IGCSE›Cambridge IGCSE Maths›Mind mapsProbability Diagrams (Tree & Venn Diagrams)Cambridge IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsSample spaceA grid lists every outcome of a combined eventTwo dice give 36 equally likely outcomesP(total=7)=636=16P(\text{total}=7)=\frac{6}{36}=\frac{1}{6}P(total=7)=366=61Tree diagramsOutcome at the end of each branchProbability written on the branch itselfBranches from one point sum to 1Using treesMultiply along the branchesAdd across different pathsWith replacement: probabilities stay the sameWithout replacement: later branches changeProbabilitytree and Venn diagramsP(A)P(A)P(A)∩\cap∩∪\cup∪Venn diagramsCircles sit inside the universal set E\mathcal{E}EP(region)=n(region)n(E)P(\text{region})=\frac{n(\text{region})}{n(\mathcal{E})}P(region)=n(E)n(region)Core: two sets; Extended: up to threeA∩BA \cap BA∩B is both; A∪BA \cup BA∪B is either or bothFrequencyRelative frequency = successes ÷ total trialsMore trials give a more reliable estimateExpected frequency = probability × trials0.2×500=1000.2 \times 500 = 1000.2×500=100Exam tipsState multiply along, add across for method marksCheck second-branch probabilities still add to 1Check Venn regions add up to n(E)n(\mathcal{E})n(E)