In a country where everyone wants a kid with a specified gender(assuming only 2 genders), each family continues having babies till they have a kid with the expected gender. After some time, what is the proportion of boys to girls in the country?(assuming probability of having a boy or a girl is the same)
Answers
Probability of boy = 0.5
Probability of girl = 0.5
Assuming no abortion and an average of three children and the family will stop having children if they have 2 boys at start and will also stop having children if they have 2 boys and they reach a size of 3 children or 4 children, some will stop if they have 4 children with less children and the family have at most will have 5 kids, as the families children increase more than 3 than their probability will become 1/2, 1/4, 1/8 etc.( all these will have huge effects)
The possibilities are : ( B for boy , G for girl)
Family 1 first child B then second child B
Family 2 first child B then second child G then third child B
Family 3 1st B 2nd G 3rd G
Family 4 1st G 2nd G 3rd B
Family 5 1st G 2nd B 3rd G
Family 6 1st G 2nd B 3rd G 4th B
Family 7 1st G 2nd G 3rd G 4th G 5th G
Family 8 1st B 2nd B 3rd B
Family 9 1st G 2nd B 3rd B
Family 10 1st B 2nd G 3rd G 4th G 5th B
Family 11 1st G 2nd G 3rd B 4th B
So all the families with 3 children
Boys = 12 Girls = 8
all families with 4 children
Boys= 4÷ 2= 2Girls = 4÷ 2 = 2
all families with 5 children
Boys= 2÷ 4 = 0.5 Girls= 8 ÷4 = 2
Boys = 12+2+0.5= 14.5
Girls = 8+2+2 = 12
Ratio of boys to girls= 14.5/12 = 1.208333
This is my approximation. Great question btw.