Suppose 5 out of every​ 10,000 individuals in a country has a rare disease. A test for the disease exists. Individuals known to have the disease test positive ​99% of the time. Individuals known to be free of the disease test negative 98​% of the time. Suppose an individual from the country is selected at random​ (with all being equally likely to be​ selected) and given the test. Given that the individual tests​ positive, what is the probability that he in fact has the​ disease? Give the probability as a decimal number to six decimal places.

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