What is the Chance That The Patient Has The Disease?

I read Nassim Nicholas Taleb's book "Fooled by Randomness", and he gave an interesting example of a mistake in calculating probablities:

A test for a disease has 5% false positives (This means that 5% of the tests given to those who do not have the disease come back positive - so if 100 people test positive, only 95 actually have the disease). 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 tests positive. What is the probability of the patient having the disease?

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