Chapter 13
Probability and Statistics
Nearly every problem in this course has had one exact answer waiting at the end. A weather forecast, a medical test result, the price of the next house sold on your street: none of those is certain, and yet people make serious decisions about all of them without simply guessing. Uncertainty turns out to be measurable. Probability pins a chance down to a number, and statistics describes a messy pile of data without misleading anyone. How can mathematics be exact about something nobody can predict?
What You'll Explore
4 lessons.
- 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
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 produce the same picture, a symmetric bell. This closing lesson asks why that shape keeps appearing, and what probability can mean for a smooth curve.