Module 3: Probability Basics
Master the fundamentals of probability! Learn to calculate chances, count outcomes, work with conditional probability, and understand probability distributions.
Prerequisites: Modules 1 & 2
This module builds on concepts from Module 1 (data types, statistical thinking) and Module 2 (measures of center and spread). You should be comfortable with basic fractions, percentages, and simple calculations.
Your Progress
Learning Objectives
By the end of this module, you will be able to:
- Calculate basic probabilities using sample spaces and probability rules
- Apply counting methods (fundamental counting principle, permutations, combinations) to solve problems
- Work with conditional probability and determine if events are independent
- Create and interpret probability distributions for discrete random variables
- Calculate expected value and variance of probability distributions
Why This Matters
Probability is everywhere! From weather forecasts ("70% chance of rain") to medical diagnoses ("85% accuracy"), understanding probability helps you make better decisions under uncertainty.
This module teaches you to:
- Quantify uncertainty with numbers (probabilities)
- Make informed decisions when outcomes aren't certain
- Understand risk and likelihood in everyday situations
- Count possible outcomes systematically (crucial for many fields!)
- Recognize when events are independent vs. related
- Build the foundation for inferential statistics
Get Started: Pre-Assessment
Before You Begin...
Take a quick 5-question pre-assessment to see what you already know about probability. This isn't graded—it's just to measure your starting point.
Why do this? At the end of the module, you'll retake the same assessment and see how much you've learned!
Recommended: Take the pre-assessment! It only takes 5 minutes and helps you track your learning.
Module Lessons
Introduction to Probability
Learn the basics: sample spaces, events, probability notation, and fundamental rules. Discover how to calculate simple probabilities and use the complement rule.
30-35 minutes
Counting Methods
Master the fundamental counting principle, permutations (order matters), and combinations (order doesn't matter). Learn when to use each method.
35-40 minutes
Conditional Probability & Independence
Explore conditional probability P(A|B), learn to use two-way tables, and discover how to test if events are independent. Essential for real-world applications!
30-35 minutes
Probability Distributions
Learn about discrete random variables, create probability distributions, and calculate expected value (mean) and variance. Connect probability to descriptive statistics!
30-35 minutes
After the Lessons
Practice Problems
Apply what you've learned with 20 practice problems covering all module topics. Probability calculations, counting, and distributions!
Practice ProblemsModule Quiz
Test your understanding with a 15-question quiz. Pass with 70% to earn your Module 3 badge!
Take Module QuizStudy Materials
Download printable study guides with all formulas and quick reference cards. Perfect for exam prep!
AI Tutor Help
Stuck on a probability calculation? Need help with counting? Chat with the AI statistics tutor for personalized guidance.
Get AI HelpTips for Success
- Draw diagrams! - Tree diagrams, Venn diagrams, and tables make probability problems much clearer.
- Practice counting - Permutations vs. combinations trips everyone up at first. The key is lots of practice!
- Check if probabilities add to 1 - All probabilities in a distribution must sum to exactly 1.00.
- Watch your fractions - Probability is often expressed as fractions, decimals, or percentages. Know how to convert!
- Think about real scenarios - Probability makes more sense when applied to concrete situations (dice, cards, real-life events).
- Connect to Module 2 - Expected value is like the mean! Variance means the same thing here!