Probability
Basic and experimental probability, independent/dependent events, and counting (permutations, combinations).
This page is a free outline of what the Probability lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- "And" vs. "Or" Probability “And” means both events happen, so you multiply their probabilities; “or” means at least one happens, so you add them (subtracting any overlap).
- Complementary Events An event’s complement is everything that isn’t it, and the two add to 1 — so P(not A) = 1 − P(A). If rain is 30% likely, no rain is 70%.
- Counting – Combinations A combination counts selections where order doesn’t matter — like choosing a 3-person committee — using nCr = n! ÷ [r!(n − r)!].
- Counting – Factorials A factorial (written n!) multiplies every whole number from n down to 1 — so 4! = 4 × 3 × 2 × 1 = 24. It counts the ways to arrange n items in order.
- Counting – Fundamental Counting Principle The fundamental counting principle says if one choice has m options and the next has n, the total number of combined outcomes is m × n.
- Counting – Permutations A permutation counts arrangements where order matters — like awarding 1st, 2nd, and 3rd place — using nPr = n! ÷ (n − r)!.
- Dependent Events Two events are dependent when the first changes the odds of the second — like drawing two cards without replacing the first — so you adjust the second probability before multiplying.
- Independent Events Two events are independent when one doesn’t affect the other, like two coin flips. Find the chance of both with P(A) × P(B).
- Probability Scale (0 to 1) Every probability falls between 0 and 1: 0 means impossible, 1 means certain, and 0.5 is an even chance. It can be written as a fraction, decimal, or percent.
- Probability – Basic/Theoretical
- Probability – Experimental Experimental probability comes from actual trials — what really happened — like 22 heads in 40 flips giving 22/40. The more trials, the closer it gets to the theoretical value.
Linked concepts (purple →) have a full explanation. Hover or tap a dotted ⓘ concept for a quick definition.
Inside the app, Probability comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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