Sick or Not?

The following question is taken from Nassim Taleb's Fooled By Randomness book which I highly recommend.

The test of a disease presents a rate of 5% false positives. The disease strikes 1/1000 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?