 2016 14:56
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Strom Cuzewon posted:Doesn't that mean we just have to be a bit more careful in distinguishing between logical paradoxes and intuitive ones? Sure, though I might call logical paradoxes "inconsistencies" instead. Like Russel's Paradox on "all sets that don't contain themselves" showed an inconsistency in naive set theory.
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Sep 7, 2016 14:57
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wateroverfire posted:What you're talking about is adding two pieces of information to what I know that are not present in the original problem. No, piece (1) is not being added: whatever coin he grabs first becomes #1 (if they are not marked), so you knew that. And piece (2) is not being added either: You have no idea when he skips coin 1, or which coin he is showing you.
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Sep 7, 2016 15:24
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wateroverfire posted:Ok, sure, if you like. So he grabs a coin that popped T and shows it to me, and we call that Coin 1. Yes, that's the case where grabs a coin that popped T and shows it to you. Which is not the only possible case.
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Sep 7, 2016 15:41
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wateroverfire posted:What other case would you lik to consider? All of them. Every possible way for one coin to be Heads must be considered to find the probability of one coin being Heads. Like he grabs one coin, and it's Heads, so he then grabs another.
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Sep 7, 2016 16:40
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wateroverfire posted:Do the math and show me what you're talking about. You did do the math in this post: wateroverfire posted:1) If Coin 1 is T, the only possible outcomes are TH and TT. This is correct and should also be intuitive if you think about it, but if you disagree then show how and let's talk it through. I am saying, P(Coin you showed is Coin 2) is not 50%. He only shows you Coin 2 in the case of HT, which does not have a 50% chance of happening. There is no added information needed. You don't know if the coin being showed is #1 or #2. Without knowing that, P(Coin you showed is Coin 2) is still not 50%. Do you agree that P(Coin you showed is Coin 2) is not 50%? If so, your final result is also not 50%. Phyzzle fucked around with this message at 18:26 on Sep 7, 2016 |
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Sep 7, 2016 16:50
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Okay, here's another one that got me thinking. Take this distribution for the weight of adult males.  (You turn it into a probability distribution by dividing it all by the area under the curve, to give it a new area of 1.) We can conclude from this distribution that "If you are an adult male, you probably don't weight 50 or 500 lbs." So picking an adult male from a phone book and getting a 50 pounder is not very likely. Doing the same thing with the distribution of population as a function of year,  We see that "If you are a human life, you are more likely to happen in the 21st century than in the 1st century." Okay, makes sense, it is likely that you would be alive now, when people are finding it particularly easy to be alive. But . . . what about the time after the 21st century? If the population keeps going, or at least levels off, that would put you at a tail-end extreme of the distribution. This is not very likely. Thus, the fact that you are living now serves as evidence that it is unlikely that the human population will not be sticking around over 7 billion for long, and we are in for a catastrophic population crash in the near future.
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Sep 8, 2016 15:02
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rudatron posted:But actually dealing with the paradox head on, I don't think it's legitimate to attempt to derive a distribution in general from a skewed example - taking the previous set up as the 'experiment', you're only sampling people who are alive right now, not in the future, so it's obviously 'very likely' that'd you be sampling people 'in the tail end' of the distribution, even assuming a plauteu for the next million years, because you're not a time traveler. So samples are very likely to be in the tail end of the distribution ... if you are, in fact, sampling people who happen to be right now in the tail end of the distribution? But that's the whole question: what is the likelihood that you are sampling people who happen to be in the tail end of the distribution? computer parts posted:Basically the second graph is not actually a probability distribution, though it might appear to be. All it's reporting is the number of people in a certain timeframe. You can extrapolate from that that people are more likely to be born when there's more people (for obvious reasons), but it's not relaying the same information. Forgetting the weights, what about this time distribution?  Can we say of a given yttrium radioactive decay product: "this probably decayed less than 150 years after the lump of strontium formed"? Or would looking at a particular yttrium atom that took 200 years to form skew the distribution, so that we cannot make statements about it's probable age? rudatron posted:I mean the fact that the same argument works in 2000 B.C, and reaches a different conclusion to using it today, should be the tip-off that it's bullshit.
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Sep 8, 2016 16:09
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Brain Bugs?! Frankly, I find the idea of a Bug that thinks offensive.
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Sep 8, 2016 17:39
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VitalSigns posted:E: serious answer, you can't draw conclusions about the population "all humans who will ever be born" from the nonrepresentative sample "all humans born before 2017" So by 'nonrepresentative', you mean 'having a specific range of values in the parameter of interest'? I could see that. Knowing the distribution of weights under 190 lbs. tells you absolutely nothing about the distribution of weights over 190 lbs.. Even though it really looks like part of a bell curve, it's mathematically illegal to just draw in the rest of the curve. You would need some other information about human weight, like "adults rarely triple in size from diet and genetic differences." computer parts posted:The other thing is that in probability distributions you try to make it as close to a consistent system as possible - for example, the first graph might be "distribution of adult male weight for 2012", so the consistent part is that all the data was from one year. In the second graph, there's a clear shift about 1500 AD that makes it unlikely that the previous data has any relation to the succeeding data. Hmm, perhaps such a relation has the opposite effect: the succeeding data might have a very sensitive dependence on events related to previous data. That would also make it very unlike a probability distribution.
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Sep 9, 2016 15:48
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