In the despotic state of Roxobia the government passed a decree which was aimed at reducing the population while increasing the number of boys available for military service. It stated that every family must stop having children as soon as a girl was born. So if a couple’s first child was a girl, then no more children were allowed. If a couple had ten boys, they could keep on having children until a girl arrived. This law was rigorously enforced. If the chances of having a boy and a girl are equal, will there eventually be more boys then girls, more girls then boys or will it be the same? Did the government succeed in its two objectives?
It’s a hit sent out by the Vos Savant family!!! RUN!!!
Same. Perhaps. No.
Not enough information to resolve it
Maybe it wouldn’t statistically matter, but I’ll ask anyway.
Is a family required to keep producing offspring until a girl is born?
No, discounting infanticide.
Assuming that the chances of having a boy or a girl are equal, and assuming there are 16 couples who want to have children in Roxobia:
First set of births will produce 8 boys and 8 girls.
The 8 couples with boys will have another child.
Second wave of births will produce 4 boys and 4 girls.
The 4 couples with boys will have another child.
Third wave of births will produce 2 boys and 2 girls.
The 2 couples with boys will have another child.
Fourth wave of births will produce 1 boy and 1 girl.
Total children so far – 15 boys and 15 girls.
Etc.
and how many kids befo they stop or die of exhaustion?
the chance that it is boy or girl has nothing to do with the past history of the parents, it is always 50/50 and so the population will be 50/50.
The difference would be in the family composition. Girls will have fewer siblings on average than boys.
This would only work if a particular couple has a tendency towards one gender or another of children - i.e. if one of your given conditions (equal chances) was not true.
If a couple has a higher chance of producing boys, then they would on average have more children than a different couple with a bias towards girls. This would allow for more boys.
I believe that in real life there are some biases in some situations and that 50% chance is not exactly right. I don’t have time to do a search right now, so flame me if you must.
I’ve heard that the male/female bias may have something to do with the pH of the woman’s reproductive tract: An acidic environment favors sperm of one sort, and a basic environment favors the others. I can’t remember, though, if it’s X or Y sperm that prefer acid.
If a family keeps having kids once they start having kids until they have a girl, then you can think of the problem as:
Take a bucket of coins. Pick one coin out and flip it until you get tails. So, maybe you get HHHT. Once you get a tail, but that family, errr, coin aside and start with a new coin. You can see that you will not change the long term expectation of heads or tails just by switching coins when you get a tail.
Actually, since you know the last coin flip you will perform will come up tails, you give a slight bias to tails (on the order of 1/(number of coin flips)).
-P
As an extension to my last post…
You can remove the requirement that they must keep having kids once they start. You can switch coins any time you please and it still won’t change the odds!
-P
It’s near the end of the day, so I haven’t worked out the system’s tendency to favor one sex over the other at each level, but assuming a trend develops to favor more male offspring, won’t this republic need to worry about an excess male population? After a few generations, finding mates for all these men might get tough.
Of course, if this republic needs men to go out and die in wars, this might not be a problem after all.
My gut feeling is that the population of men does not significantly increase by these rules. Enough couples (about half) will produce a girl first, the other half will produce a boy, and a smaller number will continue. At each step, the chances remain half and half (ignoring genetic factors that favor one sex).
Me neither, but there are more X potheads.