Brainteaser for TeamLiquid! - Page 18

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 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.

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

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

On June 11 2011 00:27 Dlok wrote:

we run it 100 times

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 ?

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.

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.

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.

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.

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.

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

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.

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".

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.

On June 11 2011 00:07 amatoer wrote:
I'm not into Math, but I think I figured it out by drawing:



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

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.