ResourceMAP - Combining Probabilities - Teacher Edition

ResourceMAP modules are relatively short and designed for flexible implementation; that is, they can be used in regular classes as well as in special test-preparation settings. Each module contains a set of contextual problems in several formats: multi-part open response, short response, and multiple-choice. Accompanying the problem set are tip sheets that serve several purposes including lists of formulas, calculator instruction, and brief reviews of the module's underlying mathematics. Also provided are teacher notes (the module purpose, the mathematical focus, and implementation commentary), answers to all problems, and (in a few cases) handout masters.

Combining Probabilities

Many important decisions are made on the basis of tests. Athletes and employees
are often tested for drug use. People are tested for medical conditions.
Environmental testing is done on food, plots of land, and bodies of water.

But most tests are not perfect. A test for cancer sometimes incorrectly indicates
the presence of the disease in a person who is healthy. Such a “false positive” may
not happen often, but it can have serious consequences.

A knowledge of probability can help us interpret the results of test procedures that
are sometimes in error.

I. Purpose
• To provide practice in computing joint probabilities
• To use tree diagrams to represent real-world probability contexts

II. Mathematical Focus
• Conditional probability
• Joint probabilities

III. Tip Sheets

Tip Sheet: Joint Probabilities includes
• addition rule for probabilities of mutually exclusive events
• conditional probability
• general multiplication rule for probabilities
• multiplication rule for independent events

Tip Sheet: Tree Diagrams includes
• using tree diagrams for counting
• using tree diagrams to represent situations involving probability