EPThttp://en.wikipedia.org/wiki/Boy_or_Girl_paradox
Brainteaser for TeamLiquid! - Page 18
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endy
Switzerland8970 Posts
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox | ||
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Logo
United States7542 Posts
On June 11 2011 00:14 endy wrote: I don't understand why people keep arguing since this is a very well known paradox. http://en.wikipedia.org/wiki/Boy_or_Girl_paradox The wikipedia article even says: The paradox has frequently stimulated a great deal of controversy. Many people argued strongly for both sides with a great deal of confidence, sometimes showing disdain for those who took the opposing view. So uh you linked us the answer your own question. | ||
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ControlMonkey
Australia3109 Posts
On June 10 2011 23:53 Logo wrote: If we do the test 100s of times the result will in fact be 1/3rd and I would gladly take you up on such odds at something less than 1/2 but greater than 1/3rd as it'd be free money. You could even write a very simple program to test it. Not understanding probability (which is very counter-intuitive) doesn't change reality. I'll also just leave this here: http://www.ted.com/talks/peter_donnelly_shows_how_stats_fool_juries.html That is an awesome vid you linked. Thanks! | ||
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Dlok
Sweden7 Posts
On June 10 2011 23:53 Logo wrote: If we do the test 100s of times the result will in fact be 1/3rd and I would gladly take you up on such odds at something less than 1/2 but greater than 1/3rd as it'd be free money. You could even write a very simple program to test it. Not understanding probability (which is very counter-intuitive) doesn't change reality. I'll also just leave this here: http://www.ted.com/talks/peter_donnelly_shows_how_stats_fool_juries.html we run it 100 times | ||
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endy
Switzerland8970 Posts
On June 11 2011 00:17 Logo wrote: The wikipedia article even says: So uh you linked us the answer your own question. Haha these two sentences from wikipedia are also ambiguous. It's unclear that the many people who argued strongly for both sides knew whether it was a paradox or not. Since that link was already posted at the beginning of the thread, I assume people here knew it's was paradox when arguing, so why simply not admit that the wording has it's importance and that it's pointless to argue forever, since both sides are right depending on how you interpret the wording ? | ||
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Ivs
Australia139 Posts
Now there are 3 camps of people 1. People interpreted the OP as the boy/girl paradox, even though OP failed. They say 1/5 2. People who don't really understand whats going on and go with the simplest reasoning. They say 1/3 3. People who are calling out OP's original wording and poor usage of "other", and also get the answer of 1/3. Chill out guys, no need for name/credential calling. There is no argument here. | ||
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Logo
United States7542 Posts
I recommend you stay away from Vegas. Do you even realize what you'd be betting on? If I win every time we get heads + heads then you'd win with heads + tails (or tails + heads) and every time we get tails + tails we'd call it a draw. You'd be a fool to give someone odds on heads + heads at > 1/3 when you're not winning on two of the 4 possible outcomes. Haha these two sentences from wikipedia are also ambiguous. It's unclear that the many people who argued strongly for both sides knew whether it was a paradox or not. Since that link was already posted at the beginning of the thread, I assume people here knew it's was paradox when arguing, so why simply not admit that the wording has it's importance and that it's pointless to argue forever, since both sides are right depending on how you interpret the wording ? The point is the paradox causes intense reactions by those who don't accept the answer as true while those who understand the right answer are... well right. I don't know why you'd think that people wouldn't argue over a paradox that's known to create controversy and argument. | ||
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oxidized
United States324 Posts
On June 10 2011 23:41 Dlok wrote: to those who say 1/5: flip two coins, then tell me one of the results in any way that does not exclude the possibility of a pair. you would give me 1/3 odds on a pair, while the odds clearly havent changed and really are 1/2. now we do this 100 times and I make alot of money. Wrong. It is the ambiguity of the paradox that causes us to say 1/5. I would not take your bet. This is the bet I would make. Flip 2 coins. For each set, throw it out if there is no heads result. Only keep the results which have at least one heads. I give you that 1/3 the sets have a pair of heads, not 1/2. | ||
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iStarKraft
United Kingdom79 Posts
