Probability Question
Drasla
probability that the unbord child is male? Is it 1/2 or 1/3?
I never really understood this question........
macavity
I didn't think there is any possible confusion in this one -
there is another version which sometimes causes confusion.
This above is equivalent to asking, given I got a head on the
first toss, what is the chance that I get heads on the second
toss of a fair coin. The "fair coin" assumption ensures that
the events are independent and probability for _any_ toss is
1/2, independent of what happened before.
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David Fabian
> If there is one male child, and the child's mother is pregnant, what is the
> probability that the unbord child is male? Is it 1/2 or 1/3?
>
> I never really understood this question........
We are missing data, so we must use variables ... namely:
OddsOfPregnantMotherHaving0OtherChildren
OddsOfPregnantMotherHavingExactly1OtherChild
OddsOfPregnantMotherHavingExactly2OtherChildren
OddsOfPregnantMotherHavingExactly3OtherChildren
...
Where odds are expressed in fractions (and, of course, the sum
of the variables is 1):
If the mother has no other children
(OddsOfPregnantMotherHaving0OtherChildren=1/1), then:
OddsThatUnbornChildIsMale = 1/1
If the mother has exactly one other child
(OddsOfPregnantMotherHavingExactly1OtherChild=1/1), then:
OddsThatUnbornChildIsMale = 1/2
If the mother has either no other children, or exactly one other child, then:
OddsThatUnbornChildIsMale =
1/1 * OddsOfPregnantMotherHaving0OtherChildren
+ 1/2 * OddsOfPregnantMotherHavingExactly1OtherChild
...
But the general formula is:
OddsThatUnbornChildIsMale =
1/1 * OddsOfPregnantMotherHaving0OtherChildren
+ 1/2 * OddsOfPregnantMotherHavingExactly1OtherChild
+ 1/3 * OddsOfPregnantMotherHavingExactly2OtherChildren
+ 1/4 * OddsOfPregnantMotherHavingExactly3OtherChildren
+ 1/5 * OddsOfPregnantMotherHavingExactly4OtherChildren
+ 1/6 * OddsOfPregnantMotherHavingExactly5OtherChildren
+ ...
Dave
loko
read it in my stats book.
Martin Julian DeMello
> If there is one male child, and the child's mother is pregnant, what is the
> probability that the unbord child is male? Is it 1/2 or 1/3?
> I never really understood this question........
The 'trick' is that the probability that a given baby is male is 1/2 (or
thereabouts - isn't it slightly skewed to the female side?), independent of
the number and sex of her other children.
--
Martin DeMello
Vince
> Drasla wrote:
> > If there is one male child, and the child's mother is pregnant, what is
the
> > probability that the unbord child is male? Is it 1/2 or 1/3?
>
> > I never really understood this question........
>
> The 'trick' is that the probability that a given baby is male is 1/2 (or
> thereabouts - isn't it slightly skewed to the female side?), independent
of
> the number and sex of her other children.
I think it's slightly more likely to be a male, but more females survive.
The chance that the mother is female is very high.
Carl G.
Martin Julian DeMello wrote in message <8mpd5n$bob$1...@joe.rice.edu>...
>The 'trick' is that the probability that a given baby is male is 1/2 (or
>thereabouts - isn't it slightly skewed to the female side?), independent of
>the number and sex of her other children.
>Martin DeMello
I believe the probability is slightly in favor of a male child (a fraction
of one percent). I have heard that one reason is that the sperms carrying Y
chromosomes are slightly lighter than those with X chromosomes, and swim
slightly faster. There are more women living in the world today than men.
One reason is that men have traditionally had riskier lifestyles, and die
earlier. The gap may be closing. On reason is that modern woman have been
taking on the riskier lifestyles. Another is that highly populated
countries, like China, have been trying to limit births to one child per
family, and many families have kept only their male children.
Carl G.
John.R...@virata.com
> I think this is more interesting:
>
> If a king declares that no couple is allowed to continue having children
> once they have a girl, how will this affect the ratio of boys to girls in
> the kingdom?
It would probably increase (more boys).
But I might not be making the intended assumptions.
--
John Rickard
David A Karr
>
>It would probably increase (more boys).
>
>But I might not be making the intended assumptions.
In particular, I guess you're not assuming that the sex of a child is
independent of the sex of previous children of the same mother.
