Topic 6 · Interactive tool

Law of Large Numbers

What actually happens (experimental) against what the math says (theoretical). After ten tries they can be far apart; after thousands they line up.

Theoretical vs experimental probability

experimental = successes ÷ trials → theoretical

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

runs 10,000 trials, quickly, so you can see the line calm down

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 Die and coin: P(even and heads) = 1/2 × 1/2 = 1/4 Custom — P =

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

Run trials

Experimental vs theoretical

Experimental · from the trials

Theoretical · from the math