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If a citizen of Anytown tests positive, what is the true probability they actually have the disease?

There is fear in the isolated community of Anytown that a rare communicable disease has
entered the population. At a citizens meeting in Anytown the voters demand that the Mayor do
something immediately to protect the citizens from this disease. The Mayor fearing a loss in
popularity responds with a plan to test every citizen for the disease and then to execute those
who test positive and cremate the remains. The doctors in Anytown have made a public
statement that while the test for the disease is 98% accurate it does have a false positive rate of 6%. Further, Anytown epidemiologists have estimated the disease to be present in only 1 in
1000 Anytown citizens. If a citizen of Anytown tests positive, what is the true probability they
actually have the disease?

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