1. ## probability

Let $\displaystyle A$ be people who are high risk, $\displaystyle B$ be people who are medium risk, and $\displaystyle C$ be people who are low risk.

Lets say $\displaystyle P(A) = p, \ P(B) = q, \ P(C) = r$ and the proportion of those in $\displaystyle A$ is $\displaystyle \hat{p}$, those in $\displaystyle B$ is $\displaystyle \hat{q}$ , and those in $\displaystyle R$ is $\displaystyle \hat{r}$, where $\displaystyle \hat{p} + \hat{q} + \hat{r} = 1$.

So $\displaystyle P(\text{high risk and in the group}) = p(\hat{p})$

$\displaystyle P(\text{person at risk}) = p(\hat{p}) + q(\hat{q}) + r(\hat{r})$ and

$\displaystyle P(\text{randomly chosen person is high risk}) = \frac{ p(\hat{p})}{p(\hat{p}) + q(\hat{q}) + r(\hat{r}) }$?

2. would it just be $\displaystyle p$ and $\displaystyle \hat{p}$?

3. or is this a poorly worded question?

4. What's your question? Because the you answered then 3 questions written correctly.

5. oh ok, so its correct?

6. yeah i think so... I've been doing probability all day so it is possible i'm not seeing this right but i'll keep looking and post if i change my mind