Probability Simulation Lab
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About This MicroSim
This interactive simulation allows students to estimate probabilities through repeated trials. Students can choose from preset scenarios (Free Throws, Coin Flips, Dice Rolls) and observe how the estimated probability converges toward the theoretical probability as the number of trials increases.
How to Use
- Select a scenario from the dropdown menu
- Click "Run 1" to see a single trial with detailed outcomes
- Click "Run 100" or "Run 1000" to quickly accumulate trials
- Adjust speed to control animation rate
- Watch the graph as the estimated probability converges
Scenarios
- Free Throws: P(success) = 0.7, success = at least 4 makes in 5 shots
- Coin Flips: P(success) = 0.5, success = at least 2 heads in 3 flips
- Dice Rolls: P(success) = 1/6, success = at least 1 six in 6 rolls
Learning Objectives
After using this MicroSim, students will be able to:
- Design simulations to estimate probabilities
- Understand how more trials lead to more accurate estimates
- Compare empirical probability to theoretical probability
- Apply the concept of convergence to real-world scenarios
Embedding This MicroSim
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Lesson Plan
Introduction (5 minutes)
Discuss why simulations are useful when theoretical calculations are complex. Introduce the scenarios.
Guided Exploration (10 minutes)
Run simulations together, making predictions about convergence at 10, 100, and 1000 trials.
Practice Activities (15 minutes)
Have students run their own simulations and record how close their estimate gets to the theoretical value at different trial counts.
Assessment
Students explain why simulations work and describe the relationship between trial count and estimate accuracy.
References
- Chapter 9: Probability Fundamentals
- Concepts: Simulation, Designing Simulations