probability and statistics
Dice (probability) — AMC & AIME Problems
47 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Dice (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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: What Is Probability?, Probability of Compound Event.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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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.
AMC 8
AMC 10
- 2004 AMC 10B Problem 11
- 2005 AMC 10B Problem 9
- 2005 AMC 10B Problem 12
- 2006 AMC 10A Problem 13
- 2006 AMC 10B Problem 21
- 2007 AMC 10B Problem 22
- 2008 AMC 10B Problem 16
- 2008 AMC 10B Problem 20
- 2009 AMC 10A Problem 22
- 2011 AMC 10A Problem 14
- 2012 AMC 10A Problem 9
- 2014 AMC 10A Problem 17
- 2014 AMC 10B Problem 16
- 2018 AMC 10A Problem 11
- 2018 AMC 10B Problem 9
- 2020 AMC 10A Problem 25
- 2021 AMC 10B Spring Problem 18
- 2021 AMC 10A Fall Problem 9
- 2021 AMC 10B Fall Problem 14
- 2021 AMC 10B Fall Problem 20
- 2022 AMC 10B Problem 12
- 2023 AMC 10A Problem 7
AMC 12
- 1974 AMC 12 Problem 24
- 1977 AMC 12 Problem 17
- 1981 AMC 12 Problem 26
- 2002 AMC 12B Problem 16
- 2005 AMC 12A Problem 14
- 2006 AMC 12B Problem 17
- 2011 AMC 12A Problem 10
- 2012 AMC 12B Problem 13
- 2020 AMC 12A Problem 23
- 2021 AMC 12B Spring Problem 19
- 2021 AMC 12B Fall Problem 11
- 2022 AMC 12B Problem 12
- 2023 AMC 12A Problem 5
More probability and statistics concepts
- Basic probability
- Bayes’ Theorem
- Binomial probability
- Complementary probability
- Conditional probability
- Data and graph interpretation
- Expected value
- Geometric distribution
- Geometric probability
- Harmonic mean
- Independent events
- Mean
- Median (data)
- Mode
- Random walk
- Range
- Recursive probability
- Sampling with replacement
- Sampling without replacement
- Weighted mean