Home → Curriculum Hub → Maths Lessons → Schemes of Work → Three-Year GCSE Foundation → Probability
This Foundation GCSE scheme of work unit covers probability in Year 9. It moves from language on a probability scale to combined events. Students write probabilities as fractions, use sample spaces and mutually exclusive events, compare experimental and theoretical results, then use trees, Venn diagrams and a permutations practice lesson.
Students have to write a probability as a fraction between 0 and 1, and to list outcomes without repeats. That listing is what later tree diagrams, set-notation questions and expected-frequency items all need.
A student who has secured this unit:
Students should be secure with the following before beginning this unit.
Probabilities run from 0 to 1. Impossible, even and certain sit at 0, 1/2 and 1. Keywords should be matched to a position, not used on their own.
P(event) is written as a simplified fraction, a decimal or a percentage. A ratio such as 1:3 is not a probability.
If events cannot happen together, their probabilities add to 1. Tree branches from one point are mutually exclusive.
Relative frequency is frequency ÷ trials. A larger sample should sit closer to the theoretical value if the trial is fair.
| Misconception | Teaching focus |
|---|---|
| Writing a probability as a ratio, such as 1:3, instead of a fraction. | Convert 1:3 into 1 out of 4 and write 1/4 next to it. Keep the ratio in a separate column labelled odds. |
| Leaving the outside region of a Venn diagram empty when the question includes ‘neither’. | Write the total first and fill the outside after the intersection is placed. |
| Repeating or omitting outcomes when listing permutations. | Use a table or a tree so each choice has its own row or branch. |
| Adding probabilities of independent events instead of multiplying along a tree. | Say ‘and means multiply along the branch’ on the first three products, then ask students to say it. |
| Treating relative frequency after 10 trials as the true probability. | Collect a class set of 10-trial results and show how they sit around the theoretical value. |
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Students learn how to arrange the likelihood of events along a probability scale.
Later, as learning progresses they use the probability scale to compare the likelihood of events happening.
Students learn how to write a theoretical probability as a simplified fraction.
As learning progresses, they are challenged to find the sample sizes when given the probability.
Students learn to draw sample space diagrams for two or more events.
Later, students use the sample space diagrams to work out probabilities as learning progresses.
Students learn how to work out the probability of mutually exclusive events.
As learning progresses probabilities are given in the form of fractions, decimals and percentages in probability tables.
Mutually Exclusive Outcomes and Events
Students learn how to calculate an expected frequency from a probability experiment, using relative frequency to estimate outcomes in real-world contexts.
Later, as learning progresses, they consider the probabilities of mutually exclusive events, comparing experimental and theoretical probability.
Students learn how to apply relative frequency to estimate outcomes in practical contexts. They work with probabilities from experiments, using them to make predictions about future events such as marbles drawn, raffle tickets, or defective products.
Later, as learning progresses, students tackle more complex problems involving profit, expected values, and comparing experimental results to theoretical models.
Students conduct a probability experiment to explore the relationship between theoretical and experimental probability.
Throughout the course of the lesson, students are challenged to assign a set of events given fixed probabilities, design an experiment to test their accuracy and discuss their findings using bias.
Students learn how to draw probability trees for independent events.
Later, as learning progresses, they use probability trees to determine the likelihood of different events.
Students learn how to calculate the union and intersection of sets using Venn diagrams.
As learning progresses, students are challenged to use the union and intersection to calculate a probability.
Students gain additional practice working out the probability of mutually exclusive events.
The problem-solving activity challenges students to combine mutually exclusive events with sharing to a ratio.
Mutually Exclusive Outcomes and Events
How to Draw a Venn Diagram to Calculate Probabilities
Students gain additional practice organising data within Venn Diagrams.
The problem-solving activity challenges students to create a Venn Diagram from a real-life problem and work out a probability.
How to Draw a Venn Diagram to Calculate Probabilities
Two-Way Tables and Frequency Trees
Students gain additional practice using writing a probability as a simplified fraction.
The problem-solving activity challenges determine the sample size when given a probability.
Students gain additional practice using probability trees to find the likelihood of independent events.
The problem-solving activity challenges students to link probability trees to setting up and solving linear equations.
Students systematically list all possible outcomes for two or more events, starting with coin flips and moving to draws with replacement. They construct sample spaces for spinner combinations and calculate theoretical probabilities.
Later, learners model expected winnings from a fayre game. By calculating long-term profit over multiple plays, students connect permutation listing to decision-making.
Students are challenged to solve a range of basic probability problems.
There are seven real-life problem-solving questions based on
Students revise how to calculate the probability of two or more independent events.
Later, learning progresses from using two-way tables and sample space diagrams to using probability trees.
Students revise how to organise events and probabilities into a Venn diagram.
Later, as learning progresses, they use set notation to solve probability problems.
Mutually Exclusive Outcomes and Events
How to Draw a Venn Diagram to Calculate Probabilities
Students revise how to write the theoretical probability of an event using fractions.
As learning progresses, they link probability to frequency trees and two-way tables.
Students revise how to calculate the probability of an event not happening using mutual exclusivity.
Later, as learning progresses, they use probabilities to calculate the expected frequency of an event occurring.
Mutually Exclusive Outcomes and Events
How to Draw a Venn Diagram to Calculate Probabilities
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