EPTTwo coins were flipped. One was heads. There are then three possible outcomes: HT, TH, HH. 67% that the unknown coin was heads. Not the second coin, the unknown coin.
Coins tosses - Page 3
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mucker
United States1120 Posts
Two coins were flipped. One was heads. There are then three possible outcomes: HT, TH, HH. 67% that the unknown coin was heads. Not the second coin, the unknown coin. | ||
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Hesmyrr
Canada5776 Posts
2/3? When you switch, right? Hmm, okay. I might not be understanding this then. Let me think about it... | ||
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lolsixtynine
United States600 Posts
On July 16 2011 03:16 Sea_Food wrote: No I dont, because if he tosses coins that many times, he will throw TT some times, in which case he cannot tell me one of the coins landed H. That is precisely why you are throwing them away. >_> Chill is right. This problem is poorly worded. The question shouldn't involve a friend at all, because you can make faulty arguments like "he wouldn't have told me that if...". Here's how the problem should be worded. You flip two coins, and you know that at least one of the coins turned up heads (but have no information as to which one, nor any other information). What is the probability that the other is heads? The answer, for reasons explained above many times, is 1/3. | ||
Chill
Calgary25981 Posts
You have two magic coins. When tossed together, at least one of them must be heads. What's the probability of one coin landing on tails? Compare that to: You throw two coins together. One of them is heads. What is the probability of one coin landing on tails? Compare that to: Your friend tosses two coins, then asks you to guess how the coins landed. You reply that you cannot know. Then your friend reveals that one of the coins he threw landed heads. What is the probability of the other coin being tails? 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. | ||
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Dave[9]
United States2365 Posts
I can see a lot of people giving up on you if you don't simply research this very WELL explained problem that's all over the internet. But if you're in a probability class, Bayes theorem would give you an answer that is satisfying( imo most bayes theorem problems give interesting results to me anyway) | ||
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Chill
Calgary25981 Posts
On July 16 2011 03:27 lolsixtynine wrote: That is precisely why you are throwing them away. >_> Chill is right. This problem is poorly worded. The question shouldn't involve a friend at all, because you can make faulty arguments like "he wouldn't have told me that if...". Here's how the problem should be worded. You flip two coins, and you know that at least one of the coins turned up heads (but have no information as to which one, nor any other information). What is the probability that the other is heads? The answer, for reasons explained above many times, is 1/3. The problem is not poorly worded. The OP is just frankly not getting it. You could word it so that it was easier to get the right answer, but that doesn't necessarily mean it's poorly worded. It's worded in a way that makes it inherently more difficult to get correct, by design. | ||
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Essbee
Canada2371 Posts
What the hell. I did it with a web calculator, I can't figure how this result comes out haha. 2.71828182845905 ^ (3.14159265358979 * sqrt(-1)) = -1 | ||
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lolsixtynine
United States600 Posts
On July 16 2011 03:24 Hesmyrr wrote: 2/3? When you switch, right? Hmm, okay. I might not be understanding this then. Let me think about it... You had a 1/3 chance of guessing the correct door. Therefore the probability of all other doors having the prize is 2/3. Since the host eliminated one door (which does not influence the chance that you originally picked the correct door), the remaining door must have a 2/3 probability of having the prize. | ||
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Dave[9]
United States2365 Posts
On July 16 2011 03:29 Essbee wrote: What the hell. I did it with a web calculator, I can't figure how this result comes out haha. 2.71828182845905 ^ (3.14159265358979 * sqrt(-1)) = -1 e^(pi*i)=-1 from Euler's identity, but don't derail this thread! | ||
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lolsixtynine
United States600 Posts
On July 16 2011 03:28 Chill wrote: The problem is not poorly worded. The OP is just frankly not getting it. You could word it so that it was easier to get the right answer, but that doesn't necessarily mean it's poorly worded. It's worded in a way that makes it inherently more difficult to get correct, by design. I don't think it's poorly worded if you assume your friend would say what he said in ALL cases where it was true. To take an extreme example, imagine a friend that would only say what he said if there were exactly one head. Then the probability of it being tails would be 100%. The friend complicates things unnecessarily. | ||
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Essbee
Canada2371 Posts
On July 16 2011 03:31 Dave[9] wrote: e^(pi*i)=-1 from Euler's identity, but don't derail this thread! Alright alright, I just found it interesting  | ||
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Hesmyrr
Canada5776 Posts
On July 16 2011 03:32 lolsixtynine wrote: I don't think it's poorly worded if you assume your friend would say what he said in ALL cases where it was true. To take an extreme example, imagine a friend that would only say what he said if there were exactly one head. Then the probability of it being tails would be 100%. The friend complicates things unnecessarily. All this discussion reminds me of certain stupid math thread xD Also, can anyone tell me what the quiz show problem is referred to as so I can google it? My brain is not just working today. | ||
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lolsixtynine
United States600 Posts
http://en.wikipedia.org/wiki/Monty_Hall_problem | ||
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Dave[9]
United States2365 Posts
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. | ||
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lolsixtynine
United States600 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. There are. I read an article about this. If I can find it I'll link it here. Unsurprisingly, it was 66%. | ||
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psychopat
Canada417 Posts
I have a standard deck of 52 cards. Without letting you see the relevant side of the cards, I tell you to pick out the Queen of Clubs. I look through all the remaining cards and throw out 50 of them, so that we now each have 1 card and I tell you that one of us has the Queen of Clubs. Do you wish to trade? If that doesn't make it really obvious, nothing will | ||
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Chill
Calgary25981 Posts
On July 16 2011 04:12 psychopat wrote: The easy way to make the Monty Hall problem is just to take it to much larger proportions: I have a standard deck of 52 cards. Without letting you see the relevant side of the cards, I tell you to pick out the Queen of Clubs. I look through all the remaining cards and throw out 50 of them, so that we now each have 1 card and I tell you that one of us has the Queen of Clubs. Do you wish to trade? If that doesn't make it really obvious, nothing will lol thats the best way ive ever seen it explained haha | ||
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Impervious
Canada4207 Posts
On July 16 2011 03:31 Dave[9] wrote: e^(pi*i)=-1 from Euler's identity, but don't derail this thread! You can prove it through the direct use of exponential, sin, and cosine taylor series (which is what I did before I learned about Euler's formula). It's still a mathematical mindfuck, even if there are multiple ways of proving it. + Show Spoiler + From Wikipedia: http://en.wikipedia.org/wiki/Euler's_formula It's about halfway down the page. It's pretty short and sweet. Also, Chill basically answered the OP about as well as anyone could..... EDIT - cleared something up a bit. | ||
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Hesmyrr
Canada5776 Posts
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Orpheos
United States1663 Posts
On July 16 2011 04:13 Chill wrote: lol thats the best way ive ever seen it explained haha yea thats how alot of people explain the game show one. say there are a hundred doors. and you pick one. then the game show host eliminates 98 of them, should you switch? you know another stupid argument we should have is whether .9999 repeating is the same thing as 1 (we really shouldnt) | ||
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