Topic 6 · Probability · Lesson 6.6

Law of Large Numbers Simulator

Pick an experiment, then run trials. After 10 flips the experimental probability bounces around; after 1,000 it tightens up; after 10,000 it sits right on the theoretical value. The Law of Large Numbers is one of those statements that makes more sense once you watch it happen than after you read it.

Theoretical vs experimental probability

P̂ = successes / trials → P as n → ∞

Flipping a fair coin: theoretical P(heads) = 0.5. After 0 flips, experimental P̂ = —. Gap to theoretical: —.

Trials run

click a +N button to start

Successes

favorable outcomes observed

Experimental P̂

—

successes / trials

Theoretical P

0.500

structural probability

Experimental probability (running average) Theoretical probability

Choose an experiment

Coin flip — P(heads) = 0.5 Die roll — P(roll a ) = 1/6 Custom — P =

Coin flip: each trial is heads (success) or tails. Theoretical P = 0.5.

Run trials