Car Talk: False Positive?

From the fantastic car talk puzzler division

RAY: There’s a rare disease that’s sweeping through your town. Of all the people who are exposed to it, 0.1 percent of the people actually contract the disease. There are no symptoms until the disease actually occurs. However, there’s a diagnostic test that can detect the presence of the disease up to a year before it strikes. You go to your doctor, and he administers the test. It comes out positive. You say, “I’m done for!” Then you get a little bit encouraged. You say, “Wait a minute, doc, is this test 100 percent accurate?” Your doctor responds, “Well, not really. It’s 95 percent accurate.” In other words, 5 percent of the people who take the test will test positive but they don’t really have the disease. Here’s the question: What are the chances that you actually have the disease?

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