Randomness, Probability, and Simulation (Lesson 5.1)
Chapter 5 - Day 1
Interpret probability as a long-run relative frequency.
Avoid common myths about randomness.
Use simulation to model chance behavior.
For today’s activity, students will be using the “Is Mrs. Gallas a Good Free Throw Shooter” applet at www.statsmedic.com/applets. They will keep track of Mrs. Gallas free throw percentage as she shoots more and more free throws. Fun fact: Mrs. Gallas was a star basketball player in high school.
We do not expect students to write out the model interpretation for probability in question #4 of the activity. Let students write in their own words, and then give them the more formal interpretation in the debrief.
In question #6-8 of the activity, students use a sampling distribution to estimate a probability. This is not the first time they have seen a sampling distribution (remember Beyonce?). Be sure to ask the right follow-up questions after “What does this dot represent?”.
For the Lesson App 5.1, we use question #2 to address the common misconception that people have that due to the “law of averages” there is a better chance that the train will be late on the 6th day because it had been on time the previous 5 days. We know that if each train is independent from another, that the probability the train is on time is 0.9 for every train, regardless of the outcome on previous days. We say “the train has no memory”. Later in Lesson 5.4, we will discuss more mathematically what it means for two events to be independent.
Lesson App question #6 is yet another preview of significance tests and P-values which will be covered later in the course (Chapter 9). The big idea is that the outcome observed by the businessman (train late 3/20 times) is quite plausible to happen purely by chance if we assume the New Jersey Transit’s 90% claim is true. We can see this in the dotplot as 30 of the simulations (out of 100) have 3 or more late arrivals. This proportion 30/100 will later become a P-value for a significance test.
Inevitably, at the end of every year of Intro 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 on quizzes and tests.