M7: Probability, Conditional Trees and Venn Diagrams
Official Cambridge & Imperial ESAT specification requirements for Probability, Conditional Trees and Venn Diagrams on the Mathematics 1 paper. Understand the syllabus boundaries, spot distractor traps engineered by examiners, and master the 2-step Sub-90 shortcuts that compress solve time well below the 88.8-second cutoff.
Official Syllabus Subtopics
Requirements specified in the UAT-UK framework
- 1Mutually exclusive events: P(A ∪ B) = P(A) + P(B)
- 2Independent events: P(A ∩ B) = P(A) × P(B)
- 3Multi-stage probability tree diagrams without replacement (conditional probability)
- 4Conditional probability formula: P(A | B) = P(A ∩ B) / P(B)
- 5Algebraic Venn diagrams, set notation, and complement rule: P(at least 1) = 1 - P(none)
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
Check whether items are sampled "with replacement" or "without replacement" (denominator decreases by 1).
Use the complement rule P(at least 1) = 1 - P(none) to avoid calculating multiple tree branches.
Examiners engineer distractor options using common algebraic expansions and sign slips. Always test structural ratios or invariants before calculating arithmetic values.
Tested Topics in Specification M7
Master the individual question patterns and Sub-90 shortcuts for this specification.
Multi-Stage Conditional Probability Trees (Without Replacement) & Algebraic Venn Overlaps
For 'at least one', always compute 1 - P(none). For 2-Group overlaps without formal set notation, use Total - Neither = Group1 + Group2 - Both.
Ready to Master Specification M7 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.