Lesson 1: 5.1 Randomness, Probability, and Simulation
Duration of Days: 2
Lesson Objective
Students will be able to interpret probability as a long-run relative frequency and use simulation to estimate probabilities.
1. If a coin lands on heads five times in a row, is it "due" to land on tails next?
2. How many times do we need to repeat an event before the "true" probability actually starts to show up?
Probability
Law of Large Numbers
Simulation
Trial
HSS-CP.A.1: Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events.
The SAT often asks students to calculate basic probabilities from data tables.
Students learn that while randomness is unpredictable in the short term, it has a very predictable pattern in the long run.
The Problem: A basketball player claims he makes 80% of his free throws. In a recent game, he missed 5 out of 10.
Task: Design and carry out a simulation to determine if missing 5 or more shots is likely to happen by chance if his true ability is 80%.
Students believe that random processes "even out" in the short term. Remind them that a coin has no memory.
Support: Use a "Probability Number Line" from 0 (Impossible) to 1 (Certain) to help visualize values like 0.05 (rare) vs. 0.95 (likely).
Extension: Have students use a spreadsheet to "flip" a virtual coin 10,000 times and graph the cumulative proportion of heads to see the Law of Large Numbers in action.
Teacher assigns examples from the textbook and other resources.
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