I am having a difficult time finding error bars on a particular quantity.
There are two random variables, let's call them $price$ and $color$; color can only be either red or blue. We don't have a probability / probability density for either variable, but we have 13000 samples. Out of these 13,000 we have found that only 10 have
$$\text{price} > 15,000$$
Of these "expensive" points, two are blue and eight are red.
We then form the statistic
$$r = \frac{\sum_{\text{red}}P_i}{\sum_{\text{all}}P_i}$$
where $P_i$ is the $i$th price. Namely, $r$ is the probability that a random dollar in the "expensive" category is red.
Given the full sample of $13~000$ points,
$$\{($313, \text{blue}), ($15001,\text{red}), ...\}$$
How do we compute error bars on our statistic $r$?