Combined Probability

Overview

Competitions and marketing campaigns offering prizes are used to develop ideas about probability through consideration of the chance of being a winner. We see how probability concerns both the people who devise competitions and the people who enter them. A simpler scenario of randomly choosing a snack is used to introduce the necessary concepts and to illustrate relevant calculations for combining probabilities. We see how to:

• represent probability, as a fraction or a decimal, on a scale from 0 to 1
• calculate the probability of a single event
• calculate the combined probability of two mutually exclusive events (using the ‘or rule’)
• calculate the combined probability for two independent events (using the ‘and rule’)
• use tree diagrams to illustrate all possible outcomes and to assist with calculation, both for a single event and for two events
• check that the sum of probabilities is 1 for all possible outcomes of a single event

The programme develops the basic ideas of combining probabilities using simple cases and straightforward arithmetic, mainly with fractions. The construction and use of tree diagrams to illustrate events and to calculate probabilities is covered in easy stages. The programme offers relevant examples, illustrated with clear graphics that will help students appreciate how tree diagrams are built and used. The programme could be used as an introduction to combined probability, particularly tree diagrams. While there is some revision of simple probability, it is assumed that students will have already met the basic ideas before viewing.

The content is linked to the requirements of GCSE Intermediate Mathematics. It includes tips for answering exam questions, and a discussion of a typical exam error (‘Tick or Trash’).