experimental probability and theoretical probability
Spin a spinner, throw a bottle cap and roll dice: 10 times, 100 times, 1000 times. Watch the relative frequency settle near the probability.
- UK: Year 7
- France: grade 6
- Germany: grade 3
- Iran: grade 7
- Afghanistan: grade 7
- Syria: grade 7
- Palestine: grade 6
- Ukraine: grade 9
- Russia: grade 7
Guide
This studio follows Iran's Year 7 lesson «احتمال و تجربه» and the KS3 work on randomness and fairness. The theoretical probability comes from the shape of the thing: favourable outcomes divided by possible outcomes, as long as the outcomes are equally likely. The experimental probability (the relative frequency) comes from trials: how many times it happened divided by the number of trials.
The big idea: with 10 trials the results jump about a lot. With 1000 trials the relative frequency is usually close to the theoretical probability, but almost never exactly equal to it. In the table, the small black tick on each bar marks the theoretical probability.
Common mistakes: "tails has come up a lot, so heads is due" (a coin has no memory); "10 rolls are enough to tell whether a dice is fair"; "there are three colours, so each has a probability of 13" (when the sections are different sizes); "the relative frequency isn't exactly 16, so the dice is biased". Each mission works on one of these. The bottle cap stands for anything whose probability can't be worked out from its shape, only estimated by experiment (a drawing pin is the textbook example).