Answer:
eventually the gender ratio of population in this society will be 50% male and 50% female.
Step-by-step explanation:
For practical purposes we will think that every couple is healthy enough to give birth as much children needed until giving birth a girl.
As the problem states, "each couple continue to have more children until they get a girl and once they have a girl they will stop having more children". Then, every couple will have one and only one girl.
We will denote for P(Bₙ) the probability of a couple to have exactly n boys.
Observe that statement 1 implies that:
[tex]P(B_{n-1})=(0.5)^{n}[/tex].
Then, the average number of boys per couple is given by
[tex]\sum^{\infty}_{n=1}(n-1)P(B_{n-1})=\sum^{\infty}_{n=1}(n-1)(\frac{1}{2} )^n=\sum^{\infty}_{n=2}n(\frac{1}{2} )^n=\\\\=\sum^{\infty}_{m=2}\sum^{\infty}_{n=m}(\frac{1}{2} )^n=\sum^{\infty}_{m=2}(\frac{1}{2} )^{m-1}=\sum^{\infty}_{m=1}(\frac{1}{2} )^{m}=1.\\[/tex]
This means that in average every couple has a boy and a girl. Then eventually the gender ratio of population in this society will be 50% male and 50% female.
