Author Topic: A Women Has 2 Kids....  (Read 4043 times)

Offline Eddy-B

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A Women Has 2 Kids....
« Reply #25 on: August 09, 2009, 08:54:38 AM »
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the ORIGINAL question was (simplified) "what is the chance that the second baby is a girl" period
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A women has 2 kids, and one of them is a girl. What is the chance that the other one is a girl?
I'd like to know how it simplified down to this because the original question states that one is a girl, it never specifies which one. It could be either one we don't know.
Regardless of which "one of them is a girl" .. you wanted to know the probability of the OTHER ONE. So if "the one girl" is the first born, than the question is about the second born. If "the one girl" is the second born, than you are asking about the first one. No matter how you look at your statement, you are asking about the other baby, in other words: the one baby that was not mentioned in the first part of your statement.


I will rephrase your question like this:
A woman has 20 kids. 19 of them are girls. What is the chance of the 20th kid to be a girl.


Answer: 50%  (give or take), and not 5%, which would be the answer if i follow your logic.

As mentioned before: the sex of all the other kids do NOT influence any next kid. The chance for a girl is still equal to the global average -wether that be 50% or 52%-



Can we close this thread?  this is getting pointless..
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Offline Hidiot

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« Reply #26 on: August 09, 2009, 09:03:48 AM »
I swear I once heard on a Discovery channel someone saying that any second or later child has less and less chances of being a boy.

Since it doesn't interest me that much, I'll let someone else do the researching.
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Offline CK9

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« Reply #27 on: August 09, 2009, 12:07:44 PM »
If you don't cut out possible sibling relations, the chances change.
« Last Edit: August 09, 2009, 12:08:08 PM by CK9 »
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Offline Kayedon

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« Reply #28 on: August 09, 2009, 01:11:35 PM »
Ultimately, it falls upon how many apples or watermelons she ate.

(Sims 3 reference)
« Last Edit: August 09, 2009, 01:12:58 PM by Kayedon »
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Offline CK9

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« Reply #29 on: August 09, 2009, 04:35:12 PM »
of course, colony opinion is split between those who think the odds of having a girl are good, and those who are genetically manipulating those odds :P
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Offline Sirbomber

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« Reply #30 on: August 09, 2009, 07:26:13 PM »
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of course, colony opinion is split between those who think the odds of having a girl are good, and those who are genetically manipulating those odds :P

Outpost Evening Star:
4/27/71 - A recent poll conducted by the Evening Star shows (not surprisingly) that colonist opinion is divided over the recent housing issues: 50% of all colonists responded that building more Residences was "important" or "extremely important" to them, while the other 50% of all colonists criticized the "pro-housers" for ignoring the recent food and oxygen shortages.  In a bold move, our fearless leader has submitted a proposal to handle both issues by limiting families to having only one child.  Couples who violate the new law will face strict punishment: one of the parents will be tossed out the nearest airlock as soon as the child is old enough to pick which parent s/he likes better.  Proponents of the new plan hail it as a shrewd plan necessary to preserve humanity, while critics condemn it as "a diabolical plan designed to encourage couples to have genetically-engineered children" which may result in a "gender imbalance" according to opposition leaders.  When asked to elaborate, Evening Star reporters received no response as a fist fight had apparently broken out between the two groups.  Reporters were forced to flee the area when the two sides broke into song and dance.  When interviewed, our fearless leader replied, "No comment."
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Offline speaker

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« Reply #31 on: August 09, 2009, 08:48:27 PM »
when you said song and dance i immediately thought west side story fighting
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Offline Sirbomber

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« Reply #32 on: August 09, 2009, 10:02:20 PM »
Yes, that was the other option I considered.
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Offline CK9

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« Reply #33 on: August 09, 2009, 10:28:08 PM »
LOL!  Great one there bomber.  Is that (partially) an actual one from the game?
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Offline Sirbomber

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« Reply #34 on: August 10, 2009, 06:41:38 AM »
I tried to copy the style and use some common phrases ("our fearless leader"), but I wrote it off the top of my head.
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Offline CK9

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« Reply #35 on: August 10, 2009, 02:04:48 PM »
very nice
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Offline Sirbomber

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« Reply #36 on: August 10, 2009, 08:06:21 PM »
I'm glad you liked it.  Maybe I should do more of them?  But then they'd get stale.
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Offline Freeza-CII

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« Reply #37 on: August 10, 2009, 08:54:35 PM »
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"a diabolical plan designed to encourage couples to have genetically-engineered children" which may result in a "gender imbalance"

ok how is this going to imbalance things when the leader is making the choice of which one is which based on computation from the savant main frame. how ever the savant steered several convec at a cliff to make these computations.


