The totalitarian government decrees that families must keep having children until they have a boy. Once they have a boy, they must stop. What is the average number of children per family, and what is the gender ratio? First correct answer gets to be the person who gave the first correct answer.
8 comments:
Gender ratio is 1 to 1 and average number of kids is 2.
Gender ratio is 1 to 1 and average number of kids is 2.
come again?
the answer is happy birthday. may your days be merry and BRIIIIGHT
But...wouldn't the gender ratio be 1 to 1 and average number of kids be two if on average everyone had a girl and then a boy? Wouldn't half the people on average have boys first and only have one kid? So the average number of children would be 1.5?
I don't know, I'm bad at math.
Luke's almost right.
If you take a theoretical country of 100 couples, 50 of them will have boys and stop. 25 of the remaining 50 will have boys and stop, and so on. In every "generation" there will be an equal number of boys and girls, and 100 couples will have 200 children, assuming they are all equally capable of having boys or girls.
Which is where things can be thrown off a little. I might be overthinking it, but isn't it conceivable that some couples could have 7,8, 9 or more girls before they produce a boy, if ever? That would tip the gender ration slightly in the girls' favor and raise the average number of kids a little, but there's really no way to account for with statistics.-
The gender ratio, once the sample size is large enough, will always be 1:1. For every girl birth there is a boy birth. Always. Doesn't matter what rules the gov't makes. Even if there are families with large numbers of girls, every birth has a 50:50 chance of being either sex. Another way to look at it, for every family whose 113th birth is a girl, there is a family whose 113th birth is a boy.
The average number of kids/family is always apporaching the asymptotic 2. After the first generation there is an average of one. Half the families stop. Half have another child. After 2 generations, the average is 1.5. After 3 generations, the average is 1.75. After 4, 1.875, and so on, approaching 2. In the hundred families country, there are 100 kids in the first generation, 50 in the second, 25 in the third, 12.5 in the fourth, etc. It approaches 200 kids for the 100 families.
Now, if the children are imaginary, that's another question!
You mean "approaching".
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