EPTCoins tosses - Page 4
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psychopat
Canada417 Posts
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Sea_Food
Finland1612 Posts
On July 16 2011 03:39 Dave[9] wrote: I just feel bad for Chill because I've sen him try to explain math to fellow teamliquidians before and eventually give up because the OP simply doesn't understand. But there are tons of resources for the Monty Hall problem online...which gives you like hundreds of perspectives on the same problem...I think the OP just needs research a little bit. P.S. You're not the only one who's had problems with this problem, even the esteemed Paul Erdos thought that the probability of switching the door (or flipping the coin) was 50%. Indeed it is very counter intuitive, but that's simply the way it is sometimes. Maybe if it helps....run a computer program to approximate the results. I bet there are people out there who have done monte carlo on this. Actually the reason I created this topic because I wanted to understand after hours of thinking about it my self. On July 16 2011 03:27 Chill wrote: OP, please answer the following questions: Compare that to: Compare that to: They're all basically the same scenario with the same logic to get the answer. They're just worded differently, which is what I think is tripping you up. I have no idea what are you trying to say with this post. And by the way to the guys telling me the door story, I know it and I accept the correct awnser, but I think its 100% different. | ||
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Sea_Food
Finland1612 Posts
On July 16 2011 03:07 Chill wrote: The entire thread has explained this. The fact that either coin could be H gives you two chances to be right, whereas there is only one chance to be wrong (HH). The other chance of being wrong (TT) was eliminated by the statement "One coin is heads". 2 / 4 now becomes 2 / 3. So please someone awnser this awnser this: Because acording to the correct math, if my friend tosses two coins 1 000 000 times, and tells me how one of the coins landed each time, I will say each time that the chacnes coins landed different sides is 67%, which means if im rigth about 677 777 times the coins did land different side. Now if he didnt tell me anything, the chances would be the coins landed different side only about 500 000 times Is that statement correct? Because if it is correct then, cant I just say in the start about 677 777 times they will land different side? | ||
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naonao
United States847 Posts
Instead of your friend telling you that one coin landed heads and wanting you to guess the result of the other coin, he tells you that the coins did not both land on tails and wants you to guess what orientation both coins landed(HT and TH are the same). So from the 4 possible outcomes: HH HT TH TT you remove TT, and are lefit with HH HT TH From here each result is equally likely so there is a 66% chance of HT/TH and a 33% chance of HH | ||
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Impervious
Canada4216 Posts
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Chill
Calgary25993 Posts
On July 16 2011 05:02 Sea_Food wrote: Actually the reason I created this topic because I wanted to understand after hours of thinking about it my self. I have no idea what are you trying to say with this post. I directly asked you to answer the questions. I'm not saying anything. Answer the questions. | ||
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Chill
Calgary25993 Posts
On July 16 2011 05:15 Sea_Food wrote: So please someone awnser this awnser this: Is that statement correct? Because if it is correct then, cant I just say in the start about 677 777 times they will land different side? Fully accept that you don't understand this question in the OP. Please stop making up analogies that don't make sense to try to prove yourself right. In the situation you quoted, here's what would happen: 1. Your friend would flip the coin 1,000,000 times. 1a. 250,000 of these times, the coins would land TT and he would say "Oh that didn't count." 1b. If these did count, you could say "They are both different sides" and be right 500,000 times [50%]. 2. 750,000 of these times, he would say "One of them is heads." 3. You say "They are both different sides" and are right 500,000 times [66.67%]. Do you see that you are right 500,000 times in both cases (1b and 3)? However, the percentage increases because 250,000 of the trials "didn't count". 4. You don't accept this and make some other non-applicable analogy. 5. I go get drunk. Be back later. | ||
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Impervious
Canada4216 Posts
On July 16 2011 05:02 Sea_Food wrote: Actually the reason I created this topic because I wanted to understand after hours of thinking about it my self. I have no idea what are you trying to say with this post. And by the way to the guys telling me the door story, I know it and I accept the correct awnser, but I think its 100% different. Sometimes, it's easier to look at a question like this, and try to figure out the chance of it being wrong, rather than right. Then, since the only two options are "right" and "wrong", the probability of it being "right" is 100% - "wrong". For the coins question: You flip 2 coins, one is blue, the other is red. There are 4 possible outcomes, all equally likely. They are: HH HT TH TT Now, you are told that one of the coins flipped heads. But you don't know which one. This information tells you that one of the outcomes is now impossible - TT cannot happen if one of the coins flipped heads. The new series of potential outcomes is: HH HT TH All of them are equally likely. Now, how often does both heads show up? Normally, without a constraint, that would be 25%. In this case, it is 33%. Since the chance of a T showing up with the 2nd coin is is 100% - chance of 2 H showing up, and the chance of a 33% chance of 2 H showing up, the chance of the 2nd coin being T is 67%. For the door question, same logic: What is the chance that your pick of 3 doors is the wrong one? 2/3 times, you choose the wrong door, so it is 67%. When the host opens a new door to show you it is empty, he does not somehow magically make it more or less likely that you picked the wrong door. The chance you picked one of the two empty doors is still the same. The chance of the other door being wrong is 100% - the chance your initial pick was wrong = 33%, since there are only 2 doors. Since the door you picked has a 67% chance of being wrong, that means it has a 33% chance of being the right door. And switching is a 67% chance of being right. | ||
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Djagulingu
Germany3605 Posts
On July 16 2011 03:39 Dave[9] wrote: I just feel bad for Chill because I've sen him try to explain math to fellow teamliquidians before and eventually give up because the OP simply doesn't understand. Yeah. The fact that Chill knows about conditional probability better than a few people in this blog combined makes it difficult to understand for some people, and that produces funny blogs. Thanks for the laughs guys. | ||
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lolsixtynine
United States600 Posts
On July 16 2011 04:30 Orpheos wrote: you know another stupid argument we should have is whether .9999 repeating is the same thing as 1 (we really shouldnt) Oh god, not that argument. I don't see what's not to get. Just look at the freaking numbers. 0.999999... 1.000000... Starting from the left, 0.9 repeating has a 0, while 1 has a 1. How can that not be enough for people, we learned this shit in kindergarten. | ||
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Bibdy
United States3481 Posts
Notice that the question also says "What's the probability of the other coin being tails?". It makes no mention of which is the first coin, and which is the second coin. It simply asks that, "given that you know all of the potential outcomes of two coins being flipped, and Tails+Tails isn't one of them, what are the odds of getting at least one tails out of those flips"? That would be 66.6667%. Your confusions stems from the usage of the word 'other' in that question. You're thinking of the two coins in absolutes and always assuming the first coin is the one that came up heads. The question doesn't say that. | ||
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JeeJee
Canada5652 Posts
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evanthebouncy!
