Combined Events and Probability Diagrams
Model combined events with sample spaces, tables, trees and Venn diagrams.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Sample spaces and frequency trees
Exam cue: Make outcomes exhaustive, multiply along a route, add disjoint routes and update probabilities when sampling changes the composition.
Concept 2
Tree diagrams
Exam cue: Check branch totals, overall probability totals and event overlap against the wording.
Concept 3
Venn diagrams and set notation
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Both tiers use tables, trees and Venn diagrams. Higher uses more complex dependent events, algebraic probabilities and formal set reasoning.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Adding probabilities along a tree route instead of multiplying them.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Tree route
Multiply probabilities along branches.
Alternative disjoint routes
Add their route probabilities.
Union A ∪ B
Outcomes in A or B, including the overlap.
Combined Events and Probability Diagrams: method
Make outcomes exhaustive, multiply along a route, add disjoint routes and update probabilities when sampling changes the composition.
Combined Events and Probability Diagrams: check
Check branch totals, overall probability totals and event overlap against the wording.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO2 reasoning · Either paper — Two fair six-sided dice are rolled. Find P(the total is 7).
Foundation · AO1 technique · Non-calculator — A coin and a fair six-sided die are used together. How many ordered outcomes are in the sample space?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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