🕹️ Practice arcade

⚡ Counting Toolkit Sprint

Ninety seconds of product-rule, sum-rule, permutation, and combination counts — as many as you can.

⚡ Advanced Counting Sprint

Circular permutations, multinomial splits, stars and bars, restrictions, and complements — pick up the pace.

⚡ Readiness Calculus Review Sprint

Geometric series, definite/improper integrals, and limits at infinity — the calculus this course leans on, drilled fast.

🔀 Conditional, Bayes & Expected Value Sprint

Conditional probability from a joint/marginal, Bayes' posterior, and E(X) from a table -- two minutes, mixed.

📊 Named Distributions PMF Sprint

Compute a single pmf value -- binomial, geometric, hypergeometric, or Poisson -- as many as you can in two minutes.

📐 Scaling & Estimation Sprint

Var(aX+b), E(aX+b), z-scores, and standard error -- plug into the rule, fast.

🎲 Pascal's Rule & Combinations Sprint

Apply Pascal's identity to a binomial coefficient, or count an unordered selection directly.

🎯 Definite Integral Properties

Reversing the bounds negates the whole answer — four in a row.

📉 Limits at Infinity Mastery

Same degree top and bottom — read the horizontal asymptote from the leading coefficients.

∫ Integral Additivity Mastery

Split and rejoin integrals over adjacent intervals — four in a row.

🎯 Probability Axioms Mastery

Complete a probability assignment correctly five times in a row.

🎯 Geometric Series Check

A geometric distribution's own validity leans on this convergence test — get it right four times in a row.

🎯 Multiset Arrangements Mastery

Count arrangements of a multiset (repeated letters and all) correctly four times in a row.