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Recursive probability — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Recursive probability — 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

2022 AMC 8 Problem 25

AMC 10

2014 AMC 10B Problem 25 • 2017 AMC 10A Problem 18 • 2019 AMC 10B Problem 22 • 2025 AMC 10B Problem 24

AMC 12

2014 AMC 12B Problem 22 • 2015 AMC 12B Problem 9 • 2017 AMC 12A Problem 22 • 2019 AMC 12B Problem 16 • 2019 AMC 12B Problem 19 • 2021 AMC 12A Spring Problem 23 • 2021 AMC 12B Fall Problem 17 • 2023 AMC 12A Problem 17 • 2025 AMC 12B Problem 20

AIME

1993 AIME Problem 11 • 1994 AIME Problem 9 • 1995 AIME Problem 15 • 2003 AIME II Problem 13 • 2018 AIME II Problem 13 • 2019 AIME II Problem 2 • 2021 AIME I Problem 12 • 2023 AIME I Problem 6

More probability and statistics concepts

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