EPTOn July 16 2011 14:01 Chill wrote:
lol this thread is a fucking train wreck. Jesus christ.
lol this thread is a fucking train wreck. Jesus christ.
We can't convince them all :<
Coins tosses - Page 6
| Blogs > Sea_Food |
|
Dave[9]
United States2365 Posts
We can't convince them all :< | ||
|
Sea_Food
Finland1612 Posts
On July 16 2011 05:30 Chill wrote: 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. This is exactly my problem from understanding. 1b was the analogy I was searching for. So does he say 1 tails, or 1 heads, I say they landed different side 67% chance 1 000 000times, but only 500 000 times did they land different side? If I have a two out of three chance to guess correctly, how can I only guess correct one out of two times? Or did you mean if we also count when he flips two tails and say one is tails I have 50% chance goess correctly? Because I would not understand why I would only have 50% chance then. PS. Im trying to prove myself wrong. | ||
Chill
Calgary25989 Posts
| ||
|
BlackJack
United States10574 Posts
On July 16 2011 11:34 RoKetha wrote: This is actually a problem with language and the framing of the problem. Your interpretation of the statement, "One of the coins is a head" determines the probability of the second coin being heads or tails. If the statement being evaluated is, "Is at least one of these coins a head?" and the coin-flipper will always either answer, "One of the coins is a head," or, "It is not the case that one of the coins is a head," then the answer is that there is a 2/3 chance that one of the coins is a tail (I'd say it's misleading to say "the other" coin is a tail because a "first" or "original" coin was never specified). If the statement the coin-flipper is answering is instead, "What side is showing on the first coin I examine?" then the answer is 50%. For more information, see this article: http://en.wikipedia.org/wiki/Boy_or_Girl_paradox most important post of this thread | ||
mikeymoo
Canada7170 Posts
| ||
|
Sea_Food
Finland1612 Posts
On July 16 2011 22:54 mikeymoo wrote: This reminds me of when I was trying to convince people that 'trucker' didn't rhyme with 'diner'. Any word rhymes with any word if the speaker tries hard enough. There is no real definition of the word rhyme. | ||
|
ComaDose
Canada10357 Posts
Chill said it best when he said its proven and you should be trying to understand why. | ||
|
Chill
Calgary25989 Posts
On July 17 2011 00:37 Sea_Food wrote: Any word rhymes with any word if the speaker tries hard enough. There is no real definition of the word rhyme. Record a voice clip of you rhyming "Coin" with "Toss". PM me it and I will unlock this blog. | ||
|
Sea_Food
Finland1612 Posts
I will probably not understand any time soon how this coin flip math actually works, I'm just that stupid. However, I would appreciate if someone who does understand replies this with an answer, so I can someday hopefully understand on my own after more thought. I am going to type claims, and you will just have to type which are the claims that are incorrect. You can explain why if you want. 1. Whenever two coins are tossed there is a 1/2 chance they both land different side up. 2. Whenever two coins are tossed, and you are told one of them landed on heads, you know there is a 2/3 chance the two coins landed different side up. 3. Whenever two coins are tossed, and you are told one of them landed on tails, you know there is a 2/3 chance the two coins landed different side up. 4. Whenever two coins are tossed, and you are told one of them landed on X, you know there is a 2/3 chance the two coins landed different side up. 5. When someone says he is going to toss two coins, but he promises he will tell you on what side one of them landed, you can before the coins are tossed already tell that there is 2/3 chance they will land different side up. 6. Two coins are tossed 1 000 000 times. Every time two tails land you are told one landed tails. Every time two heads land you are told one landed heads. When its 1 tails, one heads, you are told 50% times one landed heads, other 50% times one landed tails. No matter what, every time you are told which side up one of the coins landed, you will say there is 2/3 chance the two coins landed different side up. The rules on what base are you told what coin landed which side are not told to you. 7. Same as 6, but the rules are told to you. Predictions: + Show Spoiler + Unsure about 4, but 5, 6 and 7. But then again im the guy who dosnt even understand 2 or 3. | ||
|
Orpheos
United States1663 Posts
the point is that while the chance of heads or tails is 1/2, the additional information you get from flipping two and him telling you that one of them is heads, gives you ADDITIONAL INFORMATION. so you can say with more certainty that one thing happened over another. | ||
|
ComaDose
Canada10357 Posts
![[image loading]](http://upload.wikimedia.org/math/4/7/e/47e0d646891053c1f3b41fa8c81b6ebb.png) | ||
|
Horuku
United States405 Posts
On July 17 2011 02:05 Chill wrote: Record a voice clip of you rhyming "Coin" with "Toss". PM me it and I will unlock this blog. Any chance on the voice clip being posted?  | ||
|
Cassel_Castle
United States820 Posts
HH, TH, HT, so 2/3 of the time the second coin is heads. First coin is heads: HH, HT, so 1/2 of the time the second coin is heads. Your problem is that you don't consider that the second coin could have been the heads when you say "one coin is heads". | ||
|
Sea_Food
Finland1612 Posts
