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#1
05-07-2010, 02:19 AM
 Guest Join Date: Sep 2009 Posts: 203

## odds of having 11 children of the same sex

I just watched a TV show that had a woman who allegedly had 11 children, all boys. Am I right in thinking that the odds of this happening are 1 in 2 to the 11th power or 1/2048? Certainly statisticly possible, but also definitively unlikely.

Any replies are appreciated,
AllFree
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#2
05-07-2010, 02:27 AM
 Guest Join Date: Mar 2006 Location: Southern North Posts: 1,383
Your calculation is correct, assuming the odds of one gender over the other is in fact one in two. Studies have suggested this may not be the case, but it's close enough.
#3
05-07-2010, 02:31 AM
 Guest Join Date: Sep 2009 Posts: 203
How large is the bias and towards what sex? I imagine it must be small.
#4
05-07-2010, 02:45 AM
 Charter Member Join Date: Jan 2000 Location: My own private Nogero Posts: 6,545
Quote:
 Originally Posted by AllFreedomUnlessDefyingScience How large is the bias and towards what sex? I imagine it must be small.
About 105 boys are born for every 100 girls. Makes the odds against 11 boys in a row somewhat less unlikely.
#5
05-07-2010, 02:57 AM
 Member Join Date: Oct 2009 Posts: 6,928
Your odds are only for all families with eleven children. This has to be multiplied by the odds of a family having 11 children of any sex.
#6
05-07-2010, 02:59 AM
 Guest Join Date: Apr 2001 Location: Cape Town, South Africa Posts: 2,911
There also appears to be a small bias toward one gender or another dependent on the gender of previous children - particularly if you have had boys, but only very slightly:
Quote:
 The odds of having a girl seem decrease after having each boy, but only very slightly. Even after 3 boys, you are only 6.4% more likely to have a 4th boy than a girl ... The odds of having a boy seem to increase after having girls, except after 2 girls, when a 3rd girl is more likely.
Study reported here

Grim
#7
05-07-2010, 05:42 AM
 Retired Straight Dope Staff Charter Member Join Date: Oct 2005 Location: North Shore of LI Posts: 19,304
Also assuming that there isn't a biological reason that Y bearning sperm are not being favored for that specific couple.
#8
05-07-2010, 05:45 AM
 Member Join Date: Mar 2001 Posts: 11,049
Quote:
 Originally Posted by IvoryTowerDenizen Also assuming that there isn't a biological reason that Y bearning sperm are not being favored for that specific couple.
This is the important point. There are plenty of couples who are biologically incapable of producing children of one sex or the other. Doesn't matter how many kids they have, they will always be all the same sex.
#9
05-07-2010, 05:59 AM
 Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 26,345
Quote:
 Originally Posted by AllFreedomUnlessDefyingScience I just watched a TV show that had a woman who allegedly had 11 children, all boys. Am I right in thinking that the odds of this happening are 1 in 2 to the 11th power or 1/2048? Certainly statisticly possible, but also definitively unlikely.
What do you mean by "definitively unlikely"? I don't know how many women there are in the world who have 11 children, but it wouldn't surprise me if the number were well over 2048. In that case, even if the probability of any one set of 11 children being all boys were 1/2048, it would be extremely likely that some woman, somewhere, had 11 boys.
#10
05-07-2010, 06:15 AM
 Guest Join Date: Apr 2000 Posts: 18,812
I knew, even before opening this thread, that it had already degenerated into pointless nitpickery. By any reasonable standard, the answer is 1 in 2^11. Let it go, people. Let it go.
#11
05-07-2010, 06:32 AM
 Charter Member Join Date: Mar 2002 Location: Auburn, WA Posts: 6,303
My aunt quit after 6 boys.
#12
05-07-2010, 06:44 AM
 Charter Member Join Date: Oct 1999 Location: Sturgeon Bay, WI USA Posts: 20,920
Quote:
 Originally Posted by Blake This is the important point. There are plenty of couples who are biologically incapable of producing children of one sex or the other. Doesn't matter how many kids they have, they will always be all the same sex.
I think we're gonna need a cite for that.
#13
05-07-2010, 06:47 AM
 Guest Join Date: May 2000 Location: Uppsala, Sweden Posts: 703
Actually, it's 1 in 2^10. The odds that your first kid has some sex (1) multiplied by the odds that the next ten have the same sex as the first one (1/1024).

