Weighted Probability Simulator

Weighted Probability Simulator
Welcome to Weighted Probability Simulator. The Weighted Probability Simulator allows you to see the Law of Large Numbers in action. You can slide the Probability Slider to see how the Theoretical Mean line on the graph moves and how the experimental data eventually approaches that new target. It helps you make comparisons between Experimental and Theoretical Probability. Scroll down the page for a more detailed explanation.

 

 

1. Set Your Probability (The “Weight”)
   Before starting, use the Set Weight (Heads %) slider.
   A Fair Coin: Set it to 50%.
   A Weighted Coin: Set it to 75% or 25% to see how a “biased” coin behaves.
   Note: Adjusting this mid-experiment will automatically reset your progress so you can start a clean trial for the new percentage.
   

2. Run the Trials
   Choose how you want to generate data:
   Flip x1: Best for watching how a single “lucky” or “unlucky” flip can drastically change the average when you have very few trials.
   Flip x10: Use this to build up data points quickly while still seeing the “jaggedness” of the graph.
   Start Simulation: This is the high-speed mode. It flips the coin 1,000 times every second. This is where you see the randomness smooth out into a flat line.
   

3. Analyze the Convergence Graph
   This is the visual proof of the Law of Large Numbers:
   The Orange Dashed Line: This represents your Theoretical Probability (the weight you set).
   The Blue Solid Area: This represents your Actual Results (Experimental Probability).
   The Goal: Watch the left side of the graph. When you have only 5 or 10 flips, the blue line will jump wildly above and below the orange line. As you reach 1,000+ flips, the blue line will eventually “hug” the orange line almost perfectly.
   

Law of Large Numbers

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