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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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Should you Be Happy?

Should you Be Happy?

(p.3) 1 Should you Be Happy?
The Mathematics of Various Entertaining Subjects

Peter Winkler

Princeton University Press

This chapter discusses a method of computing probabilities called “coupling.” The idea of coupling is that, when comparing probabilities of two events A and B, one tries to put them into the same experiment. All one would need to do is compare Pr(A but not B) with Pr(B but not A). This might be quite easy, especially if most of the time either both A and B occur or neither. The chapter illustrates this method through a Venn diagram showcasing the desired situation. In addition, this chapter applies this method through a series of problems: an argument involving chess games, the probability of a baseball team winning games, and finally, an application to squash strategy.

Keywords:   coupling, probability, baseball, squash, chess

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