Is this probability theorem correct? Let me preface my question by saying that I am not a formally trained mathematician, so please forgive my informal statement of my problem.
I have the following 'theorem' of an idea that I believe to be pretty evident in probability.

Given an event E
Given the Set of all real positive integers R and
Given the set of all possible outcomes of a random Event N
Given the number of favorable outcomes n where E occurs.
p(E) = n/N
for 0 < p(E) <= 1
the probability that E will occur in R trials is 1.

I have three questions:


*

*Is there something logically incorrect about my theorem?

*Is this a well known theorem, and if so what is it called?

*How can I write this theorem, more succinctly using symbolic or mathematical notation?



This is called the Infinite monkey theorem. The statement is that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. One sometimes states the theorem with an infinite amount of monkeys but this is a mistake since one monkey (living forever) is enough. What is infinite in the theorem is the amount of time during which the keys are hit at random.
