# Probability of testing positive

**Discrete Mathematics**Level 2

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?