# Probability of testing positive

Suppose that the probability that a random person has a certain disease is $$0.005.$$ A scientist develops a device which tests a person positive for the disease with $$95$$% chance when the person really has the disease. However, the same device tests a person positive for the disease with $$1$$% chance when the person in fact does not have the disease. What is the probability that a person really has the disease when tested positive by the device?

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