Probability

Roll dice, toss coins and draw marbles thousands of times to compare experimental and theoretical probability, then build sample spaces, tree and Venn diagrams, combinations, expected value and Bayes' theorem.

13 interactive Mathematics simulations on probability.

Discrete random variables – expectation as the long-run average Mathematics · Probability Build the probability distribution table of a discrete random variable in a real-world scenario (a dice game with a... Ages 17–18
Markov chains and transition matrices – steady state, and walks with adjacency matrices Mathematics · Probability Build a state diagram (people moving between regions, market share, weather, a course with absorbing states) and its... Ages 17–18
Rolling two dice – sample space and probability Mathematics · Probability The sample space for rolling two dice has 36 equally likely outcomes, arranged in a 6×6 table. Choose an event (sum... Ages 14–15
Permutations, arrangements & combinations – choosing k from n items Mathematics · Probability n items labeled A, B, C… sit in a row; students tap to pick k of them, either ordered or unordered, and compare... Ages 15–16
Combining random variables – sums, differences, aX + b and unbiased estimators Mathematics · Probability Draw thousands of times from two independent distributions (a die, a table of values or a normal model) to build X +... Ages 17–18
Normal distribution – probabilities, z-scores and inverse normal Mathematics · Probability Drag the mean μ and standard deviation σ of X ~ N(μ, σ²), shade P(a < X < b) and read the probability, z-scores,... Ages 17–18
Addition and Multiplication Rules of Probability with Venn and Tree Diagrams Mathematics · Probability A Venn diagram with areas proportional to probability: drag event B closer to or farther from A to change P(AB), and... Ages 16–17
Dice and coin tosses – experimental probability Mathematics · Probability Roll a die or flip a coin many times; each outcome is tallied in a table and a frequency bar chart updates... Ages 11–12
Spinning wheel and bag of marbles – events and probability Mathematics · Probability A spinning wheel is divided into colored slices of different widths (or a bag holds a matching number of marbles per... Ages 12–13
Classical probability: sample space and events Mathematics · Probability List out the entire sample space Ω when tossing 2–3 coins or rolling 1–2 dice (shown as a 6 × 6 grid with dice faces... Ages 15–16
Conditional probability and Bayes' theorem: disease testing Mathematics · Probability A medical-testing problem: disease prevalence, sensitivity P(+|disease), and specificity P(−|healthy) are given. A... Ages 17–18
Galton board – Plinko probability Mathematics · Probability Drop balls through a triangular board of pegs: each time a ball hits a peg it bounces right with probability p, and... Ages 13–14
Experimental probability from repeated marble draws Mathematics · Probability A bag holds red, blue, and yellow marbles; draw one at random, record its color, put it back, and repeat N times.... Ages 13–14