This plan is more welcome then the last plan which was abortions till the correct gender was born. which again would get 100% results.
« Last Edit: August 10, 2009, 08:57:00 PM by Freeza-CII »

Offline Simpsonboy77

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« Reply #38 on: August 11, 2009, 04:35:40 PM »
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Regardless of which "one of them is a girl" .. you wanted to know the probability of the OTHER ONE. So if "the one girl" is the first born, than the question is about the second born. If "the one girl" is the second born, than you are asking about the first one. No matter how you look at your statement, you are asking about the other baby, in other words: the one baby that was not mentioned in the first part of your statement.

Ok I will write GB to show that the girl is born first and BG to show the boy is born first.

There are 3 outcomes GG, GB, BG. BB cannot occur.

Of those 3 how many are both girls? Only one. We had 3 to choose from so 1/3 is 33%.

Here is a crude method of looking at it. Assume statistics for births are 1:1, and for the sake of the example we have a perfect sample.

We ask 100 women who have exactly 2 kids what the sexes are. 25 say GG, 25 say GB, 25 say BG, and 25 say BB. We eliminate the BB group since it is an invalid data point. 25 are GG out of a remaining 75 moms.  This again leads to 1/3 or 33%.


To answer you question: 20 children 19 are girls, the chance of the unknown child being  a girl is: 4.761% (1/21) not 5%.
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Offline CK9

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« Reply #39 on: August 11, 2009, 11:06:40 PM »
that's assuming the order of birth matters.  If it does not, GB and BG are the same
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Offline Hooman

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« Reply #40 on: August 12, 2009, 08:30:33 PM »
/sigh

People are just bringing up the same points again and again.

What Eddy-B seems to be saying, is that you phrased your question very poorly. I don't believe this is about what you meant. I believe it is about whether or not what you wrote actually means what you were thinking.


And yes, for the purpose of the meaning of the question, the order does matter.
 

Offline Sirbomber

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« Reply #41 on: August 13, 2009, 03:39:41 PM »
I like how we've divided into two sides: The people who think we should be answering the "correct" question and the people who think we should answer the question that was actually asked.

The point is you should ask the question correctly the first time, then we won't get into debates about how we should answer the question.
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Offline Eddy-B

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« Reply #42 on: August 16, 2009, 06:31:52 AM »
Dear Simpsonboy77,

I will assume your line of reasoning now:
As you have correctly stated, there are 4 possibilities: BB, BG, GB and GG.
Since you know one of them is already a girl, you can rule out the BB combination. You also have said it doesn't matter which one is the girl, which means BG and GB are in fact the same. So in the end you have 2 possibilities: GG and GB - or 50% chance for a girl, 50% chance for a boy.


As you can see, your reasoning is flawed, which is clearly illustrated by the second part of your reply (my 5% was just a simple rounded figure, and it should have been 1/21 = 4.7619047619047619047619047619048 %).  Anyway: your weird logic would say, the more girls are being born from the same mother, the less the chance becomes for the next one to be a girl.
With your logic; if a woman would've given birth to 99 girls, the chances for the 100th baby to be boy would be almost negligible?
I would even dare to say the opposite!!  If such a woman would exist, the chances of getting a boy, after 99 girls i would say are astronomical. Not from a mathematicle perspective, but from a biological one: her partner probably doesn't create Y-sperm to make boys....

Hopefully you would now agree that your "logic" doesn't make much sense when you look at it.


The bottom line is: the chance for a girl are just about the same as for a boy. No matter how you look at it.

---

Hooman:
If i would ask someone: "a woman has 2 children, what are the chances of both of them being a girl?"
== the answer would be 25%
If i changed the question to: "a woman has 2 children, 1 of which is a girl, what are the chances of both of them being a girl?"
== the answer is now 50% (and NOT 33% - no matter HOW you formulate the question!!). The reason is, very simply, because you can completely ignore the mentioned girl when it comes to the sex of the other one.