In reality, that assumption is false (there is a very slight
correlation), and so your answer is correct (but I imagine the effect
is very slight).
--
David A. Karr "Groups of guitars are on the way out, Mr. Epstein."
ka...@shore.net --Decca executive Dick Rowe, 1962
Carl G.
Limey Ranko wrote in message <399388b7....@news.atl.bellsouth.net>...
>"Drasla" <dra...@mediaone.net> wrote:
>
>>If there is one male child, and the child's mother is pregnant, what is
the
>>probability that the unbord child is male? Is it 1/2 or 1/3?
>>
>>I never really understood this question........
>
>
>If a king declares that no couple is allowed to continue having children
>once they have a girl, how will this affect the ratio of boys to girls in
>the kingdom?
Spoiler
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Spoiler
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Spoiler
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Assuming that all children are given an equal chance to be born (i.e., the
female babies aren't aborted to avoid having a girl), the ratio should stay
the same.
Carl G.
John.R...@virata.com
> In article <Ttn*AH...@news.cam.virata.com>,
> <John.R...@virata.com> wrote:
[...]
> >But I might not be making the intended assumptions.
>
> In particular, I guess you're not assuming that the sex of a child is
> independent of the sex of previous children of the same mother.
That had occurred to me, but I was mainly thinking of the likely
effect of selective abortion and possibly even abandonment and
infanticide. Cf the skewing of the reported sex ratio at birth in
China in the last couple of decades, which is discussed in (for
example) <http://www.un.org/Depts/escap/pop/journal/v10n3a2.htm>. (I
admit that I haven't properly read all of that article.)
--
John Rickard
David A Karr
>That had occurred to me, but I was mainly thinking of the likely
>effect of selective abortion and possibly even abandonment and
>infanticide.
Right. If these things are allowed to happen at all, they're probably
going to have a much bigger effect than the correlation I had in mind.
I was thinking of a related problem in which the motivation is
not a king's proclamation, but simply a universal desire to have
a daughter--so much so that a couple will just keep having children
until they have a daughter, then stop. (But again you'd have to
assume no abortions to make the desired answer come out.)
Rich Grise
...
> Spoiler
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> Spoiler
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> Assuming that all children are given an equal chance to be born (i.e., the
> female babies aren't aborted to avoid having a girl), the ratio should stay
> the same.
>
> Carl G.
OK, lessee now. Say we start with 1024 couples. (fixed font please)
boys girls total boys total girls
Round 1: 512 512 512 512
512 stop.
Round 2: 256 256 768 768
256 stop.
Round 3: 128 128 Hmm - I get the point.
(and I'm too lazy to add 768+128, because the answer is
obvious by now.)
Cheers!
Rich
David Fabian
>
> I never really understood this question........
What is the probability that the "majority rules", when answering
the question above?
Dave
Lynn Johannesen
: David A Karr <ka...@shore.net> wrote:
:> In article <Ttn*AH...@news.cam.virata.com>,
:> <John.R...@virata.com> wrote:
: That had occurred to me, but I was mainly thinking of the likely
: effect of selective abortion and possibly even abandonment and
: China in the last couple of decades, which is discussed in (for
: example) <http://www.un.org/Depts/escap/pop/journal/v10n3a2.htm>. (I
: admit that I haven't properly read all of that article.)
The same is true of India.
Andrew Rothfuss
wrote:
>If there is one male child, and the child's mother is pregnant, what is the
>probability that the unbord child is male? Is it 1/2 or 1/3?
>
>I never really understood this question........
>
I think I may know the source of your confusion.
There is a classic probability problem that follows these lines and I
think the above puzzle is a failed attempt to relay this classic
puzzle. The version I have always seen goes something like this.
A mother has two children. One of them is a boy. what is the
probability that the other is a boy?
This may seem just like the above but the answer is very different.
If you care to see, I will present the answer and the reason the two
are different at the bottom of the page.
*
*
*
*
S
P
O
I
L
E
R
*
S
P
A
C
E
*
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*
if a family has two children, there are four equally probable
possibilities as to their gender.
(Capitol letter indicates older child, lowercase indicates younger)
"Bb" The older is a boy, the younger is a boy
"Bg" The older is a boy, the younger is a girl
"Gb" The older is a girl, the younger is a boy
"Gg" The older is a girl, the younger is a girl
The difference between the two problems is that in the first problem,
the reader knows that the older child is a boy while in the second
problem, you don't know if the boy is older or younger
now, with the first problem:
>If there is one male child, and the child's mother is pregnant, what is the
>probability that the unbord child is male? Is it 1/2 or 1/3?
lets advance time to after birth to make it sound more like the
correct form of the question
>A mother has two children. The *older* child is a boy.
