Chance experiments
Theory versus experiment.
Testing ideas
Theory says P(7) with two dice is ⅙. Does an experiment agree? Let us compare theoretical probability and experimental probability.
Two-dice experiment
7 came up 17 times out of 100: 0.17. Theory: 1/6 ≈ 0.167. Very close!
More trials, better estimates
Small experiments can be far from theory. Large experiments get closer. This is called the law of large numbers.
Simulations
A simulation uses a simple model. Three coins can stand for three children. Repeat many times to estimate probabilities.
What I learnt
- I can compare theoretical and experimental probability.
- I understand that more trials give better estimates.
- I can use simple simulations.