Math -> Probability
Finite-state probability modeling with PMFs, expectation, total probability, and exact discrete-process DP.
- Topic slug:
math/probability
- Tutorial page: Open tutorial
- Ladder page: Open ladder
- Repo problems currently tagged here:
1
- Repo companion pages:
4
- Curated external problems:
4
Microtopics
- probability-dp
- pmf
- expected-value
- linearity-of-expectation
- total-probability
- finite-state-process
Learning Sources
Practice Sources
Repo Companion Material
Curated External Problems
Core
| Problem |
Source |
Difficulty |
Context |
Style |
Prerequisites |
Tags |
Why it fits |
| Dice Probability |
CSES |
Medium |
Distributions |
Math; Dynamic Programming |
Basic Probability; State DP |
Probability-DP; Pmf; Dice |
The cleanest first benchmark where an exact probability answer comes from propagating a bounded sum distribution over repeated random steps. |
Stretch
| Problem |
Source |
Difficulty |
Context |
Style |
Prerequisites |
Tags |
Why it fits |
| Moving Robots |
CSES |
Hard |
Random Walks |
Math; State Transitions |
Probability DP; Independent Events |
Transition-Probability; Independence; Expectation |
A natural next step where one finite-state transition distribution is combined across many independent walkers. |
Challenge
| Problem |
Source |
Difficulty |
Context |
Style |
Prerequisites |
Tags |
Why it fits |
| Inversion Probability |
CSES |
Hard |
Expected Value |
Math; Counting |
Counting Basics |
Linearity-Of-Expectation; Pairs; Expectation |
A harder compare point where linearity of expectation beats any attempt to model the full joint distribution directly. |
Bridge
| Problem |
Source |
Difficulty |
Context |
Style |
Prerequisites |
Tags |
Why it fits |
| Candy Lottery |
CSES |
Medium |
Expected Value |
Math; Observation |
Basic Probability |
Distribution-Of-Maximum; Independence |
A strong compare point where the shortest solution derives a distribution first and only then takes expectation. |
Repo Problems
| Code |
Title |
Fit |
Difficulty |
Pattern |
Note |
Solution |
DICEPROBABILITY |
Dice Probability |
primary |
medium |
- |
Note |
Code |
Regeneration
python3 scripts/generate_problem_catalog.py