>>1069203For a family with a target size of N, the chance of it having 1 child is 51%. The chance of it having 2 is (100%-51%) * 51%, or 24.99%. The chance of it having 3 is 100% - 51% + 24.99%) or 12.2451%, or 4 is 6.00099%, and the chance of them having 5 is 2.94004851%.
That being said, since they stop at N children, the chance of them having N children is not what was described in the list above, rather 100% - all the previous chances.
That means that
100% of 40% of families will have 1 kid
51% of 34% of families will have 1 kid, while 49% of 34% will have 2
51% of 16% of families will have 1 kid, while 25% of 16% will have 2 and 24% of 16% will have 3
51% of 6% of families will have 1 kid, while 25% of 6% will have 2, 12% of 6% will have 3, and 11% of 6% will have 4
51% of 3% of families will have 1 kid, while 25% of 3% will have 2, 12% of 3% will have 3, 6% of 3% will have 4 and 5% of 6% will have 5
So now we know how many kids each family has, but not how many males vs females. First let's get the male count.
The average number of males in a family of any size is 1 - chance that all kids up to that point are female, or 1-(0.49^T)
With that, we get,
Males = 0.4*0.51 + 0.34*0.7599 + 0.16*0.882351 +0.06*0.94235199 +0.03*0.9717524751, which is 0.689235853653
Now, to find the average number of girls per family.
This number is represented by sum(0.49^n) from 1 to T where T is the target child count. Using a calculator to get this value (because its late and I am tied of being autistic),
0.40 * 0.49 +0.34*0.7301+ 0.16*0.847749 +0.06*0.90539701 + 0.03*0.9336445349 or 0.662206996647 girls per 1 family.
Doing the math, that means there are on average 1.358059996647 children per family, which, when applied to the rate of girls and guys, comes out to 0.51 guys for every 0.49 girls.
So umm, I guess feminism gets stumped by math again... (or I'm bad at math)
