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Random walk — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Random walk — a probability and statistics concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Filter by difficulty

These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.

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AMC 8

2026 AMC 8 Problem 21

AMC 10

2014 AMC 10B Problem 25 • 2020 AMC 10A Problem 13 • 2021 AMC 10A Spring Problem 23 • 2025 AMC 10B Problem 24

AMC 12

2003 AMC 12A Problem 22 • 2010 AMC 12B Problem 18 • 2014 AMC 12B Problem 22 • 2016 AMC 12A Problem 19 • 2017 AMC 12A Problem 22 • 2020 AMC 12A Problem 11 • 2021 AMC 12A Spring Problem 23 • 2021 AMC 12B Fall Problem 17 • 2025 AMC 12B Problem 20

AIME

1985 AIME Problem 12 • 1995 AIME Problem 3 • 2003 AIME II Problem 13 • 2014 AIME I Problem 11 • 2016 AIME I Problem 13 • 2021 AIME I Problem 12 • 2021 AIME II Problem 8

More probability and statistics concepts

basic probabilityBayes’ Theorembinomial probabilitycomplementary probabilityconditional probabilitydata and graph interpretationdice (probability)expected valuegeometric distributiongeometric probabilityharmonic meanindependent eventsmeanmedian (data)moderangerecursive probabilitysampling with replacementsampling without replacementweighted mean