On July 19 2011 04:14 Orpheos wrote: i think your problem is that you are too stubborn. you do understand why it is 2/3 chance. No, actually I dont. I do know all the reasoning of people saying its 2/3. Math has always been my strongest subject, but no matter how much I think of the problem, I always find all the reasoning false. On July 19 2011 04:51 Cassel_Castle wrote: One coin is heads: HH, TH, HT, so 2/3 of the time the second coin is heads. First coin is heads: HH, HT, so 1/2 of the time the second coin is heads. Your problem is that you don't consider that the second coin could have been the heads when you say "one coin is heads". I do consider it, but my mind just says that, when I know first coin is heads its 50%, when i know second coin is heads its 50%. When i know if its either first or second, I calculate it 50% + 50% / 2 = 50%, reasoning behind it being its either 1st or 2nd, the coin hes talking bout. | ||
|
Vod.kaholic
United States1052 Posts
On July 16 2011 11:34 RoKetha wrote: This is actually a problem with language and the framing of the problem. Your interpretation of the statement, "One of the coins is a head" determines the probability of the second coin being heads or tails. If the statement being evaluated is, "Is at least one of these coins a head?" and the coin-flipper will always either answer, "One of the coins is a head," or, "It is not the case that one of the coins is a head," then the answer is that there is a 2/3 chance that one of the coins is a tail (I'd say it's misleading to say "the other" coin is a tail because a "first" or "original" coin was never specified). If the statement the coin-flipper is answering is instead, "What side is showing on the first coin I examine?" then the answer is 50%. For more information, see this article: http://en.wikipedia.org/wiki/Boy_or_Girl_paradox This has been quoted before, but Roketha gets it. Chill and everyone else are doing a good job of stating the correct explanations, but they're horrible at actually explaining it because they are not properly addressing OP's misunderstanding. They're just hammering him with more re-phrasings of the same explanation without explaining WHY both sides are talking about different things. When I first saw this thread I was like "wtf it's obviously 50%" until I realized that the problem wasn't saying what I thought it was. The real problem is the wording of the problem being a little too open to interpretation, as Roketha said. | ||
|
Sea_Food
Finland1612 Posts
On July 19 2011 05:38 Vod.kaholic wrote: This has been quoted before, but Roketha gets it. Chill and everyone else are doing a good job of stating the correct explanations, but they'd be horrible teachers because they are not addressing OP's misunderstanding. They're just hammering him with more re-phrasings of the same explanation without explaining WHY both sides are talking about different things. The real problem is the wording of the problem being a little too open to interpretation, as Roketha said. This is actually not the case. | ||
|
Vod.kaholic
United States1052 Posts
EDIT: nevermind, I didn't read after this post, I didn't see your post-reopening statement. My bad. | ||
|
waxypants
United States479 Posts
On July 19 2011 05:37 Sea_Food wrote: No, actually I dont. I do know all the reasoning of people saying its 2/3. Math has always been my strongest subject, but no matter how much I think of the problem, I always find all the reasoning false. I do consider it, but my mind just says that, when I know first coin is heads its 50%, when i know second coin is heads its 50%. When i know if its either first or second, I calculate it 50% + 50% / 2 = 50%, reasoning behind it being its either 1st or 2nd, the coin hes talking bout. Man, if you are going to guess at a formula, at least think of the extreme cases to see if it's reasonable. Say you have one normal coin and one coin with tails on both sides. Then the chances of heads are 50% and 0% respectively (assuming a fair coin). According to your logic, if I told you that one coin was heads, you would conclude that the probability of both being heads would be (50% + 0%)/2 = 25% which is obviously wrong. | ||
|
The_Templar
your Country52797 Posts
On July 19 2011 05:37 Sea_Food wrote: No, actually I dont. I do know all the reasoning of people saying its 2/3. Math has always been my strongest subject, but no matter how much I think of the problem, I always find all the reasoning false. I do consider it, but my mind just says that, when I know first coin is heads its 50%, when i know second coin is heads its 50%. When i know if its either first or second, I calculate it 50% + 50% / 2 = 50%, reasoning behind it being its either 1st or 2nd, the coin hes talking bout. This exactly. Coins are independent from each other. If one of them is heads (garunteed) then the other one still has a 50% chance. Or, it's actually either coin that could be it, in which case we have HT, TH, and HH. TH and HT are redundant, so its HT(TH) and HH, either of which has a 50% chance. | ||
|
Vod.kaholic
United States1052 Posts
The problem gives you 3 options. Don't focus on which coin is which, you just have the following 3 possibilities: Coin A OR B----Coin B OR A H----------------------- H H ---------------------- T T----------------------- H HT and TH are distinct, and the question is what percentage of the possibilities contain Tails. So, 2/3, or 66%, are tails. EDIT: I'm just re-wording what chill said without adding much, because IDK what else there is to add, we can only gift-wrap the explanation differently now that I know it's not a misunderstanding. | ||
| ||
