What this topic covers
Probability has 4 subtopics:
- Probability Foundations
- Sample Spaces and Systematic Enumeration
- Combined Events and Tree Diagrams
- Conditional Probability
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GCSE AQA Higher Maths · Topic 5 of 6
Probability – GCSE AQA Higher Maths revision notes
Choose a subtopic. Probability covers Probability Foundations, Sample Spaces and Systematic Enumeration, Combined Events and Tree Diagrams, and Conditional Probability in GCSE AQA Higher Maths. 12 lessons in 4 subtopics.
Revise Probability for GCSE AQA Higher Maths, including Probability Foundations and Sample Spaces and Systematic Enumeration. 12 lessons across 4 subtopics.
12
Lessons
4
Subtopics
Probability lessons by subtopic
12 lessons, grouped by subtopic.
Probability Foundations
- Recording and Analysing Probability Experiments: Learn to record, describe and analyse the frequency of outcomes from probability experiments using tables and frequency trees. Practice organizing data from simple probability experiments and interpreting results.
- Expected Outcomes in Probability Experiments: Learn to apply concepts of randomness, fairness and equally likely events to predict and calculate expected outcomes when probability experiments are repeated multiple times. Work with theoretical probability to make predictions about future experimental results.
- Relative Frequency and Theoretical Probability: Understand how relative expected frequencies relate to theoretical probability, using appropriate mathematical language and the 0 to 1 probability scale to compare experimental and theoretical results.
- Exhaustive Sets and Mutually Exclusive Events: Understand and apply the fundamental probability properties: that probabilities of exhaustive sets of outcomes sum to 1, and that probabilities of exhaustive sets of mutually exclusive events sum to 1. Learn to identify these scenarios and use these properties to solve probability problems.
- Experimental Probability, Relative Frequency and Sample Size: Compare experimental probability with theoretical probability, interpret relative frequency, and explain how sample size affects the reliability of probability estimates.
- Probability Scale, Equally Likely Outcomes and Expected Frequency: Build probability foundations by using the 0 to 1 scale, equally likely outcomes, the total-probability rule, and expected frequency in simple contexts.
Sample Spaces and Systematic Enumeration
- Systematic Enumeration Using Tables, Grids and Venn Diagrams: Learn to systematically list and count sets and combinations using organized methods including tables, grids, and Venn diagrams to ensure all possibilities are covered without repetition.
- Constructing Possibility Spaces and Calculating Theoretical Probabilities: Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes; Calculate theoretical probabilities using possibility spaces; Identify all possible outcomes systematically using tables and lists
Combined Events and Tree Diagrams
- Calculating Probabilities from Tree Diagrams: Use tree diagrams to represent combined events, label branch probabilities clearly, and calculate probabilities by following and combining branches correctly.
- Tree Diagrams for Combined Events: Construct and interpret tree diagrams for combined events, follow branches correctly, and decide when events are dependent or independent.
Conditional Probability
- Conditional Probability from Tables, Tree Diagrams and Venn Diagrams: Learn how conditional probability changes the sample space and calculate it accurately from two-way tables, tree diagrams, and Venn diagrams.
- Interpreting Conditional Probability and Expected Frequencies: Interpret conditional probability in context, use expected frequencies to reason about it, and choose the best representation for harder exam-style problems.
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Frequently asked questions
What is Probability?
Probability covers Probability Foundations, Sample Spaces and Systematic Enumeration, Combined Events and Tree Diagrams, and Conditional Probability in GCSE AQA Higher Maths. 12 lessons in 4 subtopics.
What is a sample space diagram?
A sample space diagram is a two-way grid listing every outcome of two combined events, with one event across the top and the other down the side. The Systematic Enumeration Using Tables, Grids and Venn Diagrams notes cover this in full.
What is the law of large numbers?
At GCSE level, the law of large numbers means that as the number of trials increases, the relative frequency gets closer to the theoretical probability. The Experimental Probability, Relative Frequency and Sample Size notes cover this in full.
What is the probability scale?
Every probability is between 0 and 1: 0 means impossible, 1 means certain and 0.5 means an even chance. The Relative Frequency and Theoretical Probability notes cover this in full.
How do you calculate relative frequency?
Divide the number of times an outcome occurs by the total number of trials. The Recording and Analysing Probability Experiments notes cover this in full.
What is the complement of a set?
The complement A′ is everything in the universal set ξ that is not in A, shown on a Venn diagram as everything outside circle A. The Systematic Enumeration Using Tables, Grids and Venn Diagrams notes cover this in full.
What are exhaustive events?
Exhaustive events are events that between them cover every possible outcome of an experiment, so one of them must happen. The Exhaustive Sets and Mutually Exclusive Events notes cover this in full.
How do you find the probability of two independent events?
For independent events, P(A and B) = P(A) × P(B), because P(B|A) = P(B). The Tree Diagrams for Combined Events notes cover this in full.
What is conditional probability?
Conditional probability, written P(A | B), is the probability of event A occurring given that event B has already occurred. The Conditional Probability from Tables, Tree Diagrams and Venn Diagrams notes cover this in full.