Chapter 23: Probability

Probability measures how likely an event is. You will describe chance, use data, count outcomes and combine events.

By the end of this chapter

You will be able to:

• place probabilities on a scale and calculate probabilities for equally likely outcomes;
• use relative frequency to estimate probability and expected outcomes;
• organise outcomes in tables, frequency trees, lists and possibility spaces;
• calculate probabilities for independent and dependent combined events using tree diagrams;
• use Venn diagrams and set notation to describe groups and events;
• calculate conditional probabilities from a restricted group using tables, tree diagrams and Venn diagrams.

The chapter problem

A spinner has equal-sized red and blue regions. You will investigate the chance of landing on red, then compare a prediction with results from repeated spins.

First contact: without calculating, predict whether red will appear more than half, less than half or about half of the time over many spins. There is no score for this prediction.

Roadmap

1. 23.1 The probability scale and equally likely outcomes
2. 23.2 Relative frequency and expected outcomes
3. 23.3 Frequency trees, tables and possibility spaces
4. 23.4 Combined events and tree diagrams
5. 23.5 Venn diagrams and set notation
6. 23.6 Conditional probability
7. Review

Your turn to connect it

Where might you or someone you know use a probability estimate or compare a prediction with results? Write one example and explain what decision it could help with.