Mathematics
Probability & Statistics
SimulationWhat a Positive Test Really Means
Test 1,000 people in a 3D town square for a made-up infectious disease, gather only the positives on a stage and reveal their actual status to see the conditional probability P(disease | positive) as counts of people, a 2×2 table and a formula. Change prevalence, sensitivity and specificity, test again, and use the multiplication rule to see why even an accurate test can give more false positives than true positives.
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SimulationGalton Board
Drop steel balls through a 3D Galton board where each peg sends a ball right with probability p, and follow the thread from counting paths (Pascal's triangle, the binomial theorem) to the binomial distribution B(n, p) and the normal curve. Predict the shape 1,000 balls make, then check it.
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