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A certain medical test will return either a positive or a negative result. A positive result is intended to indicate that the person who took

A certain medical test will return either a positive or a negative result. A positive result is intended to indicate that the person who took the test has a particular rare disease, and a negative result is intended to indicate that the person who took the test does not have the disease. However, this test sometimes returns an incorrect result in that 20 in 1000 of people who do not have the disease test positive and 35 in 1000 of people having the disease test negative. If 78 people in 1000 have the disease, calculate the probability that a person who tests positive has the disease.

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