Science collection

Lottery probability

Count outcomes, distinguish exact events and understand what probability calculations do—and do not—say.

Start with Lottery Probability Explained: Count the Outcomes First, then follow the questions below. Each guide includes a worked explanation, a figure and routes to an experiment or calculator.

Lottery probability

A complete starting point for lottery odds: sample spaces, combinations, separate pools, exact matches and the limits of simulation.

Lottery probability

Distinguish unordered lottery sets from ordered digit games, with replacement rules and examples that prevent common counting errors.

Lottery probability

Compare distinct lines in one draw, duplicate lines and repeated independent draws without confusing relative improvement with a likely win.

Lottery probability

Separate special-ball pools and bonus balls drawn from the main pool need different formulas. Learn the distinction with worked examples.

Lottery probability

Derive the lottery combination formula, work through C(49,6), and learn when separate pools or ordered digits require a different count.

Lottery probability

Derive the hypergeometric formula for exactly r matches and distinguish exact, at-least and separate-pool matching events.

Lottery probability

Convert probabilities, percentages and odds against correctly, and learn why one-in-X is not a deadline for a rare event.

Lottery probability

Distinguish repeated labels, repeated full lines and repeated entries across draws, and calculate how duplicates reduce distinct outcome coverage.

Lottery probability

Understand how replacing a drawn item changes independence, duplicate possibilities and the formulas used for lottery and digit games.