Defining Probabilities Over the Prime Numbers

This paper will detail Fawcett's experience solving a problem he stumbled upon while tutoring math and statistics at Cape Fear Community College in Wilmington, North Carolina. Though at first glance the problem seemed simple, he soon realized that the solution would require knowledge about the Riemann zeta function, which is a common fascination for math enthusiasts like him. To follow the arguments in this paper, all that is necessary is some elementary knowledge about probability and Calculus II.