13 replies to this topic

[bonanova]

Spoiler for Series are not my strong point...

...but I get log(2), approx .693.

>The number of people in the society is not specified either. I assume, there are n married couples.

Spoiler for my calculation

There is exactly one girl per each family. I estimate the average number of boys per family is:
1 + 1/2ⁿ * (n - 1/2).
So, just a bit more boys than girls. When they reach marrying age, I say, send the extra boys to war abroad. Make sure all the rest are married and procreate in the prescribed fashion to maintain the population.

 
I think there is a discrepancy with bonanova's answer because...

Spoiler for

There is a difference between the proportion of boys to girls in a society and the average proprotion of boys in a family. Consider a society of only 2 families,
Family A: 0 boy, 1 girl
Family B: 2 boy, 1 girls

The proportion of boys in society is (2/4) = 1/2
The average proportion of boys in a family is (1/2)( 0/1 + 2/3) = 2/6

 

 

Sure. The gender distribution within families is terribly skewed.

1. A family can have an unlimited number of boys; a family can never have more than one girl.
2. A family can have a girl with no brothers [half!]; a family can  never have a boy with no sisters.

[Prime]

The series is infinite, and the variable term thus equals zero. There are equal numbers of boys and girls on average. Bonanova is right. It's a happy ending. In each generation everyone gets his/her mate.  

[phaze]

Spoiler for Think bonanova and prime are correct

Average family size tends to 2 for a large number of families and we know that each family has 1 and only 1 girl this means the other family member must be a boy

However as having an infinite number of families would be a nightmare for local councils there is a 50% chance that there is an extra girl. It is also an imposition to have an infinitely large family.

What would be the ratio be If all families give after 10 attempts at having a girl given that the number of families is n?

Edited by phaze, 21 February 2013 - 01:14 AM.

[bonanova]

Spoiler for Think bonanova and prime are correct

Average family size tends to 2 for a large number of families and we know that each family has 1 and only 1 girl this means the other family member must be a boy

However as having an infinite number of families would be a nightmare for local councils there is a 50% chance that there is an extra girl. It is also an imposition to have an infinitely large family.

What would be the ratio be If all families give after 10 attempts at having a girl given that the number of families is n?

 

Since it's solved, I won't spoiler this.

 

The answer is not complex. Every birth, regardless of anything that is said, done, legislated, prohibited, presupposed, calculated, imagined or hoped for, has equal chances of being a boy or girl.

 

If you flip a coin an odd number of times, then, yes, the number of heads and tails cannot be equal. But the question is for large numbers of conceptions and births - for a society - where, even though the numbers of boys and girls may not be exactly equal at every moment - each birth changes the running total - the chances of an excess of boys exactly equals the chances of an excess of girls. The question asks whether a birth control strategy can affect the society's overall gender balance in a systematic way. The answer is no, it can not.

 

No calculus needed.