A Probability Puzzle

From Randomness by Deborah J Bennett:

“If a test to detect a disease whose prevalence is one in a thousand has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person’s symptoms or signs?”

For extra credit: what percentage of the physicians, residents, and fourth year medical students at a prominent medical school who were asked this question got it right?

Extra, extra credit: why is it critically important that doctors be able to get this one right? Give one example.

This is an honor system non-open book test.

Answers in comments, please. Will highlight correct answers in a subsequent post. Hat tip to Nassim Taleb in Fooled by Randomness for citing Bennett’s test.

Answers here.