Randomness and Probability
Chapter 5 - Day 1 - Lesson 5.1
Interpret probability as a long-run relative frequency.
Activity: How good is Mrs. Gallas at free throws?
Students will use this applet for the activity today. In the applet, the claim is that 80% of free throws will be makes. This may or may not be true (the applet randomly generates the true probability). Tell students not to click the box to “Show true probability” until the end of the activity. Students should notice that there is a lot of variability in the percent made for the first series of shots, but in the long run the proportion seems to approach a set value (Law of Large Numbers!).
Preparing for Inference
As students collect more and more data, they should be thinking about whether or not they have convincing evidence against the 80% claim that is being made. Suppose that after 10 free throws, the percent made is at 50%. This provides some evidence against the 80% claim. On the other hand, if after 1000 free throws the percent made is at 50%, we have convincing evidence against the 80% claim. We want students to start thinking inferentially now, so when we get to significance testing in Chapter 9, they will be ready.
Warning about Chapter 5!
Inevitably, at the end of every year of AP Stats, students will tell us that Chapter 5 was the hardest. This may be true, but here are a few ideas you can use to ease students’ anxiety (and your own!)
Teach probability conceptually, rather than just memorizing formulas and algorithms.
Encourage students to use strategies (simulation, sample space, Venn diagrams, two-way tables, tree diagrams) before resorting to a formula.
Getting good at probability questions requires practice: practice in class, practice on homework, practice at the end of the year review.