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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

Source Type
Harvard Stat 110 Reference
MIT 18.600 Probability and Random Variables Reference
Competitive Programmer's Handbook Reference

Practice Sources

Source Type
CSES Dice Probability Practice
CSES Candy Lottery Practice
CSES Moving Robots Practice
CSES Inversion Probability Practice

Repo Companion Material

Material Type
Probability hot sheet quick reference
Dice Probability flagship note
Probability starter route starter route
Randomized Algorithms compare point

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