Author Topic: A Women Has 2 Kids.... (Read 14082 times)

Simpsonboy77 · « **on:** July 28, 2009, 08:48:39 PM »

A women has 2 kids, and one of them is a girl. What is the chance that the other one is a girl?

Good luck

Sirbomber · « **Reply #1 on:** July 28, 2009, 11:23:27 PM »

A women? How does that work? Multiple personality disorder, or something?

Simpsonboy77 · « **Reply #2 on:** July 29, 2009, 05:43:03 PM »

Thats irrelevant.

There is a family with 2 children. One is a girl. What is the chance the other child is a girl?

Is that more clear?

WalkmanSilver · « **Reply #3 on:** July 30, 2009, 04:54:05 AM »

Well it depends who has the stronger genes I suppose

Simpsonboy77 · « **Reply #4 on:** July 30, 2009, 06:06:05 PM »

This isn't the point of the question

.

Assuming the birth rate is 50:50, and for this exercise assume the child cant be both or neither.

Hooman · « **Reply #5 on:** July 30, 2009, 10:39:05 PM »

Ok, 0.5, assuming they are independent events.
If you take world averages into account, it's more like 0.52 or something.

There are cases where it doesn't appear to be independent events, however, the sample size is too small to tell if that is the case. I assume the chance of some genetic condition favouring one of the other is quite small, and so probably won't have much of an effect on average. In some specific case, I suppose it might be large difference, but again, we don't have enough info to determine that and it would vary too much between cases to give any kind of answer here.

A typical wrong answer people give to independent event questions is 0.25, as they assume the first sample somehow has an effect on the second sample.

CK9 · « **Reply #6 on:** August 01, 2009, 05:17:13 PM »

I second hooman's response. There are three main cases to consider: non-twin siblings, fraternal twins, and identical twins. The first two have a 50% chance each, and the third has a 100% chance. Therefore, 52% is the best assumption to go with.

Simpsonboy77 · « **Reply #7 on:** August 02, 2009, 03:21:22 AM »

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Ok, 0.5, assuming they are independent events.
If you take world averages into account, it's more like 0.52 or something.

A typical wrong answer people give to independent event questions is 0.25, as they assume the first sample somehow has an effect on the second sample.

The first part you are correct, its not quite 50:50, but for the purposes of this lets just say it is.

Indeed many people give the wrong answer, and sorry to say you are one of them. Yes I am considering them separate events, so no twins or anything. I think I should have posed this question as flipping 2 coins instead.

All I say in the problem is one of them is a girl, so it could be the first or second. There are 4 possible combinations, BB BG GB GG. Now since one of them is a girl you can eliminate BB.

Now you are left with 3 groups with an equal chance of occurring, GG, GB, BG. Now only one of them has BOTH as girls, and out of 3 choices, so the correct answer is 33% (assuming birth rate is 50:50)

Don't worry only like .01% of people actually get this question correct on the first try. I got it wrong also hehe.

Hidiot · « **Reply #8 on:** August 02, 2009, 05:18:44 AM »

I call flaw on that judgment.

Since BG = GB.

No mention of which came first. That's important data for the problem, so I accuse you of giving a incomplete problem (

)
[size=8](I'm kidding about the accusing, of course)[/size]

And to add to that, there's a theory according to which, if the first child is a girl, chances for the second child to be a boy are less than 50%.

Hooman · « **Reply #9 on:** August 02, 2009, 02:27:35 PM »

My initial thought was there was a flaw in the argument, although, now I'm thinking the reason being that the information given implies something about both children. If you rephrase it, it's more like, given that at least one of the two kids is a girl, what is the probability that the second kid is a girl. You lose independence of events in this case. If the first is a boy, then you were talking about the second kid. If the second is a boy, then you were talking about the first kid. If they are both girls, then it doesn't matter which kid you were talking about.

When I first read it, I suppose I didn't quite read it carefully enough. I figured there was some trick to it that I wasn't quite seeing, which is mostly why I wrote that second part. Thought that might be the trick.

Of course, with the way the question is written, if "one" kid is a girl, then the probability of the other kid being a girl might very well be 0.

