# Math Help - Maths help! Desperate!

1. ## Maths help! Desperate!

Take a look at the photo
May I have the method aswell for future reference?
Many thanks!

2. ## Re: Maths help! Desperate!

Ok what you do here is construct a probability tree for a single couple. Each couple probabilistically behaves the same so the overall ratio for the population is just the same as that for a single couple

Note that this all assumes the children don't themselves start forming couples (from other families hopefully) and themselves reproducing.

if you work through the thing you'll find that

$$Pr[\mbox{k girls, 1 boy}]=\left(\frac{1}{2}\right)^{k+1}$$

thus

$$P[\mbox{n children}]=\left(\frac{1}{2}\right)^{n}$$

For n children the ratio of girls to boys is

$$r[n]=\frac{1}{n-1}$$

and so you end up with a discrete probability distribution for certain ratios, i.e.

$$Pr\left[r[n]\right]=\left(\frac{1}{2}\right)^{n}$$

and zero for all other numbers. To make things a bit more concrete

\begin{align*} &Pr[\infty]=\frac{1}{2} \\ \\ &Pr[1]= \frac{1}{4} \\ \\ &Pr\left[\frac{1}{2}\right]=\frac{1}{8} \\ \\ &\mbox{and in general for n>1} \\ \\ &Pr\left[\frac{1}{n-1}\right]=\frac{1}{2^n} \end{align*}