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Representing probabilities: medical testing

This is a problem solving lesson, intended to assess how well students are able to:

  • Understand and calculate the conditional probability of an event A, given an event B
  • Represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams

The problem is set in the context of a new test having been discovered for a disease. Experiments have shown that:

  • If a person has the disease the test will always be positive
  • If a person does not have the disease, then the probability of the test being wrong is 5%, a ‘false positive result’

A series of questions follow regarding two different sample sizes.

This is a problem solving lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.

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