Question

Bayes Theorem question

Answer 1

The question is: In a certain region of the country it is known from past experience that the probability of selecting an adult over 40 years of age with cancer is 0.05. If the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of incorrectly diagnosing a person person without cancer as having the disease is 0.06, what is the probability that an adult over 40 years of age is diagnosed as having cancer?

I'm confused about how to even set this up. So far I've been looking at it like these:
And this isn't even considering the over/under 40 aspect...I can't tell if that's relevant at all for this problem.