Last edited by Sofis; 05-07-2010 at 06:48 AM.
#14
05-07-2010, 06:58 AM
 Guest Join Date: Apr 2000 Posts: 18,812
Quote:
 Originally Posted by Sofis Actually, it's 1 in 2^10. The odds that your first kid has some sex (1) multiplied by the odds that the next ten have the same sex as the first one (1/1024).
Well, the OP asked for the odds of "this" happening. It's unclear whether "this" refers to all the kids being boys or all being the same gender. So it's either 1 in 2^10 or 1 in 2^11, depending on which one he meant.

Dammit, now I'm pointlessly nitpicking!
#15
05-07-2010, 07:04 AM
 Guest Join Date: May 2000 Location: Uppsala, Sweden Posts: 703
If you read the thread title, there's a hint that, I feel, clears up this ambiguity.
#16
05-07-2010, 08:35 AM
 Guest Join Date: Apr 2000 Location: Within Posts: 12,468
If daddy, biologically, can't throw that X chromosome, it will be "boy" everytime.
#17
05-07-2010, 08:48 AM
 Charter Member Join Date: Mar 1999 Location: Tysons Corner, VA, USA Posts: 12,883
Quote:
 Originally Posted by needscoffee Your odds are only for all families with eleven children. This has to be multiplied by the odds of a family having 11 children of any sex.
What the heck does this mean? The odds that a family with 11 children has 11 children of any sex is 100%.

Last edited by CookingWithGas; 05-07-2010 at 08:49 AM.
#18
05-07-2010, 09:16 AM
 Guest Join Date: Mar 2002 Posts: 12,037
It may be worth noting that the chance of getting on a TV show devoted to the interesting distribution of the sex of your 11 children improves if they are all boys.
#19
05-07-2010, 09:27 AM
 Guest Join Date: Oct 2007 Posts: 3,303
Needscoffee wrote:
Your odds are only for all families with eleven children. This has to be multiplied by the odds of a family having 11 children of any sex.

Quote:
 Originally Posted by CookingWithGas What the heck does this mean? The odds that a family with 11 children has 11 children of any sex is 100%.
I think Needscoffee meant something like "What are the odds that any two people who start having kids will end up with exactly 11 kids of the same gender". (I presume that this is a misunderstanding of the original question, which presumably is "Given that a couple has 11 kids, what are the odds that all 11 will be the same gender".)

Last edited by cjepson; 05-07-2010 at 09:28 AM.
#20
05-07-2010, 09:28 AM
 Guest Join Date: Jul 2002 Location: Dammam, Saudi Arabia Posts: 12,490
My mother was the youngest of nine girls.
#21
05-07-2010, 09:28 AM
 Guest Join Date: Aug 2000 Location: NY/NJ, USA Posts: 5,079
Quote:
 Originally Posted by needscoffee Your odds are only for all families with eleven children. This has to be multiplied by the odds of a family having 11 children of any sex.
Quote:
 Originally Posted by CookingWithGas What the heck does this mean? The odds that a family with 11 children has 11 children of any sex is 100%.
What needscoffee meant is this:

Suppose someone says that "The odds of a family having 3 children who are all boys is 1/8." Taken literally, that would mean that 1/8 of all families ought to have exactly 3 boys and 0 girls. But that's not true. Lots of families have fewer than 3 kids, or more than 3 kids.

A more correct statement would be that "If a family has exactly 3 children, the odds that they are all boys is 1/8." And if X% of all families have exactly 3 children, then the odds of a family having 3 children who are all boys is (X%)*(1/8).
#22
05-07-2010, 09:44 AM
 Guest Join Date: Apr 2000 Posts: 18,812
Quote:
 Originally Posted by Sofis If you read the thread title, there's a hint that, I feel, clears up this ambiguity.
You may have a point...

Quote:
 Originally Posted by Wilbo523 If daddy, biologically, can't throw that X chromosome, it will be "boy" everytime.
Sure. But I have never heard of a condition that causes this, in all my years of studying biology. If you have, then by all means enlighten me. I can't think off the top of my head how it would work, though. At least in humans. The dad's X chromosome is obviously viable, or dad would be dead. I suppose you could postulate some sort of extreme meiotic drive mechanism, but that generally only works in polar body-generating females. When spermatocytes go through meiosis, all four products mature into sperm cells, so you'd have to somehow kill off X-bearing sperm, presumably by having the Y chromosome code for some sort of toxic protein which could travel through the shared cytoplasm, but then since it IS shared, how would you prevent the toxic effect from spreading to the Y-bearing sperm? Hmm...