Simpsonboy77 · « **Reply #10 on:** August 02, 2009, 08:05:48 PM »

Yea I'm good at math but I fail at english (well not really its just significantly weaker).

Yes the given information takes both into account, it is not meant to be interpreted as ONLY the first or (more like XOR) the second.

I think the better way to phrase it would have been: "A women has 2 kids, and at least one of them is a girl. What is the chance that both children are girls?

EDIT: Forgot to address Hidiot's points

Hidiot BG is not equal to GB. They both are separate. If you combine them then you must take into account the weighted chance since GG will occur half the amount of times of BG or GB. If you take all 3 as separate then they all have equal chances.

"And to add to that, there's a theory according to which, if the first child is a girl, chances for the second child to be a boy are less than 50%"
In the problem if you know the gender of the first then you can narrow it down quite easily. If it is B then the second kid must be G, otherwise its a 50:50. Or are you talking about real life, if so please elaborate I'm interested in this.

Hidiot · « **Reply #11 on:** August 03, 2009, 02:07:58 AM »

I was not very clear with BG=GB thing. It only happens when the order is not specified.

I'm talking about real life. I can't elaborate, it's something I heard about a few years back.

CK9 · « **Reply #12 on:** August 03, 2009, 03:29:07 AM »

simpson, I have to say that I'm shocked that I didn't think of it in that way. Expecially since I did so well in the genetics portion of my bio class, it's the same basic thing as dmoinant and ressant traits with how you're looking at it

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example
___|__B_|__b_
_B_|_BB_|_Bb_
_b_|_bB_|_bb_

however, for all intents and purposes, Bb is considered the same as bB, as both result in the same possible genetic exchanges.......

If you stated it with coins, though, I would have gotten it. With children, you have too many additional factors that you have to consider when choosing your wording.

Eddy-B · « **Reply #13 on:** August 03, 2009, 09:35:42 AM »

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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 still say 50% chance (if assuming the ratio is 1:1 for boys:girls)

The first part can be totally ignored: it DOES NOT MATTER what sex the "one" child is, because the question is: what is the sex of THE OTHER ONE , which is still a 50-50 chance of being a girl.

No matter how you ask the question; the chance remains 50:50.
If you rephrase the question:
What is the chance the second born is a girl, when you know at least 1 of them is a girl?
The chance of any child being born a girl is still 50% and 50% for a boy - nothing changes that!

Next problem please

Freeza-CII · « **Reply #14 on:** August 03, 2009, 12:49:33 PM »

Its another hooman trick question

the real answer is hermaphrodite

Hooman · « **Reply #15 on:** August 03, 2009, 02:47:31 PM »

But Eddy, you're fogetting that they didn't specify which child. The selection of the kid for which information is given is done after both are born, and the sex is determined. If they first kid was a boy, then they must have been talking about the second. If the second kid was a boy, then they must have been talking about the first. Hence, the information given isn't actually for a single kid, but rather a merging of the info for both kids.

Remember conditional probability rule:
P(A|B) = P(A intersect B) / P(B)
The probability of A, given B, is the probability of A and B, divided by the probability of B.

The probability of A intersect B, that is, that both kids are girls, is 1/4. The probability of B, that at least one is a girl, is 3/4. Therefore the probability of both kids being girls, given that at least one kid is a girl is (1/4)/(3/4) = 1/3.

But yes, it would be more clear if it was worded, "What is the probability that both kids are girls, given that at least one kid is a girl".

Simpsonboy77 · « **Reply #16 on:** August 03, 2009, 08:12:16 PM »

I'm sorry for posting a trick question in a terrible form. Hooman's wording is best.

Your friend flips two coins, and does not tell you the outcome of each one. Instead he tells you that at least one of the 2 coins turned up heads. What is the chance that they are both heads?

Now for flipping coins you have 4 possibilities
HH
HT
TH
TT

We can eliminate TT since he said that at least one is heads. We are looking for BOTH to be heads which occurred 1 time, but there are only 3 valid outcomes. If you try this by your computer and you get TT, then consider that a reflip of BOTH.

