GCSE›AQA GCSE Maths›Mind mapsCombined Events and Conditional ProbabilityAQA GCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsIndependent, dependentIndependent: one outcome does not affect the otherDependent: first outcome changes the secondWithout replacement makes events dependentWith replacement keeps probabilities the sameMultiplication ruleP(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)Independent events onlyCoin and dice: 12×16=\frac{1}{2} \times \frac{1}{6} =21×61= 112\frac{1}{12}121Tree diagramsMultiply along a pathAdd paths that give the same outcomeBranches from one point sum to 1Dependent: update later branchesCombined eventsand conditionalP(A∣B)P(A|B)P(A∣B)ConditionalP(A∣B)P(A|B)P(A∣B): A given B has happenedVenn or table: in bothtotal in B\frac{\text{in both}}{\text{total in B}}total in Bin bothCondition row or column is the new total40 of 80 study English also maths → 12\frac{1}{2}21Addition lawP(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 to avoid double-countingMutually exclusive: overlap is 00.3+0.2−0.05=0.3 + 0.2 - 0.05 =0.3+0.2−0.05= 0.45Exam tipsWrite the rule out in your workingCheck branches sum to 1Use the condition's total as the denominatorAsk: does the first outcome change the total?