0
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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:$$(\Omega,\mathscr A,P).$$

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.