Quick Logic Problem

KingCondanomation said:
Ok, just so you are on record, despite this being a documented WELL-KNOWN example in probability theory with presumably thousands of people with degrees (including the algebra teacher, Dano, MottleyDude, Trog, the smartest woman in the world who does this for a living) , they have all been wrong all this time and you, Damo and Thorn are right, is that right?

Maybe you can't understand it, fine, but don't suggest something so ludicrous as all those who have studied this exact well known case and understand why it is 1 in 3 chance of having 2 boys when one boy is known to exist of 2 kids. Just accept it as something that is true but you can't understand.
For example, I don't understand the theory of relativity, does that mean it's not true?
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You're confusing yourself with irrelevancies like birth order.

Trog was not on your idiot side either.
 
KingCondanomation said:
Jane has a 1 in 3 chance of having a boy and then a girl, a 1 in 3 chance of having a girl and then a boy and a 1 in 3 chance of having a boy and then a boy.

Joan has a 1 in 2 chance of having a boy and then a boy and a 1 in 2 chance of having a boy and then a girl.
Joan's oldest child is a boy so those are the only 2 logical combinations left.

Thus combined there is a 1 in 6 chance that they have all boys ( 1/3 * 1/2).
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Dude, you didn't include the possibility in there that there is another boy boy combo.
 
DigitalDave said:
Dude, you didn't include the possibility in there that there is another boy boy combo.
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This.

Given - Boy
Boy - Given
Girl1 - Girl2
Girl2 - Girl1
Given - Girl
Girl - Given

Strike the chances that are not salient as they do not include the Given.

Given - Boy
Boy - Given
Given - Girl
Girl - Given

You have four equal chances... Only two of which fit within the parameters given... 2/4 = 1/2... so forth.

Hey, he has a website though.
 
This:
Jane has a 1 in 3 chance of having a boy and then a girl, a 1 in 3 chance of having a girl and then a boy and a 1 in 3 chance of having a boy and then a boy.

Should read:
Jane has a 1 in 4 chance of having a boy then a girl, a 1 in 4 chance of having a girl and then a boy, a 1 in 4 chance of having a boy and a boy, a 1 in 4 chance of having a boy and a boy.

It should read that way because the boy can be either the oldest or the youngest, but definatly one has to be a boy. If I have to break it down because you don't get it, I will. Will tag each boy with youngest and oldest.

Jane has a boy, could be younger or older than his sibling so here are the possibilities:

x and boy (youngest)
boy and x (oldest)

So fill in x with the possibilites:

boy and boy (youngest)
girl and boy (youngest)
boy and boy (oldest)
boy and girl (oldest)

Your odds are still 50%, duh!
 
KingCondanomation said:
Ok, just so you are on record, despite this being a documented WELL-KNOWN example in probability theory with presumably thousands of people with degrees (including the algebra teacher, Dano, MottleyDude, Trog, the smartest woman in the world who does this for a living) , they have all been wrong all this time and you, Damo and Thorn are right, is that right?

Maybe you can't understand it, fine, but don't suggest something so ludicrous as all those who have studied this exact well known case and understand why it is 1 in 3 chance of having 2 boys when one boy is known to exist of 2 kids. Just accept it as something that is true but you can't understand.
For example, I don't understand the theory of relativity, does that mean it's not true?
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Dude, you're all wrong because you refuse to acknowledge a second boy-boy combo. It's not hard. There was apossiblity that you all refused to acknowledge.
 
King displays a horrid realization of the "critical thought by concensus" virus that is spreading through society, and truly turning people into zombies.
 
In order to properly do the "survey"

You would have to find a random number of people with two kids. Then you would remove those from the list with no boys at all because they do not fit within the parameters.

Then you'd have to split them in half, in one half you would set "Given" to firstborn, remove the ones from the "survey" that do not have a boy firstborn from the survey.

Then you'd have to take the second half and set "Given" to secondborn. Any in the group that do not fit within the parameter would be removed from the survey.

The reason for this is because the "Given" has an equal chance of being first or secondborn. If you do not do it you skew your results because you ignore the probability of the "Given" being first or second born....

With those two groups randomly selected you would get salient results. And it would be 50% plus or minus a smidge depending on size of the sample.
 
KingCondanomation said:
Do 1000 coin tosses of 2 coins at a time. Eliminate all those tosses where BOTH coins show as heads, leaving you with only those tosses where there are either (your goal here is to see the chances of getting both as tails):
1. heads on first coin, tails on second coin
2. tails on first coin, heads on second coin
3. tails on first coin, tails on second coin

Damo is saying that if I name those coins, I would somehow be able to reverse the last case (to get a 1 in 2 shot of having both as tails, but somehow I am NOT allowed to reverse the first 2 cases).

