Probability

Probability measures how likely something is, from 0 (impossible) to 1 (certain). In Year 7 you found probabilities by counting equally likely outcomes and compared them with experiments. In this topic you'll work with two events at once: listing every combination with tables and tree diagrams, using "and", "or" and "not", sorting outcomes into Venn diagrams and two-way tables, and spotting events that can't happen together. Doctors, engineers, insurers and weather forecasters all use these tools to make careful decisions.

What you'll learn

• 10.01 Calculate probability: sample spaces, and probabilities for two- and three-step experiments using lists, tables and tree diagrams.
• 10.02 Intersection and union: A and B (∩), A or B (∪), not A (the complement), and why P(not A) = 1 − P(A).
• 10.03 Venn diagrams: reading, completing and drawing Venn diagrams with two and three sets, and finding probabilities from them.
• 10.04 Two-way tables: completing two-way tables, swapping between tables and Venn diagrams, and finding probabilities from them.
• 10.05 Mutually exclusive events: events that can't happen at the same time, and adding probabilities with the addition rule.
• Investigation: probability simulations. Toss coins and roll dice, then use a spreadsheet to run a thousand trials of compound events and compare the results with your predictions.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: coins, dice and small groups, with more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: three-step experiments, three-set Venn diagrams, unknowns and problems with more steps, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.