Senior Maths Topics: Probability

Phoenix Senior Maths Topics provide thorough and detailed explanations, worked examples, summaries and practice exam questions on essential senior maths topics. Each book is a detailed treatment of a topic selected because of its importance in senior maths. They can be used at school, to supplement the textbook, providing more detail and exercises, and at home, to aid home study and exam preparation.

These books are for senior secondary students, particularly those who:

• want to study a topic in more depth
• are having difficulty with a topic

Phoenix Senior Maths Topics books can be used:

• to learn and understand the topic: a full and detailed treatment of the topic with clear step-by-step explanations and plenty of worked examples.
• as a study and revision aid: a separate summary contains the information which has to be learned, as well as exercises and sample tests with typical examination questions. Solutions are provided.
• as a reference: all the relevant information is easy to find and easy to understand.

Contents

About this book

Chapter 1 Basic definitions and ideas

• Random experiments. Equally likely outcomes
• Non-equally likely outcomes
• Simple events
• Composite events
• Sample space
• Favourable outcomes

Chapter 2 Diagrammatic representation of sample spaces

• Tree diagrams
• Geometric representation of sample space
• Contracted form of tree diagrams

Chapter 3 The probability of an event

• Definition
• Successive outcomes
• The multiplication principle
• Probability by tree diagrams
• Probability that an event does not occur
• The box-filling technique

Chapter 4 Conditional probability

Chapter 5 Sets and the Venn diagram

• Intersection
• Union

Chapter 6 The addition principle

• Mutually exclusive events
• Events that are not mutually exclusive
• Using Venn diagrams

Chapter 7 The product theorem of probability

• Multi-stage random experiments
• Product rule
• Summary of the 'product theorems' results
• Using complementary events

Chapter 8 Probability trees

Chapter 9 Miscellaneous

• The addition and product theorems
• Sampling without replacement

Chapter 10 Permutations and combinations

• Permutations
• Combinations
• Circular arrangements of unlike things

Chapter 11 The binomial theorem

Chapter 12 Further probability

• Application of counting techniques
• Binomial probability distribution
• Expected value

Summary

Sample tests

Answers