He played as zerg. He played as terran. He played as protoss. Zerg will occur 1/3 of the time. Therefore the answer is 1/3. There is absolutely no purpose to writing out the different combinations of games (ZZ PP TT PT TP... etc.), as we only need to find the probability he played one game as zerg, since we already know one of his games was zerg. I will happily respond to any counter-arguments, but I would most likely be rewording / repeating myself. (^_^) iSK | ||
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oxidized
United States324 Posts
On June 11 2011 00:33 Logo wrote: I recommend you stay away from Vegas. Do you even realize what you'd be betting on? If I win every time we get heads + heads then you'd win with heads + tails (or tails + heads) and every time we get tails + tails we'd call it a draw. You'd be a fool to give someone odds on heads + heads at > 1/3 when you're not winning on two of the 4 possible outcomes. Read his bet carefully. He does not throw out tails/tails, which is different from what we expect when we say 1/5. See my above post for details. | ||
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jambam
United States324 Posts
On June 11 2011 00:29 Ivs wrote: People are still arguing because OP wanted to present the Boy/Girl paradox, but messed up the wording. Now there are 3 camps of people 1. People interpreted the OP as the boy/girl paradox, even though OP failed. They say 1/5 2. People who don't really understand whats going on and go with the simplest reasoning. They say 1/3 3. People who are calling out OP's original wording and poor usage of "other", and also get the answer of 1/3. Chill out guys, no need for name/credential calling. There is no argument here. I can't thank you enough for posting this. This is how I see it as well. | ||
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MisterD
Germany1338 Posts
On June 10 2011 10:11 theDreamStick wrote: Solution: I've played two games. Then the possible combinations are: ZZ, ZP, ZT, PZ, PP, PT, TZ, TP, TT. However, I've said I played Zerg. Then that eliminates PP, PT, TP, TT. Then I am restricted to ZZ, ZP, ZT, PZ, TZ. ZZ is one out of five possible choices, and that is the only which corresponds to "The other game is Zerg." Then the correct answer is 1/5. I don't get this: why do you say "i've played two games" and then enumerate the possible pairings for only one game? And then, regaring only one game, i believe you are wrong. Why is the probability for ZZ 1/5? In the solution spoiler, it states: "Then I am restricted to ZZ, ZP, ZT, PZ, TZ. ZZ is one out of five possible choices" But i think, this is wrong. Here's the possible stuff. Note that [Z] means "you" [Z]Z [Z]P [Z]T Z[Z] P[Z] T[Z] if you don't mark yourself, you get ZZ and ZZ, which looks exactly the same and you would thus - when writing it into a set - resolve those to leave only one ZZ. But it's actually two separate events if you count the positions of the players. So, either [Z]Z and Z[Z] are separate events, or ZP and PZ and ZT and TZ are equal as well. Adding this up: there are 2/6 ZZ (namely [Z]Z and Z[Z] out of the six mentioned above), or there is 1/3 ZZ (namely ZZ out of ZZ, ZT, ZP). So the Probability for ZZ is actually 1/3, not 1/5? This in mind - i think the whole discussion about conditional probability is completely pointless. Why on earth would you argue "this is conditional probability, so it's counter intuitive" and bla bla, but then post a solution where the word "conditional" is not mentioned once? Your answer is not based on conditional probability, and in addition i believe it's wrong because you miscounted the possible events. /edit: clarified wording a little | ||
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chocorush
694 Posts
On June 11 2011 00:29 Ivs wrote: People are still arguing because OP wanted to present the Boy/Girl paradox, but messed up the wording. Now there are 3 camps of people 1. People interpreted the OP as the boy/girl paradox, even though OP failed. They say 1/5 2. People who don't really understand whats going on and go with the simplest reasoning. They say 1/3 3. People who are calling out OP's original wording and poor usage of "other", and also get the answer of 1/3. Chill out guys, no need for name/credential calling. There is no argument here. There is no error in the original wording. The statement, "Given that I played zerg at least once, I played zerg both times," and "I played zerg once and I played the other game zerg as well" are equivalent. People are just misconceiving how many choices they actually have, thinking that "the other game" is in reference to a specific game, when it can not be. | ||
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foxmeep
Australia2337 Posts
