Probability Simulation
Uniform Model: Coin Flip
A fair coin has a 50% chance of landing on Heads. This is the Theoretical Probability. Let's see what happens in a real experiment.
Tap to Flip ({{ flips.length }}/10)
Theoretical (Heads):
50%
Experimental (Heads):
{{ flips.length > 0 ? Math.round((headsCount / flips.length) * 100) + '%' : '--%' }}
{{ headsCount }} H
{{ flips.length - headsCount }} T
Non-Uniform Model: Basketball
A player makes {{ bballTarget }}% of their free throws. Build a spinner model to simulate this.
Drag to Build
🏀
Make
❌
Miss
Spinner Slots (Each slot = 25%)
{{ slot === 'make' ? '🏀' : '❌' }}
{{ slot === 'make' ? 'Make' : 'Miss' }}
+
Current Model: {{ currentSpinnerPercent }}% Make
Perfect model!
Law of Large Numbers
You built a {{ bballTarget }}% model. Running it 4 times won't always give perfect results. Let's run it many times!
Slide to Spin
{{ simCount }} Spins
10
1000
Simulation Results
Theoretical
{{ bballTarget }}%
Experimental
{{ simPercent }}%
🏀 Makes ({{ simResults.makes }})
{{ simPercent }}%
❌ Misses ({{ simResults.misses }})
{{ (100 - simPercent).toFixed(1) }}%
Notice how close the experimental probability gets to the theoretical probability at 1000 spins!
Build a Lottery Model
A lottery has a {{ lotteryTarget }}% chance of winning. Using a 100-ticket model, how many winning tickets should there be?
Tap to Select ({{ lotteryCount }} / {{ lotteryTarget }})
⭐
You Did It!
You've built probability models, simulated experiments, and proved the Law of Large Numbers!
Key Takeaways:
- ✅ Uniform Model: All outcomes are equally likely (Coin flip).
- ✅ Non-Uniform Model: Outcomes have different probabilities (Basketball).
- ✅ Simulation: The more trials you run, the closer experimental results get to theoretical predictions!