13 replies to this topic

[BMAD]

In a society in which people only want girls every family continues to have children until they have a girl. If they have a boy, they have another child. If they have a girl, they stop. What is the proportion of girls to boys in this society?

[bonanova]

Spoiler for Looks like

If the birth probability is .5 for boys and .5 for girls,

they will occur in equal numbers.

[witzar]

Spoiler for reversal

In a society in which people only want boys, every family continues to have children while they have a boy. If they have a boy, they are enthusiastic and keep making babies. If they have a girl, they stop having sex in despair. What is the proportion of girls to boys in this society?

[BMAD]

Spoiler for reversal

In a society in which people only want boys, every family continues to have children while they have a boy. If they have a boy, they are enthusiastic and keep making babies. If they have a girl, they stop having sex in despair. What is the proportion of girls to boys in this society?

there is a 50% chance of having a boy or girl in this society since it wasn't implied. I should had stated it as being stacked in the favor of boys to make the ratio more fun, but oh well

Edited by BMAD, 20 February 2013 - 01:41 PM.

[Yoruichi-san]

Spoiler for Series are not my strong point...

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

[Prime]

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.

 

[Prime]

Oops, seems I messed up again.

Spoiler for More girls

The result of the series for the average number of boys per family should be:
1 - (n+1)/2ⁿ⁺¹ 
Send extra girls to war.

 

[bonanova]

Spoiler for Consider

This topic was posted here a few years back.
At the time, I summed the series and in parallel forwarded it to a friend.

His reply was this.

There is a 50% chance if having a boy or girl in this society.

He simply highlighted in my email the words that corresponded to that statement.
It's like asking, after 999 consecutive coin flips that came up HEADS, the chance that the next flip will be HEADS.

Tossed coins and flailing sperm alike have no knowledge of the state of the outside world, nor its future or history.

[bushindo]

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

[Prime]

Spoiler for Marriage procedure

The proportion is roughly the same, but not exactly. Since there are only n married couples (where n happened to be a power of 2,) the following marriage procedure must be instituted.
First, the girls who have no brothers (1/2 of the families) pick one boy each from the remainnig half of the families. Then 1/4 of the girls whose only brother was taken pick their husband from the other 1/4 of the families. That leaves 1/8 of the families where all boys were taken.
And so the procedure of choosing mate must continue. In the end, one girl would remain without a match. She must go to war abroad. The number of couples in the next generation would decrease by 1.

 

The above procedure for choosing mate may be a hint at how to construct a closed-form expression for the series.