Mostly standard tools from an intro probability course:
- conditioning on first event
- simple recurrence relations
- linearity of expectation
- indicator variables
- total probability and Bayes’ rule
- small Markov chains (finite state, no measure theory)
- basic counting with complements
Nothing here uses advanced machinery (no measure theory, no martingales, no generating functions). Curated subset; I solved more than I wrote up because writing clean derivations takes longer than computing the answers.
- not research
- not contest-level problem solving
- not an attempt at general n asymptotics
- not a tutorial or teaching resource
- not automated or AI-generated notes
It’s just a record of me learning the subject in a structured way.
Because when the algebra is straightforward, the only real failure mode is being wrong with confidence. A 20-line Monte Carlo script is a cheap way to avoid that. It also matches how people working with stochastic systems often sanity-check ideas before chasing a closed form.
- Python 3.10+
- No dependencies outside the standard library
- Tested on macOS
MIT — use/modify without asking.