Sample Space Explorer
Run the Sample Space Explorer Fullscreen
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About This MicroSim
This interactive visualization helps students understand sample spaces and events for common random phenomena. Students can explore different scenarios (single die roll, two coin flips, two dice sum, and card suits) and select outcomes to define events. The probability is calculated in real-time as students add or remove outcomes from their event.
How to Use
- Select a phenomenon from the dropdown menu
- Click on outcomes to add them to your event (highlighted in green)
- Watch the probability update in real-time as P(Event) = favorable/total
- Reset to clear your selection and try different events
Learning Objectives
After using this MicroSim, students will be able to:
- Identify sample spaces for common random phenomena
- Define events as subsets of sample spaces
- Calculate probabilities using the classical definition P(Event) = favorable outcomes / total outcomes
- Understand how different phenomena have different sample space structures
Embedding This MicroSim
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Lesson Plan
Introduction (5 minutes)
Introduce the concept of sample space as the complete set of all possible outcomes. Discuss how probability is calculated by counting favorable outcomes.
Guided Exploration (10 minutes)
Have students explore each phenomenon type, predicting what events will have probability 1/2, 1/3, etc.
Practice Activities (10 minutes)
Challenge students to select events with specific probabilities (e.g., "Create an event with probability 0.5 for a die roll").
Assessment
Students can demonstrate understanding by correctly identifying sample space sizes and calculating event probabilities.
References
- Chapter 9: Probability Fundamentals
- Concept: Sample Space, Event, Probability