TL,DR: I am looking for an introductory text in probabilistic methods that are suitable for an undergraduate student who has not taken Analysis/Algebra level classes. Below is the detail.
I am a math PhD student and am mentoring an undergraduate student in a directed reading program. The topic is probabilistic methods and heuristics, but it can be flexible as long it incorporates usage of probabilistic methods.
But so far I am having a hard time finding an appropriate reference/ text for my student on the said topic. The amount of reading they are expected to is 4 hours per week and a 10 minute presentation at the end of semester. There is no required writing, problem sets etc. In other words, this project should be less of a priority than the student's actual classes and only serve to introduce them to the glimpse of a topic in pure math.
I have looked at $\textit{Introduction to Analytic and Probabilistic Number Theory}$ from Tenenbaum and $\textit{The Probabilistic Method}$ by Noga Alon. However, both of them are much more rigorous than the level we are aiming for.
As of right now, I am leaning more towards working on random graphs and Ramsey theory, but I still think it would be a lot to digest for the student.
I would appreciate any reference/guide!
I am a high school student and the two following texts have introduced me to the probabilistic method:
One is from a graduate course in combinatorics (lecture 11-13). It introduces probability basics and problems that can be solved using probabilistic method without using techniques such as deletion method or The Lovász Local Lemma.
Second one is the article by Evan Chen for purpose of high school math olympiad. It doesn't focus much on the knowledge part (which can be compensated by reading the first source) but rather applications, where deletion method, The Lovász Local Lemma are introduced.