Hooman has the math behind it, I didn't want to bore you with it yet.

Spikerocks101 · « **Reply #17 on:** August 05, 2009, 01:35:37 PM »

But you cant count HT and TH as 2 different things, since they are the same, because if I flip a coin right now, and it gets heads, I am pretty sure, that if I flip it 10,000 years form now on New Terra, it still has a 50% chance of getting heads, assuming the coin has no flaws what so ever. Its 50%, not 33%, or 25%. 33% is just making it confusing, but 25% is just wrong...

Edit: I agree with Hooman's refrasing of the question, for that makes sence...

Sirbomber · « **Reply #18 on:** August 05, 2009, 03:23:10 PM »

How did this turn into a debate? This shouldn't even be considered a trick question, unless you lack an understanding of basic genetics, which I shall now explain even though it's probably not necessary.

Basic genetics time (only looking at sex-determining genes, and assuming "normal" parents and children):
Father's genes: XY
Mother's genes: XX

XY + XX =

There's a 25% chance for any 4 of those possibilities being "chosen", but possibilities 1 and 3 are the same, as are 2 and 4. For all intents and purposes there are 2 possibilities, each having a 50% chance of being "chosen". And yes, "XY" and "YX" are the same thing, making Simpsonboy77's 33% argument wrong. Poor wording does not make something a "trick" question; it just makes it stupid.

Edit: Forgot to mention: the global average is 52F:48M because men tend to die younger than women.

Hooman · « **Reply #19 on:** August 05, 2009, 07:37:27 PM »

Quote

Edit: Forgot to mention: the global average is 52F:48M because men tend to die younger than women.

Hmm, interesting point. I used to assume there was a difference in the birth rate rather than the death rate.

Still, there is a difference between BG/GB or HT/TH. You are not simply reflipping the same coin here and writing down the values in any order.

This problem is equivalent to having a 4 sided die, rolling it, telling someone that one of the sides that didn't come up (after rolling), and then asking them what the probability of any of the remaining sides comming up is. There are 3 equally likely outcomes left to choose from.

Edit: Btw, those genetic X/Y chromosone things are really irrelevant here. The problem is about two separate children. All you're stating with those charts is that the probability of a single child is 50:50, which we've already agreed upon.

Simpsonboy77 · « **Reply #20 on:** August 05, 2009, 08:59:21 PM »

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How did this turn into a debate? This shouldn't even be considered a trick question, unless you lack an understanding of basic genetics...

This wasn't even supposed to be a question of genetics, but a question of probability.

Agreed male to female birth ratios are close enough to be considered 50:50 (it is actually 106 males to 100 females) Living rates are flipped, as he stated above its 52:48.

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There's a 25% chance for any 4 of those possibilities being "chosen"

Agreed.

Quote

but possibilities 1 and 3 are the same, as are 2 and 4. For all intents and purposes there are 2 possibilities, each having a 50% chance of being "chosen

Agreed.

Quote

And yes, "XY" and "YX" are the same thing, making Simpsonboy77's 33% argument wrong. Poor wording does not make something a "trick" question; it just makes it stupid.

I agree here as well, sort of. XY and YX are the same, but that is not what I was referring to. I was using BG and GB to show both children at once. The second you narrow it down to one child it instantly becomes 50%. This is because you added a restriction, you checked the second child knowing the outcome of the first.

We are talking about different levels in the problem. I never brought genetics into the equation. I took each possibility of occurring to be 50%, which you agree in point 2.

Now thinking that your table represents both children at the same time, it was made incorrectly. The Y axis should also be X and Y not X and X. I don't think this is the case since it is correct for a one child birth.

Let me try to break this down into the most atomic steps as possible. Tell me where you start to disagree with me.

1. Assume that birth rates are strictly 50% for each.
2. Assume a boy and boy birth cannot happen. This is stated in the question since at least one child is a girl.
I will branch right now in 2 paths.
3. First child is a boy so the second child MUST be a girl.
This is one possible outcome and it does not satisfy the desired outcome (GG). 0 out of 1 so far.
4. Assume a girl is born first.
5. Two outcomes are a girl birth and a boy second birth.
6. The second girl birth gives the desired scenario so we are 1 out of 2 right now.
7. The boy second birth is valid yet it is not what we want. So we are now 1 out of 3.

