Probability

Probability describes uncertainty. Learn to calculate chances, interpret experimental results and choose diagrams that make combined events easier to understand.

Follow the lessons in order or revisit a specific method. Lessons 1–5 give the shared Foundation & Higher route, with clearly marked Higher extensions. Lesson 6 develops conditional probability for Higher students.

Dependent trees and suitable without-replacement problems are part of Foundation as well as Higher. Set symbols are explained in words; Edexcel assesses union and intersection notation at both tiers, while OCR does not require those symbols or complement notation at either tier.

Probability and representations

Foundation & Higher

1. Probability Basics and Rules

Use the probability scale, equally likely outcomes, complements and the rules for mutually exclusive events.

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Foundation & Higher

2. Experimental Probability and Expected Frequency

Estimate probabilities from data, interpret frequency trees and predict expected numbers of outcomes.

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Foundation & Higher

3. Sample Spaces and Two-Way Tables

List outcomes systematically and use grids and two-way tables to calculate probabilities.

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Sets and combined events

Foundation & Higher

4. Venn Diagrams and Set Notation

Read and construct Venn diagrams, understand set notation and account for overlapping events.

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Foundation & Higher

5. Tree Diagrams and Combined Events

Combine independent and dependent events, including replacement and without-replacement situations.

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Higher

6. Conditional Probability

Use given information to restrict a sample space and calculate probabilities from tables, Venn diagrams and trees.

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Useful prerequisites

Review Fractions, Decimals & Percentages, Calculating with Fractions and Systematic Listing and Counting when the arithmetic or listing is the difficult part.

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For predictions that scale with the number of trials, revisit Direct Proportion.