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Unformatted text preview: 251ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiICS141: Discrete Mathematics for Computer Science IDepartment of Information and Computer SciencesUniversity of HawaiiStephen Y. Itoga252ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiLecture 25Chapter 6. Discrete Probability6.1 An Introduction to Discrete Probability6.2 Probability Theory 253ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiSome material in these slides were taken/adapted from the slides made by Prof. Michael P. Frank and Prof. Jonathan L. Gross which are provided through the publisher of Discrete Mathematics and Its Applications written by Kenneth H. Rosen.Some slides were done by Prof. Baek254ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiChapter 6:Discrete Probability255ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiWhy Probability?In the real world, we often dont know whether a given proposition is true or false.Probability theory gives us a way to reason about propositions whose truth is uncertain.It is useful in weighing evidence, diagnosing problems, and analyzing situations whose exact details are unknown.256ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiExperiments & Sample SpacesA (stochastic) experimentis any process that yields one of a given set of possible outcomes and the outcome is not necessarily known in advance.The sample spaceSof the experiment is justthe set of all possible outcomes.The outcomeof an experiment is the specific point in a sample space.257ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiEventsAn eventEis any set of possible outcomes in S.That is, ES.E.g., the event that less than 10 people show up for our next class is represented as the set {0, 1, 2, , 9}of values of # of people here next class.We say that event Eoccurswhen the actual outcome ois in E, which may be written oE.Note that oEdenotes the proposition (of uncertain truth) asserting that the actual outcome will be one of the outcomes in the set E.258ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiUniform Probability MeasureIf Sis a finite sample space of equally likelyoutcomes, and Eis an event, that is, a subset of S, then the probabilityof Eis p(E) = E / SExample: Coin tossSample space: S= {H, T}EventsE= , then p(E) = 0E= {H}, then p(E) = 1/2E= {T}, then p(E) = 1/2E= {H, T}, then p(E) = 1259ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiExample: BallsandUrnSuppose an urn contains 4 blue balls and 5 red balls....
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This note was uploaded on 09/12/2008 for the course ICS 141 taught by Professor Idk during the Fall '08 term at Hawaii.
 Fall '08
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