I have a feeling you are going to say that step 3 has a 50% chance of happening while 6 and 7 are both 25%. Remember once the first child is picked to be a boy there is still a 50% chance in that subset that the outcome is invalid. They all have equal possibilities, thus no weighted average is needed.

___|__B_|__G_
_B_|_BB_|_BG_
_G_|_GB_|_GG_
Here you can see there is a 25% chance of each happening, but BB is not possible due to the restrictions given. You are now down to 3 choices, but the chances do not change since they are "locked in".

When I said I worded it poorly, I was referring to just using people in general. I thought it would have sounded a bit more interesting than coin flips.

Eddy-B · « **Reply #21 on:** August 06, 2009, 12:52:24 AM »

Hooman:
i know what was the point of the "riddle" but the way the question is asked, the answer is still a simple 50:50 as it does not matter what sex the first one is, or even which child is the girl that was mentioned.
All that matters is the question at hand: WHAT IS THE CHANCE of the second baby to be a girl, which -simply put- is the global average of 48:52 or 50:50 as mentioned.

It's a simple given fact that the chance of ANY baby being born to be evenly split into boys or girls - and yes i had 2 years of mathematical chance calculus in highschool, as well as 6 years of biology (i was an A+ student at both) in which i learned about recessive & dominant genes and how to calculate those chances - but still : they don't apply to this question: the ORIGINAL question was (simplified) "what is the chance that the second baby is a girl" period.

CK9 · « **Reply #22 on:** August 07, 2009, 03:32:59 AM »

And that's why riddles have to be carefully worded, lol

Freeza-CII · « **Reply #23 on:** August 07, 2009, 02:05:29 PM »

that chances of the other one being a girl is 100% due to the fact of modern gene manipulation. you just got owned with science!

Simpsonboy77 · « **Reply #24 on:** August 07, 2009, 11:45:55 PM »

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Hooman:
i know what was the point of the "riddle" but the way the question is asked, the answer is still a simple 50:50 as it does not matter what sex the first one is, or even which child is the girl that was mentioned.
All that matters is the question at hand: WHAT IS THE CHANCE of the second baby to be a girl, which -simply put- is the global average of 48:52 or 50:50 as mentioned.

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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 still disagree, poorly worded, yes, but it does tell you all the needed information. It is not a 50% chance no matter how it is sliced, once again ignoring slight changes in birth rates. It asks for the chance of the second tested, not necessarily the second born, but it does include the needed clue, that one of them is a girl. If they are both girls, one of them is still a girl. If it said the first child is a girl, then yes it would be 50%, but it said one of them, which is referring to both children at once.

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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. Say for instance that we are given both girls. IF the clue was based on the first child GG so it is asking what the chance the other untested child is (non underlined). The underlined child is which child the "one" is referring to form the problem. (This makes it sound like it should be Neo from The Matrix, but I digress) Otherwise it is the exact reverse. If there is strictly one girl then it is an obvious which child the clue was based on. The clue can be generated from GG or GG or BG or GB. The first two are the same exact thing, so it does not effect the chance of outcome, it is just a different way of verifying the clue.

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It's a simple given fact that the chance of ANY baby being born to be evenly split into boys or girls - and yes i had 2 years of mathematical chance calculus in highschool, as well as 6 years of biology (i was an A+ student at both) in which i learned about recessive & dominant genes and how to calculate those chances

I think most of us are quite intelligent, nerds and geeks tend to play old awesome games. And calculus has nothing to do with this, its statistics and probability

. Respectfully, recessive and dominant genes have nothing to do with this problem, all that genes determine is the ratio that males are born vs females, which we agree on is slightly off from 50%, but it is close enough just to consider it equal. I am not quite sure why Sirbomber brought that up.

I'm kind of tired right now, so don't quote any of this until the morning as I probably will come back and edit it.

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Author Topic: A Women Has 2 Kids.... (Read 14082 times)