Funny(?) Probability Problem

families are supposed to continue having children until their first male child

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Possible families

b (p = 0.5)
gb (p = 0.25)
ggb (p = 0.125)
gggb (p = 0.0625)
ggggb (p = 0.03125)
gg.... (p = 0.5^length)

So every family will always have exactly óne boy for sure (total_p=1). But let's prove that.

Girls

The amount of girls you have is basically:

0.5 * 0
0.25 * 1
0.125 * 2
0.0625 * 3
0...... * 4

The extra amount of girl per n is 0.5^(n+1) * n. Summing this formula:

Boys

The amount of boys you have is similar:

0.5 * 1
0.25 * 1
0.125 * 1
0.0625 * 1
0...... * 1

So the extra amount of boy per n is 0.5^(n+1). Summing this formula:

So the ratio is 1:1!

A birth is either a new male or a new female, each with probability $1/2$. This is clearly the case regardless of laws or policies, so by linearity of expectation the expected ratio of males to females in the population will remain $1:1$.

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Edit: If you disagree with the minor simplifying assumption that boys and girls are equally likely, just replace $1/2$ with some fixed $p$ and $1-p$, and $1:1$ with $p:(1-p)$.

Here is some JavaScript code to simulate this for $1$ million families:

var heads = 0;
var tails = 0;
for(var i=0; i<1E6; i++){
   var gotTails = false;
   while(!gotTails){
      if(Math.random() < 0.5){ 
         heads++ 
      }
      else{
         tails++;
         gotTails = true;
      }
   }
}
console.log(heads + "," + tails);

The law will change the sexual habits of people and the number of children born, but it will not change the laws of nature. In the assumed model these are as follows: The sex of a child is determined at the moment of conception, and if conception takes place the probability that the child is a boy is ${1\over2}$, independently of social circumstances.