Math
Unit 8
10th Grade
Lesson 8 of 10
Make decisions about medical testing based on conditional probabilities.
In terms of pacing, this lesson should spread over two days due to the depth of this content.
In a certain population, 30% of people get a particular disease. A test was developed to determine if any given person has the disease, but it isn’t perfect. The test has a 90% chance of accurately predicting that someone has a disease, BUT it also has a 5% chance of predicting someone has the disease who doesn’t —a false positive. Find the number of people in a random sample of 2,000 people who take the test for the disease who get results that are true positive, false positive, true negative, and false negative in the two-way table and tree diagram below.
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 where 1% of the people have mononucleosis. If a randomly selected patient’s test result is positive, what is the probability that they have mononucleosis? Explain.
False Positive Test Results, accessed on June 15, 2017, 9:22 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 7
Lesson 9
Topic A: Conditional Probability and the Rules of Probability
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