MAT-144 · Mathematical Reasoning Topic 06 · Probability
Topic 06 · Welcome

Welcome to Probability.

This week is probability — the math of uncertainty. By Sunday you'll be fluent in the probability ratio (favorable / total), the fundamental counting principle that powers every "how many possible outcomes" question, permutations vs combinations (does order matter?), and the expected value machine that puts a fair price on any game of chance.

Topic 6 is the second half of the data side of the course. Topic 5 was descriptive — how to read a data set you already have. Topic 6 is predictive — what to expect from a process whose outcome isn't decided yet. The Major Assignment 3 anchor stitches these tools together on a real-world probability scenario.

Start Lesson 01 Topic overview

By the end of this week, you'll be able to:

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

Four phases, in order. Don't skip ahead — each one sets up the next.

Phase 01 · Mini lessons
6 lessons
≈ 3 hours total
  • L01 · Simple probability.
  • L02 · Fundamental counting principle.
  • L03 · Sample spaces and the addition rule.
  • L04 · Permutations and combinations.
  • L05 · Expected value.
  • L06 · Theoretical vs experimental probability.
Phase 02 · Discussions
2 DQs
≈ 2 hours total
  • DQ 1 · Autofill a 1,000-row and a 4,000-row simulation column, Compute empirical probability with a locked-denominator formula, Compute theoretical probability for a fair n-sided die, Compare average deviation across two sample sizes (Law of Large Numbers)
  • DQ 2 · Decide permutation vs combination on six game scenarios, Compute sample-space size with =PERMUT and =COMBIN, Compute probability via favorable / total, Convert probability to "1 to X" odds against winning
Phase 03 · Major Assignment
Major Assignment 3: Statistical Analysis
100 pts · ≈ 3 hours
  • Component 1 · Analysis
  • Component 2 · Visualization
Phase 04 · ALEKS Review
6 questions
≈ 2 hours · 35 pts
  • Q1 · Probability involving one die or choosing from n distinct objects
  • Q2 · Counting principle
  • Q3 · Probability of selecting one card from a standard deck
  • Q4 · Permutations and combinations: Problem type 2
  • Q5 · Computing expected value in a game of chance
  • Q6 · Experimental and theoretical probability for compound events

Plan for the whole week. These are typical times, not maximums — go faster if it clicks, slower if you're getting stuck.

Mini lessons (6) ≈ 3 h
Discussions (2 DQs) ≈ 2 h
Major Assignment 3: Statistical Analysis ≈ 3 h
ALEKS review (6 questions) ≈ 2 h
Total ≈ 10 h

You won't get through every lesson on the first try. Here's where to look:

Cheat sheet
Topic 6 cheat sheet →
Key formulas, common mistakes, quick reference. Printable.
Glossary
Topic 6 glossary →
Every vocab term in one study sheet, lesson by lesson.
Interactive tools
Tools & resources →
2 interactive playgrounds for hands-on practice.
Walkthroughs
Each DQ + MA component has a Scribe walkthrough.
Watch once, then build it on your own.

Ready to start?

Start Lesson 01