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From Logic Puzzles to Lottery Odds

These calculators cover foundational probability rules, Bayes updates, and the combinatorial counting techniques used in contests, quality assurance, and applied research. Pair them with the Probability & Combinatorics – Research Notes to keep formulas, edge cases, and teaching scripts aligned.

Probability Fundamentals

Events & Updates

Basic Probability Calculator

Complements, unions, independent checks, and quick Venn diagrams for two events.

Probability & Counting Toolkit

Step-by-step workflows for complements, unions, and scenario-based probability questions.

Probability Experiment Simulators

Monte Carlo simulations for coins, dice, birthday paradox, Monty Hall, and custom experiments.

Bayes & Diagnostic Testing

Conditional Thinking

Bayes' Theorem & Diagnostic Tests

Prevalence-driven posterior probabilities, natural frequency reports, and what-if scenarios.

Likelihood Ratio Explorer

Switch between sensitivity/specificity or likelihood ratios to show Bayesian updating paths.

Combinatorics & Counting

Arrangements & Selection

Permutations & Arrangements

Linear, circular, repeated, and restricted permutations with inclusion–exclusion templates.

Combinations & Lottery Odds

Binomial coefficients, stars-and-bars distributions, and hypergeometric lottery probabilities.

Counting Principles & Inclusion–Exclusion

Product rule planners plus inclusion–exclusion tables for overlapping set problems.