
Bayes Problem
Can't seem to figure this one out. Any help would be appreciated:
A positive result on a test for diabetes is correct 90% of the time, and a negative result is correct 95% of the time. If 10% of the population has diabetes, what is the probability that a randomly selected person will have a false positive test result?

I'm not sure you stated the problem correctly. In this form it's not a Bayesian problem.
As it is now, you are looking for a person who belongs to the nondiabetes group (.9 probability) and then gets an incorrect positive test result. (.1 probability) You then multiply these to get your answer.
It would be a Bayesian problem if the question was: Given a positive result, what is the chance that person has diabetes?

Hypothesis are
$\displaystyle H_1:=\{person\, has \, diabetes\} \Rightarrow P(H_1)=0.1$
$\displaystyle H_2:=\{person\, doesn't\, have \, diabetes\} \Rightarrow P(H_1)=0.9$
Define events
$\displaystyle A=\{test\, is \, positive\}$ and $\displaystyle B=\{test\, is \, negative\}.$
Then
$\displaystyle P(AH_1)=0.9 $
$\displaystyle P(AH_2)=0.1 $
$\displaystyle P(BH_1)=0.05 $
$\displaystyle P(BH_2)=0.95 $
You have to find the probability that person has a false positive result hence you have to find $\displaystyle P(A\cap H_2)=P(AH_2)P(H_2)=0.1 \cdot 0.9=0.09=9\%$

Thank you both. I found the wording of the problem somewhat confusing.