Chance is a number. This unit puts every chance on one scale from 0, which cannot happen, to 1, which must, and then asks two questions: what could happen, and how often should we expect it? The first part is counting, with organised lists, tables and tree diagrams. The second part divides the outcomes you want by all the outcomes, and then checks that answer against what an experiment gives.
The experiments and the simulation in this unit are fixed runs, so they look the same each time you open them and every number in them can be checked. No lesson needs a calculator.
The lessons, in order
- Lesson 1 · The probability scale The 0 to 1 scale, impossible and certain, and one probability as a fraction, a decimal and a percentage. Change how many of 20 counters are red and watch the marker move along the scale from 0 to 1. No calculator
- Lesson 2 · Listing every outcome Sample spaces for two-stage events, organised lists and two-way tables, and counting outcomes by multiplying. Choose how many results each of two spinners has and watch every pairing fill a grid. No calculator
- Lesson 3 · Tree diagrams Tree diagrams for two and three stages, counting complete paths, and outcomes that meet a condition. Toss a coin one, two or three times and light up the paths with a chosen number of heads. No calculator
- Lesson 4 · Favourable over total Theoretical probability for equally likely outcomes, and the probability of an event not happening. Pick a total from two dice and see which of the 36 equally likely cells make it. No calculator
- Lesson 5 · What an experiment tells you Experimental probability as relative frequency, comparing it with theory, and the effect of the number of trials. Roll a fixed run of a die up to 500 times and watch the relative frequency of sixes settle. No calculator
- Lesson 6 · Expecting and simulating Expected frequency, simulating an event with random digits, and comparing a simulation with theory. Simulate families of three children from a fixed run, then check the result against the theory. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.