Addition Rule Visualizer
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About This MicroSim
This interactive visualization demonstrates the addition rule for probability using a dynamic Venn diagram. Students can adjust P(A), P(B), and P(A∩B) using sliders and immediately see how these values affect P(A or B). The mutually exclusive toggle shows the special case where P(A∩B) = 0.
How to Use
- Adjust the sliders for P(A), P(B), and P(A∩B)
- Observe the Venn diagram update to show the relationship between events
- Check "Mutually Exclusive" to see what happens when events can't occur together
- Toggle "Show Steps" to see the full calculation
Key Formulas
- General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B)
- For Mutually Exclusive Events: P(A or B) = P(A) + P(B)
Learning Objectives
After using this MicroSim, students will be able to:
- Apply the addition rule to calculate P(A or B)
- Understand why we subtract P(A∩B) to avoid double-counting
- Recognize when events are mutually exclusive and apply the simplified rule
- Visualize probability relationships using Venn diagrams
Embedding This MicroSim
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Lesson Plan
Introduction (5 minutes)
Review the concept of "or" in probability (inclusive or). Explain why simply adding probabilities can lead to overcounting.
Guided Exploration (10 minutes)
Walk through examples with different P(A), P(B), and P(A∩B) values. Show how the intersection affects the total.
Practice Activities (10 minutes)
Give students specific probability scenarios and have them predict P(A or B) before checking with the visualization.
Assessment
Students explain in their own words why we subtract the intersection and when we don't need to.
References
- Chapter 9: Probability Fundamentals
- Concepts: Addition Rule, General Addition Rule, Mutually Exclusive Events