Probability and Combinatorics: Analyzing Events and Card Draw Scenarios

Covers probability and combinatorics.

Daniel Mitchell

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ProbabilityandCombinatorics:AnalyzingEventsandCardDrawScenarios1.IfAandBindependenteventsandifP(A)=.45,P(B)=.5andP(AB)=.7,determineP(B|4).AstheeventsareindependentsoP(B|A)=P(B)=0.5Answer:0.52.Anurncontains8white,5redand3bluechips.Apersonselects4chipswithoutreplacement.Determinethefollowingprobabilities:(Leaveanswersinfractionformanddonotmultiplyoutanyfractions.)a)P(Exactly2chipsarewhite)P(Exactly2chipsarewhite)=P(2arewhiteand2arenonwhite)=(8*T*8*7)/(16*15%14*13)=14/195Answer:T4195b)P(Thethirdchipisred)P(Thethirdchipisred)=P(1*isred,2°isred,3"isnon-red)+P(1*isnon-red,2"isred,3"isnon-red)+P(1*isred,2°isnon-red,3isnon-red)+P(1*isnon-red,2*isnon-red,3"isnon-red)=(S*4*11*13)/(16%15%14%13)+(11*5*10%13)/(16%15%14%[3)+(S*11*10%13)/(16%15%14%13)+(11%10%9%13)/(16*15%14*13)—Study

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