But, as I say, I've never heard of that happening.
#23
05-07-2010, 09:45 AM
 Guest Join Date: Mar 2010 Location: MD outside DC Posts: 5,465
More nitpickery:

There is also the issue of identical twins. If some among the 11 are identical twins then they should be counted as a single unit rather than 2 individuals in the calculations.
#24
05-07-2010, 10:05 AM
 Retired Straight Dope Staff Charter Member Join Date: Oct 2005 Location: North Shore of LI Posts: 19,304
True, but then you have to factor in the probability of twinning.
#25
05-07-2010, 10:31 AM
 Guest Join Date: Apr 2009 Location: Toronto Posts: 7,232
Quote:
 Originally Posted by Smeghead Sure. But I have never heard of a condition that causes this, in all my years of studying biology. If you have, then by all means enlighten me. I can't think off the top of my head how it would work, though. At least in humans.
Here's a link to a New York Times article on the subject, referring to a study published in Evolutionary Biology. Here's the relevant quote:

"Mr. Gellatly found evidence that men carry a gene that determines the percentage of X and Y chromosomes in their sperm, and that the gene comes in three alleles, or versions. One produces mostly X chromosomes, another mostly Y, and the third yields equal numbers of both."
#26
05-07-2010, 10:33 AM
 Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 26,345
Quote:
 Originally Posted by Keeve A more correct statement would be that "If a family has exactly 3 children, the odds that they are all boys is 1/8."
Perhaps still more nitpickery: A more correct statement would be "If a family has exactly 3 children, the probability that they are all boys is 1/8." While some people use the words "probability" and "odds" interchangeably, others (see, for example, Wikipedia) do not: they use the word "odds" to refer to the ratio of favorable to unfavorable outcomes, and would say that the odds of all boys would be 1 to 7.
#27
05-07-2010, 10:47 AM
 Charter Member Join Date: Mar 2000 Posts: 7,912
The question that somebody SHOULD be asking is statistical rather than probabilistic - how many children of identical gender does one couple have to produce before you reject the notion that each conception FOR THAT COUPLE is an independent event with probability 0.5 of producing a child of either gender?
#28
05-07-2010, 11:02 AM
 Guest Join Date: Apr 2000 Posts: 18,812
Quote:
 Originally Posted by hogarth Here's a link to a New York Times article on the subject, referring to a study published in Evolutionary Biology. Here's the relevant quote: "Mr. Gellatly found evidence that men carry a gene that determines the percentage of X and Y chromosomes in their sperm, and that the gene comes in three alleles, or versions. One produces mostly X chromosomes, another mostly Y, and the third yields equal numbers of both."
I've got no problem with "mostly". I'm questioning the earlier statement of "can't".
#29
05-07-2010, 11:09 AM
 Charter Member Join Date: Jun 2000 Location: Dallas, TX Posts: 8,303
Quote:
 Originally Posted by Smeghead Sure. But I have never heard of a condition that causes this, in all my years of studying biology. If you have, then by all means enlighten me. I can't think off the top of my head how it would work, though. At least in humans. The dad's X chromosome is obviously viable, or dad would be dead.
Not quite the same thing, but you could postulate that both parents each carry one copy of a recessive on the X chromosome that causes a very early miscarriage. Both parents are obviously viable, but the father contributes one copy of the recessive to each female embryo. About half the time, the mother will also contribute a copy. As a result, you would expect that roughly half of the female embryos would not be viable. It wouldn't guarantee that all the kids would be boys, of course, but it would definitely change the odds.

That's just a hypothetical case; I don't know of any specific examples of such a situation.
#30
05-07-2010, 11:20 AM
 Charter Member Join Date: Oct 2000 Location: Lethbridge, AB. Posts: 49,084
Quote:
 Originally Posted by racer72 My aunt quit after 6 boys.
I come from a family of five girls. Everyone I know with kids has one sex only, no mixed bags. The idea that men produce one sex over the other and resist regular probability seems plausible to me.
#31
05-07-2010, 11:22 AM
 Charter Member Join Date: Feb 2004 Location: Eastern Connecticut Posts: 16,661
Quote:
 Originally Posted by Thudlow Boink What do you mean by "definitively unlikely"? I don't know how many women there are in the world who have 11 children, but it wouldn't surprise me if the number were well over 2048. In that case, even if the probability of any one set of 11 children being all boys were 1/2048, it would be extremely likely that some woman, somewhere, had 11 boys.
My friends Pat and Tim have 6 girls. They did nothing specific to select for girls, and there were no abortions.
#32
05-07-2010, 11:24 AM
 Charter Member Join Date: Oct 2000 Location: Lethbridge, AB. Posts: 49,084

