GCSE›Edexcel GCSE Maths›Mind mapsCombined Events and Conditional ProbabilityEdexcel GCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsEvent typesMutually exclusive: cannot both happenIndependent: one does not affect the otherIndependent events can happen togetherP(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)P(A and B)=P(A)×P(B) if independentAddition ruleP(A or B)=P(A)+P(B)−P(A and B)P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)P(A or B)=P(A)+P(B)−P(A and B)Subtract the overlap counted twiceMutually exclusive: overlap is zeroConditionalP(B∣A)P(B|A)P(B∣A) = B given A has happenedP(B∣A)=P(A and B)P(A)P(B|A) = \frac{P(A \text{ and } B)}{P(A)}P(B∣A)=P(A)P(A and B)P(A and B)=P(A)×P(B∣A)P(A \text{ and } B) = P(A) \times P(B|A)P(A and B)=P(A)×P(B∣A)Without replacement → dependent events4 red, 3 blue: P(blue | red first) =36= \frac{3}{6}=63Combined eventsand conditional probability∪∩A'Tree diagramsBranches at each point sum to 1Multiply along a pathAdd paths for a combined eventDependent: second branches changeVenn diagramsA∪BA \cup BA∪B = union, A∩BA \cap BA∩B = intersectionA′A'A′ = complement, ξ\xiξ = universal setFill the intersection firstRegions must sum to the totalExam tipsDon't confuse independent with mutually exclusiveUpdate both numerator and denominatorList outcomes systematically(1,2) and (2,1) are different outcomes