On June 11 2011 01:16 MisterD wrote: I don't get this: why do you say "i've played two games" and then enumerate the possible pairings for only one game? And then, regaring only one game, i believe you are wrong. Why is the probability for ZZ 1/5? In the solution spoiler, it states: "Then I am restricted to ZZ, ZP, ZT, PZ, TZ. ZZ is one out of five possible choices" But i think, this is wrong. Here's the possible stuff. Note that [Z] means "you" [Z]Z [Z]P [Z]T Z[Z] P[Z] T[Z] if you don't mark yourself, you get ZZ and ZZ, which looks exactly the same and you would thus - when writing it into a set - resolve those to leave only one ZZ. But it's actually two separate events if you count the positions of the players. So, either [Z]Z and Z[Z] are separate events, or ZP and PZ and ZT and TZ are equal as well. Adding this up: there are 2/6 ZZ (namely [Z]Z and Z[Z] out of the six mentioned above), or there is 1/3 ZZ (namely ZZ out of ZZ, ZT, ZP). So the Probability for ZZ is actually 1/3, not 1/5? This in mind - i think the whole discussion about conditional probability is completely pointless. Why on earth would you argue "this is conditional probability, so it's counter intuitive" and bla bla, but then post a solution where the word "conditional" is not mentioned once? Your answer is not based on conditional probability, and in addition i believe it's wrong because you miscounted the possible events. /edit: clarified wording a little you've misinterpreted. ZZ means you were Zerg the first game, and Zerg the second game. it isn't a "matchup". | ||
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Dlok
Sweden7 Posts
On June 11 2011 00:33 Logo wrote: I recommend you stay away from Vegas. Do you even realize what you'd be betting on? If I win every time we get heads + heads then you'd win with heads + tails (or tails + heads) and every time we get tails + tails we'd call it a draw. You'd be a fool to give someone odds on heads + heads at > 1/3 when you're not winning on two of the 4 possible outcomes. The point is the paradox causes intense reactions by those who don't accept the answer as true while those who understand the right answer are... well right. I don't know why you'd think that people wouldn't argue over a paradox that's known to create controversy and argument. Every time you say Heads i say it will be pair of heads, if you say tailes i say pair of tails, now we know 50 out of a hundred are likely to be pairs so i will do fine. If i say i take only pair of heads i will win 1/4 of said 100 but if im allowed to withdraw when atleast one is not heads i raise my odds to 1/3. This however was not how the problem was stated, and I cant se how it could be interpited that way. | ||
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MisterD
Germany1338 Posts
On June 11 2011 01:30 foxmeep wrote: you've misinterpreted. ZZ means you were Zerg the first game, and Zerg the second game. it isn't a "matchup". ahhh okay, that's how it's meant! xD thanks. okay, then this sounds fine. Still, the point about discussing conditional probabilities stands - this answer does not use them, so don't argue they are needed ^^ | ||
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teamsolid
Canada3668 Posts
On June 11 2011 01:16 chocorush wrote: There is no error in the original wording. The statement, "Given that I played zerg at least once, I played zerg both times," and "I played zerg once and I played the other game zerg as well" are equivalent. People are just misconceiving how many choices they actually have, thinking that "the other game" is in reference to a specific game, when it can not be. Exactly, the two statements are logically equivalent. The only difference is that the 2nd one is misleading, encouraging the reader to focus more on the "other game" and disregard the given information. The 3 groups of people should be: 1. People who messed up by reading the question too quickly (even though they understand conditional probability). So, instead they to try to convince themselves and others that the OP was wrong, not them. 2. People who don't really understand whats going on and go with the simplest reasoning. They say 1/3 3. People who got the correct answer 1/5. | ||
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EchelonTee
United States5260 Posts
On June 11 2011 00:07 amatoer wrote: I'm not into Math, but I think I figured it out by drawing: ![[image loading]](http://www.abload.de/img/brainteaserotie.jpg) So there are 5 possible answers (playing 2 games rnd of which 1 or more as Z) but only one that leads to ZZ so it's 1/5 this picture should be in the op | ||
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Malinor
Germany4736 Posts
Sometimes you have to embrace being stupid, that's what I'm doing here. edit: yeah, as the poster below me said, the poll question still says "Probability that my other game was Zerg?". What kind of english is that? | ||
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piegasm
United States266 Posts
On June 11 2011 01:16 chocorush wrote: There is no error in the original wording. The statement, "Given that I played zerg at least once, I played zerg both times," and "I played zerg once and I played the other game zerg as well" are equivalent. People are just misconceiving how many choices they actually have, thinking that "the other game" is in reference to a specific game, when it can not be. The unedited OP didn't say "other game as well". It just said "other game". The poll itself STILL says "other game". People are going to continue to say 1/3 because, regardless of the explanation at the beginning, the poll itself still asking the probability of drawing Zerg in a single game. | ||
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