Title
Olympic Drug Testing (October Crowell)
Goals
(1) Students will investigate discrete probability concepts.
(2) Students will calculate the probability of a true positive test result given test accuracy.
Abstract
This activity allows students to investigate the actually outcomes of drug testing in terms of probability of successive events. The activity should be used after some exposure to combined probability and probability trees.
Problem Statement
Drug testing among Olympic athletes has been a hot topic at each Olympic games. But how accurate are these tests? Are they reliable enough to ruin an athletes' shot at a gold medal just because he or she tests positive? For this activity, assume that each athlete is given the test only once.
Instructor Suggestions
(1) Describe the problem to the students.
(2) Encourage students to use the concepts of combined probability and probability trees to investigate the problem.
(3) Have each student complete the activity individually except for the last question.
(4) Once everyone is finished with the individual work, have students discuss in small groups possible answers to the last question.
(5) Discuss students answers to the last question as a whole group.
Materials
"Olympic Drug Testing" activity sheet
Time
Introduction (5 min), Individual work (15 min), Group discussions (15 min), Class discussion (10 min)
Mathematics Concepts
Discrete Mathematics Concepts
combined probability, probability trees
Related Mathematics Concepts
decimal multiplication, ordering
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Statistics, Probability, Discrete Mathematics.
Colorado Model Content Standards Addressed
Number Sense (1), Algebraic Techniques (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedure s(6)
Curriculum Integration
This activity could be integrated into any curriculum when basic probability concepts are taught.
Further Investigation
Students could investigate different types of tests that are administered and the probability of their accuracy.
Variations/Comments
References/Resources
Colorado State Content Standards. Colorado Department of Education.
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics across the curriculum, K-12, Reston, VA; National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics, (1989). Curriculum and evaluation standards for school mathematics. Reston, VA; Author.