>What is the probability that the *younger* child is a boy?
you know that the first child is a boy, this means that only the first
two possibilities apply, e.g. "Bb" and "Bg". Only one of these leaves
the younger child as a boy, namely Bb. And as expected the
probability of the younger child being a boy is one out of two or 1/2
the fun begins with the second problem
>A mother has two children. One of them is a boy.
>What is the probability that the other is a boy?
Here, you don't know if the boy is the first or the second child.
This means that there are *three* equaly likely possibilities that
apply, Namely "Bb", "Bg" and "Gb". Again, only one of these
possibilities results in the other child being a boy. However,
because there are now three possibilities that can occur, the
probability of the other child being a boy is 1/3.
If that all seems a bit confusing, try and think about it like this
there are four families, and each one has one of the four different
combinations of children.
family 1 has Bb
family 2 has Bg
family 3 has Gb
family 4 has Gg
>A mother has two children. The *older* child is a boy.
>What is the probability that the *younger* child is a boy?
You pick one family at random and find out that their oldest child is
a boy. you obviously did not pick family 3 or family 4 because their
oldest child is a girl. this means that you have picked either
family1 or family2. Now, becasue you picked the family at random,
probability is equally distributed abong families 1 and 2. this means
that the probability of picking family 1,(the only one with a boy as
the youngest child) is 1/2, therefore, the probability of the youngest
child being a boy is 1/2.
>A mother has two children. One of them is a boy.
>What is the probability that the other is a boy?
You pick one family at random and find out that they have a boy.
you obviously did not pick family 4 because they only have girls.
this means that you have picked either family1 family2 or family3.
Now, becasue you picked the family at random, the probability is
equally distributed abong families1, 2 and 3. this means that the
probability of picking family 1,(the only one with two boys) is 1/3
therefore, the probability of the family you chose of having 2 boys is
1/3.
Patrick A. O'Donnell
> Limey Ranko wrote in message <399388b7....@news.atl.bellsouth.net>...
> >once they have a girl, how will this affect the ratio of boys to girls in
> >the kingdom?
.
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.
Spoiler
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.
Spoiler
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> Assuming that all children are given an equal chance to be born (i.e., the
> female babies aren't aborted to avoid having a girl), the ratio should stay
> the same.
You're also assuming that all families keep having children until they
have a girl.
mark edward hardwidge
> You're also assuming that all families keep having children until
> they have a girl.
No you aren't. Each time someone has a baby, it has a 50%
chance of being female. It doesn't matter what rule you use to decide
when to stop having children; the probability of each child born being
female doesn't change.
You could do a Monty Carlo simulation with more complex
stopping rules (say, one girl OR three boys), and you will get the
same result.
--
Mark E. Hardwidge
hard...@uiuc.edu
Carl G.
Patrick A. O'Donnell wrote in message ...
>"Carl G." <cgi...@microprizes.com> writes:
>> Limey Ranko wrote in message
<399388b7....@news.atl.bellsouth.net>...
>> >If a king declares that no couple is allowed to continue having children
>> >once they have a girl, how will this affect the ratio of boys to girls
in
>> >the kingdom?
>
>
> Spoiler
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> Spoiler
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>> Assuming that all children are given an equal chance to be born (i.e.,
the
>> female babies aren't aborted to avoid having a girl), the ratio should
stay
>> the same.
>
>have a girl.
It doesn't make a difference. The king's rule may help keep population
down, but it doesn't alter the ratio of boys to girls. Having a girl would
only reduce the population that can have more children, it wouldn't change
the probability that the next child born would be male or female.
Carl G.
Nis Jørgensen
Ranko) wrote:
>If a king declares that no couple is allowed to continue having children
>once they have a girl, how will this affect the ratio of boys to girls in
>the kingdom?
Possible answers:
More boys, since some girls will be killed just after birth.
More boys, since those parents who have a higher probability of
getting male offspring will have more children.
Fewer children overall, because of the fear of having your
children taken away if you have a girl (you are not allowed to
continue having them!)
More proforma marriages/divorces to form more couples.