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?

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Probability of testing positive

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.