It's a common mistake and is talked about in the link that I gave. You would find that each case would occur about 1 out of 3 times, including the case with both coins showing as tails.
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You don't calculate probabilities through process of elmination. If you want to try to simplify the problem, lets just say you do use your three distinct possibilities (BB, BG, GB) which ARE NOT EQUAL IN FREQUENCY WHEN IT IS KNOWN THAT ONE IS A BOY! If one is a boy then BB is a 2 out of 4 chance (because there are two scenarios where this can be true), where as GB is a one out of 4, and BG is a one out of 4. So You have 50% still.
 
Damocles said:
In order to properly do the "survey"

You would have to find a random number of people with two kids. Then you would remove those from the list with no boys at all because they do not fit within the parameters.
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Correct and this is what she asked.

Damocles said:
Then you'd have to split them in half, in one half you would set "Given" to firstborn, remove the ones from the "survey" that do not have a boy firstborn from the survey.

Then you'd have to take the second half and set "Given" to secondborn. Any in the group that do not fit within the parameter would be removed from the survey.

The reason for this is because the "Given" has an equal chance of being first or secondborn. If you do not do it you skew your results because you ignore the probability of the "Given" being first or second born....

With those two groups randomly selected you would get salient results. And it would be 50% plus or minus a smidge depending on size of the sample.
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Dude you can't do that, remember that the ENTIRE case was predicated on NOT knowing the order for the woman who has one boy. That's why it ends up as a 1 in 3 chance, because they are revealing to you only one child's sex, that does influence the probability of the other child's sex. There are 2 different ways that other child could be a girl, a girl as the first and a girl as the 2nd. But only one way of having 2 boys.
 
KingCondanomation said:
Correct and this is what she asked.


Dude you can't do that, remember that the ENTIRE case was predicated on NOT knowing the order for the woman who has one boy. That's why it ends up as a 1 in 3 chance, because they are revealing to you only one child's sex, that does influence the probability of the other child's sex. There are 2 different ways that other child could be a girl, a girl as the first and a girl as the 2nd. But only one way of having 2 boys.
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I can, because it gives the correct probability within the "given". It is the only accurate way to do the survey.

Given has an equal chance of being first or second born. Pretending that this second probability is not salient is what is giving the "paradox" its silliness and perpetuating the inanity.

BB - 50% (the reason for this is there are two chances for the BB combo if you are being honest when you create your graph).
BG - 25%
GB - 25%
 
Damocles said:
I can, because it gives the correct probability within the "given". It is the only accurate way to do the survey.

Given has an equal chance of being first or second born. Pretending that this second probability is not salient is what is giving the "paradox" its silliness and perpetuating the inanity.

BB - 50% (the reason for this is there are two chances for the BB combo if you are being honest when you create your graph).
BG - 25%
GB - 25%
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You still keep dodging when I ask you if this VERY well known probability question is wrong?

You are looking at it wrong. Each mother knows what BOTH her kids sex are, all you are told is that one of the Mom's kids is a boy and you must guess the other (now this is the important part) where that "other" could be the first or the second child.
 
Again, it doesn't matter if one of the subjects of the survey "knows". You have to base it on the probability structure.

Since BB has two different possibilities it must be factored in or you skew the poll and get hilariously long threads as the result. In order to make a valid survey you must take all pieces of the probability into account and negate those factors that would skew the result of probability.
 
Damocles said:
Again, it doesn't matter if one of the subjects of the survey "knows". You have to base it on the probability structure.

Since BB has two different possibilities it must be factored in or you skew the poll and get hilariously long threads as the result. In order to make a valid survey you must take all pieces of the probability into account and negate those factors that would skew the result of probability.
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You must truly be a buddhist.... to have the patience to continue with this thread.
 
Superfreak said:
You must truly be a buddhist.... to have the patience to continue with this thread.
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And I don't?

Sometimes I wonder if this is a popularity contest with those joining in later.

In any case, I would urge anyone reading this thread to disregard both mine and Damo's argument and simply look at this VERY well known example in probabibility theory that deals with this exact case:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

I simply fail to understand how ANYONE could read that and pretend that out of all the hundreds of professors and thousands of students who have gone over that well-known case, why if there is not a SINGLE dissentation to it on Wikipedia, how they can actually claim that all those people missed it, that it's wrong and that they are right.
I know the term gets thrown around loosely on here, but this is insane.
 
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