Probability of Disease

A test of a disease presents a rate of 5% false positives. The disease strikes 1/1,000 of the population. People are tested at random, regardless of whether they are suspected of having the disease. A patient’s test is positive. What is the probability of the patient being stricken with the disease?

I found this quiz given to medical doctors in a popular book. Most doctors answered 95%. Do you agree?

Will post the answer later.