DOI
https://doi.org/10.25772/B592-JM97
Defense Date
2005
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Dr. D'Arcy P. Mays
Abstract
Probability theory is a branch of mathematics concerned with determining the long run frequency or chance that a given event will occur. This chance is determined by dividing the number of selected events by the number of total events possible, assuming these events are equally likely. Probability theory is simply enumerative combinatorial analysis when applied to finite sets. For a given finite sample space, probability questions are usually "just" a lot of counting. The purpose of this thesis is to provide some in depth analysis of several combinatorial methods, including basic principles of counting, permutations and combinations, by specifically exploring one type of probability problem: C ordered possible elements that are equally likely s independent sampled subjects r distinct elements, where r = 1, 2, 3, , min (C, s) we want to know P(s subjects utilize exactly r distinct elements). This thesis gives a detailed step by step analysis on techniques used to ultimately finding a general formula to solve the above problem.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
June 2008