Probability

Probability tells you how likely something is, from 0 (impossible) to 1 (certain). In Year 8 you listed outcomes, used Venn diagrams and two-way tables, and found probabilities with "and", "or" and "not". In this topic you'll estimate probabilities from real data, tell the two kinds of "or" apart, and use arrays and tree diagrams for events with two, three or more steps, including drawing objects with and without putting them back. Engineers, doctors, farmers and weather forecasters all use these ideas to make careful decisions when the future is uncertain.

What you'll learn

• 10.01 Experimental probability: relative frequency from experiments and data, expected frequency, and why more trials give a better estimate.
• 10.02 Venn diagrams and two-way tables: probabilities of "A and B", "A or B" (inclusive) and "A or B but not both" (exclusive), from Venn diagrams, tables and data.
• 10.03 Arrays and simple tree diagrams: listing every outcome of a two-step experiment, and multiplying along the branches of a tree.
• 10.04 With and without replacement: how the probabilities change when the first object is not put back.
• 10.05 Multi-stage probability: experiments with three or more steps, and "at least one" using 1 − P(none).
• Investigation: simulation of compound events. Use random numbers by hand and on a spreadsheet to compare simple events with compound events, and to estimate a probability that is hard to work out by counting.

Which level should I pick?

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

• Level 1 · Warm-up: smaller numbers, coins and dice, and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: unknowns, three-set Venn diagrams 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.