---

Sirbomber:
There may seem to be 2 "sides" of people here, but there really is only 1 answer to the question, unless you can re-formulate the question so that the answer becomes 33% (which i'm sure you can't).
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Offline Sirbomber

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« Reply #43 on: August 16, 2009, 08:35:10 AM »
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Sirbomber:
There may seem to be 2 "sides" of people here, but there really is only 1 answer to the question, unless you can re-formulate the question so that the answer becomes 33% (which i'm sure you can't).
That's what I was saying you fool.  I'm not saying there are two answers, I'm saying there are the people who have the right answer (you, me, CK9, etc) and the people who have the wrong answer/broken logic (Hooman/Simpsonboy99).
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Offline Hooman

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« Reply #44 on: August 16, 2009, 11:15:23 AM »
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Hooman:
If i would ask someone: "a woman has 2 children, what are the chances of both of them being a girl?"
== the answer would be 25%
If i changed the question to: "a woman has 2 children, 1 of which is a girl, what are the chances of both of them being a girl?"
== the answer is now 50% (and NOT 33% - no matter HOW you formulate the question!!). The reason is, very simply, because you can completely ignore the mentioned girl when it comes to the sex of the other one.

A woman has 2 children. What are the chances of both of them being a girl, given that at least one of them is a girl?

Quote
You also have said it doesn't matter which one is the girl, which means BG and GB are in fact the same. So in the end you have 2 possibilities: GG and GB - or 50% chance for a girl, 50% chance for a boy.
This is false.

If the first kid is a girl, you can't have another kid and then suddenly call that first girl your second kid now. P(GB|G?) = 50%, P(BG|G?) = 0%. Saying that GB = BG for the sake of this question is nonsense.

This would appear to be the sticking point for the problem, based on what you've said.


The whole point of the ordering, is that you can't simply ignore the information about the kid that is given, as you don't know which kid it was.

What you're talking about is: A woman gives birth to a girl. What are the chances of a second birth also being a girl. This is not the qestion that was intended. It is also NOT the following question: A women has two kids, then one is chosen at random, and determined to be a girl, what is the probability that both kids are girls? The reason it is not this question either, is that the choice is not random. The only time the choice could have been made randomly, is if both kids were girls. In the other two cases, nature determines which one you're giving the information about.

The whole point is, both kids come first, the choosing comes second, and the choosing depends on the outcome of what the kids actually were. This is not a random choice.

 

Offline Eddy-B

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« Reply #45 on: August 16, 2009, 11:16:16 PM »
SirBomber: LOL :P
Hooman:
What you are saying is this:
the chances of any of the 4 possibilities is obviously 25%:
BB : 25%
BG : 25%
GB : 25%
GG : 25%
Everyone should be able to agree with me on this one (not taking into account the 52:48 ratio).
So going with this, there is a 25% chance for both kids to be a girl, correct?

Now, you are saying is that if you know the sex of one of them, the natural chance of the GG combination suddenly changes?? Chances don't change with new information about an existing situation. The chance for both of them being a girl is still 25%. It always will be, since there's a 50:50 ratio for sex.

Based on the question at hand "what is the chance of the OTHER one to be a girl", the question is about one specific event, NOT both births, and the answer is a simple 50:50 chance as it is for any child being born on this planet.

=====

Now, let's review the following situation:
Q1:  A woman gives birth to a girl. She gets pregnant again. What is the chance of this second baby to be a girl as well?  Is it 33%, or is it 50% ???   (i'll leave this question open for you to answer).

Q2: A woman gives birth to 2 children. The second baby was a girl. What is the chance of the first one being a girl?  Is it 33%, or is it 50% ???

=====

As i said before: new information does not chance an already calculated chance. Here's another example, in which i will provide new information, but in doing so, change the situation at hand (in which case the answer to the problem changes with it):

There's 100 randomly selected women, all of them have 2 children.
Chances are that 25 of them have 2 girls. Another 25 have 2 boys, and the rest (50) have a boy and a girl. This would illustrate my answer of 25%.
Now let's change the situation: let us select all the women that have at least one girl and discard the others: you are left with a DIFFERENT sample of only 75 women, since the other 25 have no girls.
This changes the answer to your 33%, although it is still the same 25 women we are talking about.

The essence here is that the sample has changed from 100 to 75, so the 2 answers cannot be compared with each other as they are from 2 totally different situations.



The question that simpsonboy asked is about 1 woman. The sample never changes, not even when i say one of the kids is a girl.

The simple fact remains that any person being born has a 50% chance of being female, no matter what the sex of his/her siblings is. Not even if he/she has 100 siblings (theoretically speaking).
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Offline Highlander

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« Reply #46 on: August 17, 2009, 10:09:51 AM »
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Edit: Forgot to mention: the global average is 52F:48M because men tend to die younger than women.
Bleh, what a funny, but utterly useless topic in the end.

