Math Question

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

 

Exactly 94,232 more boys than girls were born in the U.S. during 2004

http://usgovinfo.about.com/od/censusandstatistics/a/moreboys.htm

The highest sex birth ratio occurred in 1946 (1,059 male births per 1,000 females) while the lowest occurred in 1991 and again in 2001 (1,046 male births per 1,000 females).

Edit: Even with more boys than girls being born, women still outnumber men in the United States. In 2003, the Census Bureau estimated a total of 144,513,361 females of all ages, compared to 138,396,524 males.

 

Math question, assuming 50% probablity

 

Unless you are killing off some of the girls it will be 50-50 right?

 

1:1

 

Pretty much, as far as I can tell. Or, there'd be 1 more boy than girl.

Start with 100 families.

50 boys born, they stop reproducing
50 girls born, they try again.

50 families

25 boys born, they stop(75 total boys now)
25 girls born, they try again(75 total girls now)

25 families

Let's say 13 boys, 12 girls.

THen 6 boys, 6 girls.

Then 1 boy, 2 girls.

Then 1 boy, 1 girl.

THen 1 boy. Done. 97 boys, 96 girls born. Will work out pretty close, on average, to 50-50.

 

based on the info you gave us its hard to come up with the right answer, becouse its ALLWAYS 50/50 that its a girl, so they have to keep on going. You cant decrease the 50/50 odds, unless its born a hermaphrodite, like Mamba.

 

I think you can simply justify it by taking the sum of the infinite series =1.

1/2 + 1/4 + 1/8 + 1/16, .... =1 for boys, and then girls is the same assuming 50%probability of having either boy or girl.

 

Do we factor in the frequency rate of twins or multiples?

 

if there are paternal twins, male and female, and the male comes out first, does the female have to stay in indefinitely?