A simulation imitates a chance process with random numbers so you can estimate a probability that is hard to calculate. Pick a scenario, run trials one at a time or a thousand at once, and watch the relative frequency settle down. That is the law of large numbers at work.
Choose a scenario, set its chance, and run trials. Each trial uses random numbers just as you would with a random digit table or a calculator.
A random process has outcomes we cannot predict for any single trial, but the outcomes show a regular pattern over many trials.
The probability of an event is the proportion of times it would happen in a very long series of repetitions of the random process.
As the number of trials grows, the simulated relative frequency gets closer to the true probability. It does not mean outcomes "even out" in the short run.
(1) Assign random numbers to outcomes so the chances match. (2) Describe one trial. (3) Say what you record. (4) Repeat many times and divide.
For a 70% chance, use 70 of the 100 two-digit numbers (00–69) for "success." Each number must be equally likely, so 1-digit labels give 10% steps.
If each outcome is independent (free throws, dice), repeated digits are fine. If you are choosing different people, skip repeated labels so no one is picked twice.
How to assign random numbers for common situations.
| Situation | Assign | One trial | Record |
|---|---|---|---|
| A 30% chance of rain each day for a week | Digits 0–2 = rain, 3–9 = no rain | Read 7 digits | Whether it rains on at least 3 days |
| A 72% free-throw shooter takes 10 shots | 00–71 = make, 72–99 = miss | Read 10 two-digit numbers | Number of makes |
| Choose 4 students from a class of 25 (8 are seniors) | Label students 01–25; 01–08 = seniors | Read two-digit numbers, skip 00, 26–99, and repeats, until 4 are chosen | Number of seniors chosen |
| 6 equally likely prizes in cereal boxes | Digits 1–6 = the prizes; skip 0, 7, 8, 9 | Read digits until all 6 prizes appear | Number of boxes bought |
| Roll a fair die | Calculator: randInt(1, 6) | One call per roll | The face showing |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 2.3. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 2 terminology guide.