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Course format
Topic 06 · Probability
Unit 3 · Topic 06 · Probability

Probability

Counting, permutations and combinations, theoretical vs. empirical probability, and expected value — anchored by Major Assignment 3.

Start Lesson 1 Play all 17 videos First time? Tour the week →
ORBITAL · TOPIC 06PROBABILITY17 VIDEOS · 1H 15M0

Lessons

6 lessons · each with a video, a worked example and practice
  1. 3:52 Lesson 1: Simple probability.Probability of any simple event is favorable outcomes over total outcomes. The whole topic builds from this one ratio.
  2. 3:05 Lesson 2: Fundamental counting principle.When a process has multiple independent steps, the total number of outcomes is the product of the number of choices at each step. The single most-used move in the topic.
  3. 3:54 Lesson 3: Sample spaces and the addition rule.P(A or B) = P(A) + P(B) − P(A and B). The standard deck of 52 cards is the canonical playground.
  4. 4:14 Lesson 4: Permutations and combinations.Permutations count ordered arrangements; combinations count unordered selections. The first question to ask: does swapping two picks give a different answer?
  5. 3:46 Lesson 5: Expected value.Expected value is the average outcome per trial if the experiment were repeated indefinitely. The math of fair games, insurance premiums, and casino edges.
  6. 3:40 Lesson 6: Theoretical vs experimental probability.Theoretical probability comes from the math; experimental probability comes from the data. As you run more trials, the two converge. The closing idea of the topic.

Then

the rest of the week
Discussion DQ 1: Discussion Walkthrough, posting rhythm, and what the DQ is really asking. Discussion DQ 2: Discussion Walkthrough, posting rhythm, and what the DQ is really asking. Major assignment Major Assignment 3: Statistical Analysis 2 components — walkthrough for each. 6 questions Review Six worked questions to practice before ALEKS. Self-check Mastery Check 4 quick questions - 2 multiple choice, 2 calculations. Perfect score earns one substantive participation post.
Unit 3 This topic is assessed on Exam 3, together with Topic 5. See what is on it

What you'll learn

180 pts 160 pts in Unit 3 4 objectives

What you'll learn

  1. Compare, compute and interpret theoretical and empirical probabilities.
  2. Develop and use the fundamental counting principle.
  3. Develop a procedure for finding expected value.
  4. Compute and interpret expected values.

Interactive tools

Playground Expected Value Lab Define each outcome of a chance situation — value and probability — and watch E(X) compute live. Try the carnival, lottery, and insurance presets to see why every gambling operation is engineered for a negative expected value to the player. Playground Law of Large Numbers Simulator Pick coin, die, or a custom probability, then run trials in batches of 10, 100, 1,000, or 10,000. Watch the experimental probability bounce around at low n and converge on the theoretical value as n grows — the Law of Large Numbers in real time.

Tools & Resources

Library Topic 6 resource library Curated extras across all 6 lessons. 2 items available so far. Study aid Glossary Every vocab term across the 6 lessons in one study sheet. 31 terms so far. Study aid Cheat sheet Key formulas, common mistakes, and quick-reference factors. Printable for the test.
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