🪙 Coins and Two-Color Counters
Build intuition with binary models. Compare theoretical and experimental probability.
Model Setup
Convergence — Experimental P(Event) —
Last Trial
Run a trial to generate an outcome.
Running Stats
Trials
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Event Hits
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Exp. P(Event)
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Theoretical
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Model Notes
🎲 Dice and Number Cubes
Explore sums, compound events, and non-uniform distributions.
Dice Setup
Convergence — Experimental P(Event) —
Last Trial
Run a trial to generate an outcome.
Running Stats
Trials
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Event Hits
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Exp. P(Event)
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Theoretical
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Instructional Note
With two or more dice, some sums occur more often because they can be formed in more ways. The convergence chart shows how experimental probability approaches theoretical over many trials.
🌀 Spinner
Design a custom probability model — drag sector edges to resize, edit labels and weights.
Convergence — Experimental P(Event) —
Last Trial
Run a trial to spin the spinner.
Running Stats
Trials
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Event Hits
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Exp. P(Event)
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Theoretical
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Classroom Prompt
Design a spinner where P(landing on Red) = 0.5. What does that look like? As you run trials, does the experimental probability approach your theoretical value?
🃏 Cards
Single-card draws for simple event probability with a standard 52-card deck.
Card Setup
Convergence — Experimental P(Event) —
Last Trial
Run a trial to draw a card.
Running Stats
Trials
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Event Hits
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Exp. P(Event)
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Theoretical
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Model Notes
📊 Data Capture
Review frequencies, relative frequencies, and graphs for the current tool.
Active Tool
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Trials
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Event Hits
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Exp. P(Event)
0.000
Chart
Frequency Table
Interpretation
Run trials in any module, then return here to analyze the data.
⊞ Sample Space Builder
Visualize all ordered pairs for two devices. Click cells to shade an event — theoretical probability updates live.
Device Setup
Shaded
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Total
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P(Event)
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How to Use
Each cell shows an ordered pair (A, B). Click any cell to shade it — shaded cells turn orange.
Switch to Σ Sums view to see the sum in each cell; cells with the same sum share a color, revealing the diagonal pattern.
Click a bar in the Sum Distribution chart to instantly shade all cells with that sum.
Event Summary
Select devices and click cells to define an event.
Classroom Prompt
How many outcomes are in the sample space? How does the number of outcomes for each device affect the total?
Sample Space Size
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🌿 Tree Diagram Builder
Build multi-stage probability trees. Edit branch labels and probabilities — leaf products update live.
Tree Setup
✓ Probabilities valid
Leaf Outcomes
Build a tree to see leaf outcomes.
Branch Editor
Build a tree to edit branches.
Classroom Prompt
Multiply probabilities along a path to find the probability of that outcome. What do all the leaf probabilities add up to? Why?
🔵 Conditional Probability Explorer
Drag circles to change overlap. Watch P(A|B) and P(B|A) update live — synced to the two-way table.
Setup
Venn Diagram
drag circles to reposition · drag edge to resize
Two-Way Table
Probabilities
Highlight Region
Classroom Prompt
P(A|B) asks: given that B happened, what's the chance A also happened? Try making A and B completely separate — what happens to P(A|B)? Now make them identical — what happens?