How I “Hated” It, and How I Ended Up TA-ing for Two Years.

Probability (420)

Table of Contents

• Introduction
• The DOing Matters
• TA Life
• Problem One
• Problem Two

Introduction

Another core AMS course, and one I dreaded. I went in knowing I was “bad” at it—AMC 8/10/12 had already scarred me, because not once did I solve those dreaded combinatorics problems. But I also knew probability was one of those classes—freaking important, unavoidable, foundational. So, there I was: struggling through discrete random variables, then continuous ones. I met a zoo of distributions, tried to play with them, sometimes got along, sometimes didn’t.

The DOing Matters

Here’s what I discovered: when you don’t understand something, sometimes you just need to see enough of it. Do the problems. Do more problems. People say, “There’s only so much they can ask; if you’ve seen them all, you’re good.” I don’t quite buy that. For me, the more I practiced, the more each little misunderstanding chipped away. Confusion dissolved problem by problem. Eventually, I was nailing it—my course average was something like 98%—but I had also poured in exponentially more time than any sane person should.

TA Life

Now, two years of TA-ing later, I’m still fascinated by how probability works its way into everything. There are a few classic problems I always go over with students in recitation, and each time, I catch myself re-falling in love with the logic.

Problem One

Placeholder for problem statement / slide / equation: My thought process:

1. First thought: won’t that be the same?
2. Second thought: hmm, intuition—shouldn’t one be bigger?
3. Third thought: okay, symbols down, write the equation, solve.
4. Last thought: can I solve this another way? (conditional probability!)

Problem Two

Placeholder for problem statement / equation: \(\text{Infinite Geometric Sequence…??}\) My thought process:

1. First thought: infinite geometric sequence… that’s going to be a lot to calculate.
2. Second thought: wait—check intuition again.
3. Last thought: do it the easy way first, then circle back to the hard way if time allows. Beyond the Class This course flipped my perspective. From something I thought I’d always “hate,” probability became something I teach, explain, and keep learning from. I still wouldn’t say I’m a natural at combinatorics (AMC me would like to testify), but now I see probability less as a wall to climb and more as a toolkit I get to wield.