Probability Lab
Toss coins and roll dice thousands of times in seconds. A few throws are unpredictable, but many throws settle down to exactly what theory says.
Theory vs experiment
The theoretical probability of an event is (favourable outcomes) ÷ (all equally likely outcomes): ½ for heads, ⅙ for a six. The experimental probability is (times it happened) ÷ (trials). With 10 throws they can be far apart. The law of large numbers says that with more and more trials, the experimental value gets closer and closer to the theoretical one.
Why is 7 the luckiest sum?
Two dice have 6 × 6 = 36 equally likely outcomes. A sum of 2 happens only one way (1 + 1), but a sum of 7 happens six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so P(7) = 6/36 = ⅙. The bars make a triangle. Counting outcomes carefully is the heart of probability (and of permutations and combinations).