United States12796 Posts
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josemb40
Peru611 Posts
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deathly rat
United Kingdom911 Posts
On July 16 2011 06:11 josemb40 wrote: a coin can also land on its border/edge, not being heads or tails.. how do you like that into your probability calculous It's a hypothetical mathematical problem. Also, I defy you to show me a video of someone flipping a coin in the air and legitimately landing it on a hard smooth surface. I think it's so improbable to not be worth calculating, like soooooooooooooo improbable. | ||
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Adeny
Norway1233 Posts
On July 16 2011 05:52 lolsixtynine wrote: Oh god, not that argument. I don't see what's not to get. Just look at the freaking numbers. 0.999999... 1.000000... Starting from the left, 0.9 repeating has a 0, while 1 has a 1. How can that not be enough for people, we learned this shit in kindergarten. However. We know that if we multiply by X then divide by X we get the original number, right? Example: 10 * 2 = 20, 20 / 2 = 10. Now take the number one. Divide it by 3, we get 0.33.., What happens when we multiply that by 3 again? 0.999.. | ||
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Bibdy
United States3481 Posts
On July 16 2011 06:40 Adeny wrote: However. We know that if we multiply by X then divide by X we get the original number, right? Example: 10 * 2 = 20, 20 / 2 = 10. Now take the number one. Divide it by 3, we get 0.33.., What happens when we multiply that by 3 again? 0.999.. The infinitely recurring 3 brings that multiple back to 1. And here comes the off-topic train. | ||
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hypercube
Hungary2735 Posts
On July 16 2011 02:38 Chill wrote: Random: HH x HT o TH o TT x 50% After knowing at least one was heads: HH x HT o TH o 66.6% O_o I think you're just thinking about it wrong. His knowledge isn't affecting the outcome - the outcome was random but he gave you specific information about the result that eliminates one of the possibilities. If he flipped a coin, told you it was heads, and then flipped the other coin, there would be a 50% chance one of them was tails. But that's not the same thing. In scenario 1, TT was an option was that later eliminated with information. In scenario 2, TT is never a possibility so it doesn't factor in. How about this: Random: HH -> H HT -> T TH -> T TT -> H 50% After knowing at least one was heads: 1 x HH -> H 0.5 x HT -> 0.5T 0.5 x TH -> 0.5T 50% I don't see a clear reason to prefer your distribution to mine. For example if he just looked at one of the coins in secret and told what he saw then the second distribution is the correct one (because for HT and TH he'd say tails 50% of the time). edit: to clarify, everyone who got 2/3 was assuming that every time one of the coins comes up heads your friend will say so. If that's true you are correct to just count up the cases. However, this assumes that he has an a priori preference for heads, i.e for HT he'll always say one of them is heads and never that one of them is tails. I just don't feel like that assumption is justified, given the description of the problem. | ||
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Symmetry
Canada294 Posts
On July 16 2011 06:40 Adeny wrote: However. We know that if we multiply by X then divide by X we get the original number, right? Example: 10 * 2 = 20, 20 / 2 = 10. Now take the number one. Divide it by 3, we get 0.33.., What happens when we multiply that by 3 again? 0.999.. I believe there is a 99.999...% chance that he was joking. | ||
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ch33psh33p
7650 Posts
On July 16 2011 05:52 lolsixtynine wrote: Oh god, not that argument. I don't see what's not to get. Just look at the freaking numbers. 0.999999... 1.000000... Starting from the left, 0.9 repeating has a 0, while 1 has a 1. How can that not be enough for people, we learned this shit in kindergarten. I cannot believe you actually can't understand they are the same. I feel so sorry for you. If Chill is drunk enough, he just might ban you for ignorance. EDIT: On the off chance you're joking, well played. | ||
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