For a given couple with two children of the same sex, what is the
probability that the third child will also be of that sex?

This is not the same as: What proportion of three-child families are
all the same sex.

Please cite sources.

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Request for Question Clarification by pafalafa-ga on 26 Nov 2006 18:33 PST

If you had asked about coins, the answer would be 50-50.

That is, if the first two coin tosses are heads (or tails), they don't
have any bearing on the odds of the third coin toss, which still has a
50-50 chance of being heads or tails.

Assuming the coin is fair, of course.

For childbirth, the outcomes are similar to coins, although not all
parents are "fair" in a statistical sense.  Some parents might be
biologicially predisposed to produce more boys than girls, or vice
versa.

Still...overall...I think the odds are still pretty close to 50-50 for
the third kid, regardless of the gender of the first two.

Are you looking for that sort of generalized answer?  Or did you want
more in-depth biology to back up the answer?

pafalafa-ga

otraub-ga,

Disregard my comment, above, as I found the actual statistics.

There is a small effect of gender "running in the family" for a third
birth, if the first two children are of the same gender.


There is a well-written presentation of the data here:


http://www.in-gender.com/XYU/Odds/Gender_Odds.aspx
The Odds of Having a Boy or a Girl



and as you can see from two "Previous Children" tables fairly far down
in the article, the odds of the third child being the same gender as
the first two are:


First two are boys -- Odds are 53.3% the third will be a boy, vs 46.7%
it will be a girl


First two are girls -- Odds are 54.0% the third will be a girl, vs
46.0% it will be a boy



Thus, there is a shift from the usual pattern of births, which is 51%
boys, 49% girls.  The shift is fairly small, but noticeable just the
same.


I trust this information fully answers your question.  

However, please don't rate this answer until you have everything you
need.  If you would like any additional information, just post a
Request for Clarification to let me know how I can assist you further,
and I'm at your service.

All the best,

pafalafa-ga


search strategy -- Google search on [ birth gender statistics "first two" ]

Take a look to the following question (and answer of course):
http://answers.google.com/answers/threadview?id=465659

Are you viewing this as strictly a mathematical problem where the
probability of a boy and girl are both exactly 50%, or as a real life
problem where the probabilities are slightly different?

If the problem is simply a mathematical exercise:

If you are asking what is the probability that the the third
(youngest) child will be the same sex as the first two, the answer is
1/2.  The birth of the third child is independent of the first two and
will either match the sex of the first two or not with equal
probability.

If however, you selected two of the three children at random, rather
than the oldest two and discovered that they were the same sex, the
answer is also 1/2 but the reasoning is different.  Consider the
possible cases.

MMM  3
MMF  1
MFM  1
MFF  1
FMM  1
FMF  1
FFM  1
FFF  3

If you select one of the eight possible combinations at random and it
happens to be MMM or FFF.  The probability that two of the three
children selected at random will be the same sex is 1 or 3/3.  For the
other six combinations the probability that two of the three selected
at random will be the same sex is 1/3.  So the likelihood of MMM or
FFF being selected is three times as likely as one of the other six
given that two of the children selected at random are the same sex.

Therefore the probability that the sex of the third child (but not
necessarily youngest) is the same as the two selected at random is:

(3+3)/(3+1+1+1+1+1+1+3) = 6/12 = 1/2

Its the man that determines the sex of the child. So, if you have a
third child of the same sex, slap your hubby across the head ;)

Steph53

steph,

multiple children of the same gender leads to drastically reduced
clothing costs (assuming they don't wear out).  also, you can more
easily warehouse all of them in the same bedroom instead of giving
each one their own room, saving on housing costs.

so instead of smacking your husband for a third kid of the same
gender, i recommend thanking him.  maybe a set of golf clubs.

-cab