I'll add to the confusion I suppose.

The world average might be 52%/48% Female/Male. As Sirbomber said, this is due to Male's overall going around dying more than women. But in this question it is a matter of Birth Rates and not surviving population.

Nature does in fact "calculate" in the loss of Male's, so in terms of birthed children, I believe the % is 51.x% is born as males while 48.x% is born female.


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Offline speaker

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« Reply #47 on: August 17, 2009, 12:58:11 PM »
http://en.wikipedia.org/wiki/Hasty_generalization

the first and second child are independent, therefore regardless of whether the first child is a boy or a girl there is a 50:50% chance of the second being a boy or a girl.  Just like flipping a coin once and getting heads does not change the likelihood of getting a head on the second flip.
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Offline Simpsonboy77

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« Reply #48 on: August 17, 2009, 04:58:53 PM »
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SirBomber: LOL :P
Hooman:
What you are saying is this:
the chances of any of the 4 possibilities is obviously 25%:
BB : 25%
BG : 25%
GB : 25%
GG : 25%
Everyone should be able to agree with me on this one (not taking into account the 52:48 ratio).
So going with this, there is a 25% chance for both kids to be a girl, correct?

No need to keep restating something we all agree on, but yes true.

Quote
Now, you are saying is that if you know the sex of one of them, the natural chance of the GG combination suddenly changes?? Chances don't change with new information about an existing situation. The chance for both of them being a girl is still 25%. It always will be, since there's a 50:50 ratio for sex.

Based on the question at hand "what is the chance of the OTHER one to be a girl", the question is about one specific event, NOT both births, and the answer is a simple 50:50 chance as it is for any child being born on this planet.

Ok with the chances we agreed on in the previous quote eliminate the BB one. GG is still 25%, but there is only a total of 75% of births that we should consider since 25% of them are BB and have been eliminated. Now do you see where your logic is flawed? You are taking into account something the question has stated as invalid.


Quote
Now, let's review the following situation:
Q1:  A woman gives birth to a girl. She gets pregnant again. What is the chance of this second baby to be a girl as well?  Is it 33%, or is it 50% ???   (i'll leave this question open for you to answer).

Q2: A woman gives birth to 2 children. The second baby was a girl. What is the chance of the first one being a girl?  Is it 33%, or is it 50% ???
A1: 50%
A2. 50%

This proves nothing you eliminated a layer of uncertainty. In my question one of the two births is a girl, we have no information about one. You cannot break them up anymore. Your question is about 2 separate events.

Lets change your question slightly.
Q3 A woman gives birth to 2 children. The at least one of babies was a girl. What is the chance of the first one being a girl?  Is it 33%, or is it 50% ???

Quote
There's 100 randomly selected women, all of them have 2 children.
Chances are that 25 of them have 2 girls. Another 25 have 2 boys, and the rest (50) have a boy and a girl. This would illustrate my answer of 25%.
You have a flawed selection, and are using that in your final answer.

Quote
Now let's change the situation: let us select all the women that have at least one girl and discard the others: you are left with a DIFFERENT sample of only 75 women, since the other 25 have no girls.
This changes the answer to your 33%, although it is still the same 25 women we are talking about.

YES, YES THIS IS CORRECT!!!!!!

Quote
The essence here is that the sample has changed from 100 to 75, so the 2 answers cannot be compared with each other as they are from 2 totally different situations.
They are not. You are reducing the general statistics to meet the

Look at it this way. From our 25:25:25:25 we know that we get one GG for every GB and BG. So if we combine them we get TWO girl/boy (order unspecific now) for every girl/girl.

75 women surveyed which means 50 have one girl one boy, and 25 have 2 girls because we must have a 2:1 ratio.

By your 50% logic if we interviewed 100 women who has 1 girl, then half of them will be GG, and 25% will be GB and 25% will be BG. How can this be if we established at the very top that GG, GB, and BG all had equal chances of occurring. You have changed the odds now.
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Offline Eddy-B

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« Reply #49 on: August 17, 2009, 08:43:48 PM »
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http://en.wikipedia.org/wiki/Hasty_generalization

the first and second child are independent, therefore regardless of whether the first child is a boy or a girl there is a 50:50% chance of the second being a boy or a girl.  Just like flipping a coin once and getting heads does not change the likelihood of getting a head on the second flip.
My point exactly.
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