# Making a model when sampling by replacement

We're drawing from a bag of 20 balls (10 white and 10 red)

Let Z be the number of red balls in 12 draws. Suggest a model for Z when we sample by replacement.

So I understand the concept of sampling with replacement and that the probability of getting a red ball always equals to 1/2; however, I don't quite understand what kind of model I'm supposed to make.

One possible outcome of such an experiment is $$\color{black}{rrrr}wrwwrwwr.$$All the outcomes are such sequences of $r$s and $w$s. There are $2^{12}$ of them. Let $\Omega$ denote the set of all these sequences and let $\mathscr A$ denote the set of all subsets of $\Omega$. The probabilities of the individual elements of $\Omega$ equal. Namely all are of probability $2^{-12}$. So for a set (an event) $A$ in $\mathscr A$ $P(A)=i2^{-12}$ where $i$ is the number of elements in $A$.
The model is the triplet I've just defined:$$(\Omega,\mathscr A,P).$$