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Unformatted text preview: 11COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 5.2, pp. 224233InclusionExclusionVersion 2.0: Last updated, May 13th, 2007Slidesc2005 by M. J. Golin and G. Trippen21Unions and Intersections•The Probability of a Union of Events•The Principle of Inclusion and Exclusionfor Counting•The Principle of Inclusion and Exclusionfor Probability31The Probability of a Union of EventsInP(E) +P(F), weights of elements ofE∩Feach appeartwice, while weights of all other elements ofE∪Feach appear exactlyonce.Venn Diagram32The Probability of a Union of EventsInP(E) +P(F), weights of elements ofE∩Feach appeartwice, while weights of all other elements ofE∪Feach appear exactlyonce.Venn Diagram33The Probability of a Union of EventsInP(E) +P(F), weights of elements ofE∩Feach appeartwice, while weights of all other elements ofE∪Feach appear exactlyonce.Venn DiagramSample Space34The Probability of a Union of EventsInP(E) +P(F), weights of elements ofE∩Feach appeartwice, while weights of all other elements ofE∪Feach appear exactlyonce.Venn DiagramSample SpaceEvents41John Vennb. 1834, d. 1923British Mathematician who continuedthe work of Boole. Although he wasnot the first person to use diagramsin formal logic, he seems to have beenthe first to formalize their usage andgeneralize them.For more, see the survey of Venn diagrams athttp://www.combinatorics.org/Surveys/ds5/VennJohnEJC.html5112152P(E)+P(F)counts probability weights ofeach element ofE∩Ftwice.12153P(E)+P(F)counts probability weights ofeach element ofE∩Ftwice.121Thus, to get a sum that includes probability weight of eachelement ofE∪Fexactlyonce, we mustsubtractweight ofE∩FfromP(E) +P(F).54P(E)+P(F)counts probability weights ofeach element ofE∩Ftwice.121Thus, to get a sum that includes probability weight of eachelement ofE∪Fexactlyonce, we mustsubtractweight ofE∩FfromP(E) +P(F).P(E∪F) =P(E) +P(F)P(E∩F)(*)61If you roll two dice, what is the probability of eitheran even sum or a sum of8or more (or both)?62If you roll two dice, what is the probability of eitheran even sum or a sum of8or more (or both)?EventE: Sum is evenEventF: Sum is8or more63If you roll two dice, what is the probability of eitheran even sum or a sum of8or more (or both)?EventE: Sum is evenEventF: Sum is8or moreP(E) =1264If you roll two dice, what is the probability of eitheran even sum or a sum of8or more (or both)?P(F) =536+436+336+236+136=1536EventE: Sum is evenEventF: Sum is8or moreP(E) =1265If you roll two dice, what is the probability of eitheran even sum or a sum of8or more (or both)?P(F) =536+436+336+236+136=1536EventE: Sum is evenEventF: Sum is8or moreP(E) =12P(8)P(9)P(10)P(11)P(12)66If you roll two dice, what is the probability of eitheran even sum or a sum of8or more (or both)?...
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This note was uploaded on 08/25/2010 for the course COMP COMP170 taught by Professor M.j.golin during the Spring '10 term at HKUST.
 Spring '10
 M.J.Golin
 Computer Science

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