Some probabilities on the sum of counting numbers

• Main Authors: Cabugao, Anna Lissa, Marzan, Leonilla
• Format: text
• Language: English
• Published: Animo Repository 1992
• Subjects: Probabilities; Numbers, Theory of; Congruences and residues
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16020
• Institution: De La Salle University

This thesis presents some problems of chance on the sum of counting numbers. It gives the probability that the sum is a perfect square, odd, even, equal to n or equal to n - 1. These probabilities were proven by means of mathematical induction.This study also gives the probability that the sum is relatively prime to n, using the Euler phi-function. The theoretical discussion is based on the article by Robert W. Prielipp entitled The Euler -Function and a Problem of Chance. A table of sums of integers from 1 to n when n = 2 to n = 12 is given. Illustrations and examples are provided. The proofs of lemmas, theorems and corollaries in the preliminary framework and the main body are presented in a very detailed manner.