Probability

Probability is the maths of chance: how likely something is to happen. In this topic you'll learn the words for describing chance, write probabilities as numbers from 0 to 1, work them out by counting outcomes with dice, coins, spinners, cards and marbles, and compare them with what really happens when you do an experiment. Weather forecasters, doctors, engineers and sports coaches use probability to make good decisions.

What you'll learn

• 15.01 Language of probability: words from impossible to certain, trials, outcomes, events and listing the sample space.
• 15.02 Probability as a number: the probability scale from 0 to 1, probabilities as fractions, decimals and percentages, and the chance an event does not happen.
• 15.03 Theoretical probability: working out probabilities by counting equally likely outcomes, with dice, spinners, cards, marbles and letters.
• 15.04 Experimental probability: relative frequency from experiments and data, comparing it with theoretical probability, and predicting how often something will happen.
• Investigation: simulations. Toss coins, roll dice and spin spinners, then use a spreadsheet to run thousands of trials and see how the results compare with your predictions.

Which level should I pick?

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

• Level 1 · Warm-up: dice, coins and simple spinners, with more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: unequal spinners, playing cards, working backwards from a probability 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.