May 20, 2015

False Positive Test Results

A certain test for mononucleosis has a 99% chance of correctly diagnosing a patient with mononucleosis and a 5% chance of misdiagnosing a patient who does not have the infection. Suppose the test is given to a group where 1% of the people have mononucleosis. If a randomly selected patient's test result is positive, what is the probability that she has mononucleosis? Explain.

An exercise, commentary, and solution from Illustrative Mathematics

- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.