Last edited by Cat Whisperer; 05-07-2010 at 11:25 AM.
#33
05-07-2010, 02:11 PM
 Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 81,761
Quote:
 The question that somebody SHOULD be asking is statistical rather than probabilistic - how many children of identical gender does one couple have to produce before you reject the notion that each conception FOR THAT COUPLE is an independent event with probability 0.5 of producing a child of either gender?
That depends on what you take as the prior for that possibility, which would probably be derived from study of large numbers of families.

Quote:
 Not quite the same thing, but you could postulate that both parents each carry one copy of a recessive on the X chromosome that causes a very early miscarriage. Both parents are obviously viable, but the father contributes one copy of the recessive to each female embryo. About half the time, the mother will also contribute a copy. As a result, you would expect that roughly half of the female embryos would not be viable. It wouldn't guarantee that all the kids would be boys, of course, but it would definitely change the odds.
If that were the case, then the father would be already dead. It's not that you need two copies of a recessive gene for it to be active; it's that you need to not have a dominant gene. Since the Y chromosome contains almost nothing, a man with a recessive gene on his X will always express it. This is why hemophilia and colorblindness, among others, are so much more common in men than women.
#34
05-07-2010, 02:15 PM
 SDSAB Join Date: Jun 2004 Location: my Herkimer Battle Jitney Posts: 81,697
If the parents are biologically incapable of having any kids at all, then the kids they don't have may be of either sex.
#35
05-07-2010, 02:35 PM
 Charter Member Join Date: Mar 1999 Location: Tysons Corner, VA, USA Posts: 12,883
Quote:
 Originally Posted by Elendil's Heir If the parents are biologically incapable of having any kids at all, then the kids they don't have may be of either sex.
If I do that, will my post count get that high too?
#36
05-07-2010, 03:27 PM
 Guest Join Date: Feb 2000 Location: Montréal, Québec Posts: 8,772
There is a link between the sex chromosome contained in a sperm and its motility, though I'm not well enough versed in the science to really be able to sum it all up. I think X-chromosome sperm tend to live longer (giving a longer window for successfully fertilizing an egg) but also tend to be slower (giving the boys a chance to get there first). Or perhaps it's the other way around.

So it doesn't have to be a matter of certain sperm not being viable, but rather that certain sperm have a lower chance of fertilizing an egg than others based on its "sex". This is probably also strongly affected by the woman as well; the environment the sperm find themselves in will affect their survival and motility.

Anecdotally, I know of a family with 4 boys, but when the man remarried after a divorce, his new wife had 2 daughters by him.
#37
05-07-2010, 03:42 PM
 Guest Join Date: Mar 2001 Location: Phoenix, AZ Posts: 15,368
Quote:
 Originally Posted by Smeghead I knew, even before opening this thread, that it had already degenerated into pointless nitpickery. By any reasonable standard, the answer is 1 in 2^11. Let it go, people. Let it go.
First we must assume all the children are spheres.
#38
05-07-2010, 04:03 PM
 Guest Join Date: Aug 2008 Location: "Hicksville", Ark. Posts: 35,833
Quote:
 Originally Posted by CookingWithGas If I do that, will my post count get that high too?
No, but if you feel the need to follow every joke post you don't like with a post, you'll be up there in no time.
#39
05-07-2010, 04:40 PM
 Charter Member Join Date: Mar 2003 Location: Minneapolis, MN Posts: 14,651
For statistical purposes on a large population, the odds are generally considered 50-50 for either gender. (In actuality, there is a slight (about 5%) bias toward males, and a very small number who fit both or neither category).

But for any specific couple, there can be a significant bias toward either gender. Anecdotal stories of this are common. Personally, I know a neighboring family who had 7 boys, then later 1 girl. Famous families of mostly one gender are numerous: the Andrews sisters, the Jacksons, the Kennedys, etc.

This is well known in horse breeding. One of the common stats considered when evaluating a stallion is the gender percentage of his get.

