Chapter 13
Probability and Statistics
Nearly every problem in this course has had one exact answer. A weather forecast, a medical test result, the next house sold on your street: none of those is certain, yet people make serious decisions about them without guessing. Uncertainty turns out to be measurable. This chapter counts how many outcomes are possible, turns those counts into chances, builds honest summaries of real data, and closes with one curve that keeps reappearing wherever many independent small effects add up, without hiding a data set's shape or its outliers. How can mathematics be exact about something nobody can predict?
What You'll Explore
4 lessons.
Some lessons are marked Advanced because they go beyond core Algebra II. Skip them or explore them if you are curious.
- Counting Principles, Permutations, and Combinations
A race with ten runners can finish in more different orders than anyone would want to list by hand. Ask instead which three reached the podium, and the count changes completely. This lesson is about counting possibilities without writing them out, and about what happens when the order stops mattering.
- Introduction to Probability
You have found the chance of a single roll or a single draw before. Almost nothing worth asking has that shape: people want the chance of at least one success in ten tries, or of one thing happening given that another already has. Combining events like that is where this lesson goes.
- Data Distributions and Statistics
Five houses on a street sell, four at ordinary prices and one for a fortune. Their average and their middle value land nowhere near each other. Which of the two describes the street? What each summary of a data set actually measures, and when it stops being trustworthy, is the question here.
- The Normal Distribution Advanced. This lesson goes beyond core Algebra II. You can skip it.
Measure the heights of ten thousand adults, the weights of ten thousand loaves of bread, and the errors in ten thousand readings of one star. Three unrelated experiments all end up approximating the same picture, a symmetric bell. This closing lesson asks why that shape keeps appearing, and what probability can mean for a smooth curve.