# Maths GCSE: Probability

Mathematician and comedian Matt Parker demonstrates how to handle probabilities using probability and frequency trees for students struggling with their maths GCSE.

Designed to revise and reinforce independent probability calculations, Matt tackles GCSE Foundation approaches to theoretical and experimental probability.

With clear graphics and using probability trees and successive dice rolls, we explore theoretical results and apply proportional reasoning to frequency trees which display experimental results.

Aimed at the foundation syllabus, this video does not explore dependent probabilities.

This short film is from the BBC series, The Maths Show.

### Teacher Notes

During the video:

• Pause while Matt is calculating his playing card probabilities to see if your students can get the correct answer.
• Elicit if students can fill in the rest of the probability tree - emphasize that the top set of branches in the second roll should be the same as the bottom set as it’s the same experiment.
• During the frequency tree experiment explore whether students fully understand where the numbers come from.

After the video:

• Explore filling in other probability trees - if students know one probability can they fill in the rest? Identify errors and key rules to ensure students don’t make the same error - ‘pairs’ of branches should always add to one - for Foundation GCSE the top and bottom set should be the same per event.
• Use and/or rules applied to probability trees and probabilities written in a table. Can students find simple ‘and’ probabilities from word questions - the probability of rolling a six and flipping a head?
• Extend to exploring relative frequency and theoretical probability, and proportional reasoning questions drawn from frequency trees - as a new topic this is often an under explored area.
• If time allows a simple experiment could be carried out to work out expectation vs theoretical probability, for example drawing balls or cards out of an envelope then replacing to estimate the fraction of different colour balls/cards.

### Curriculum Notes

Suitable for teaching maths at GCSE in England, Wales and Northern Ireland and National 4/5 or Higher in Scotland.