Last edited by Tim@T-Bonham.net; 05-07-2010 at 04:41 PM.
#40
05-07-2010, 05:27 PM
 Charter Member Join Date: Jan 2003 Location: Home of the haggis Posts: 30,588
A friend is the first of 8, 4 boys and 4 girls.
#41
05-07-2010, 05:44 PM
 Guest Join Date: Dec 2008 Location: Pittsburgh PA Posts: 31
My father was the oldest of 11 boys, no girls. Didn't seem to be a gender bias in the next generation, though.
#42
05-07-2010, 05:50 PM
 Guest Join Date: Feb 2006 Posts: 3,426
This is a common statistical mistake (maybe even has a name, but can't find it right now).

The equation that states "the odds of X occurring are 1:Y therefore the odds of X occuring N times is Y to the power of N", is only correct if the odds are always 1:Y. For most real world cases the odds of X occurring once may be 1:Y but once X has occurred the chances of it occurring again drop dramatically (and likewise for the third, fourth, etc. occurrence).

Most likely as others have pointed out there is a genetic predisposition to producing children of a particular gender, so by the time she had 10 kids that were all boys the chances of the 11th one being a boy are nowhere near 50:50.

Last edited by griffin1977; 05-07-2010 at 05:52 PM.
#43
05-07-2010, 07:20 PM
 Charter Member Join Date: Jun 2000 Location: Dallas, TX Posts: 8,303
Quote:
 Originally Posted by Chronos If that were the case, then the father would be already dead. It's not that you need two copies of a recessive gene for it to be active; it's that you need to not have a dominant gene. Since the Y chromosome contains almost nothing, a man with a recessive gene on his X will always express it. This is why hemophilia and colorblindness, among others, are so much more common in men than women.
Fair point. For the sake of the hypothetical, I was assuming that the recessive was something that could be masked by the Y chromosome somehow. It does seem highly unlikely that such a thing actually exists, though.
#44
05-07-2010, 09:28 PM
 SDSAB Join Date: Jun 2004 Location: my Herkimer Battle Jitney Posts: 81,697
Quote:
 Originally Posted by CookingWithGas If I do that, will my post count get that high too?
Not have kids? Very likely. You'll have more time for the Dope that way.
#45
05-07-2010, 10:32 PM
 Charter Member Join Date: Jul 2000 Location: America's Wing Posts: 29,415
WOOOO! I'm not having kids like a motherfuck!
#46
05-07-2010, 11:18 PM
 Guest Join Date: Nov 2000 Location: Montreal, QC Posts: 58,485
Quote:
 Originally Posted by Bosstone First we must assume all the children are spheres.
In a vacuum.

Incidentally, if there was some biological mechanism in play, it isn't necessarily on the father's side. I can imagine a woman who spontaneous aborts XY embryos while keeping XX ones (or vice-versa) who may not even be aware of how many rejected embryos she is tossing.
#47
05-08-2010, 02:39 AM
 Member Join Date: Nov 2002 Location: Ainran Posts: 11,449
If a woman has 10 male children, what are the odds that the 11th will be Hitler?
#48
05-08-2010, 02:59 AM
 Guest Join Date: Mar 2003 Location: Denver Posts: 7,800
I read somewhere--maybe here?--that having given birth to a child of one sex, you are slightly more likely to give birth to subsequent children of that same sex, whatever it is.

In other words, that there are slightly more families with multiple siblings of the same sex than with multiple siblings of both sexes.

This is certainly true in my family. Among my cousins there is a preponderance of boys. But the one who had girls had ONLY girls. The rest had only boys. (I have four.)
#49
05-08-2010, 06:46 AM
 Guest Join Date: Mar 2002 Posts: 12,037
Quote:
 Originally Posted by Hilarity N. Suze I read somewhere--maybe here?--that having given birth to a child of one sex, you are slightly more likely to give birth to subsequent children of that same sex, whatever it is. In other words, that there are slightly more families with multiple siblings of the same sex than with multiple siblings of both sexes.
The second statement doesn't follow from the first, unless you confine the discussion to families with just two children.
#50
05-08-2010, 11:34 AM
 Charter Jays Fan Moderator Join Date: Jun 2000 Location: Oakville, Canada Posts: 40,713
Quote:
 Originally Posted by Cat Whisperer I come from a family of five girls. Everyone I know with kids has one sex only, no mixed bags. The idea that men produce one sex over the other and resist regular probability seems plausible to me.
You have never in your life met someone with kids of both genders?

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