Inclusion and Exclusion probability

William W.S. Chen

William W.S. Chen The George Washington University Washington D.C. 20013, USA

Keywords: Begins with a vowel, Consecutive appearance, Ends with a vowel, Inclusion and exclusion probability, Kolomogorov axioms. Poincare Formula, Probability space, Randomly selected 5-letter word

Abstract

We use mathematical induction method to prove the Poincare Formula. To demonstrate the usefulness of this formula, we provide five examples. This formula is related to a broad class of counting problems in which several interacting properties either all must hold, or none must hold. When there are only two or three events that need to be counted, we usually use a Venn diagram. In section 4, we present a general mathematical formula to count any finite number of inclusion and exclusion events. This leads to an easy way to apply the Poincare Formula to define the probability.

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Author Biography

William W.S. Chen, The George Washington University Washington D.C. 20013, USA

Department of Statistics

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