Integrated Math 3 / Unit 8: Statistics and Inference
8.6 Simulations
Notes
A simulation uses random numbers to imitate a chance process many times.
- Assign random digits to match the probabilities: for a 40% event, use 4 of the 10 digits (such as 0 to 3).
- For a 35% event use two-digit numbers 00 to 34, since that is 35 of the 100 numbers.
- Run many trials and record how often the outcome happens. The more trials, the closer the results tend to be to the true probability.
- A fair die can imitate a $\displaystyle \frac{1}{3}$ chance by letting 1 and 2 mean success.
Practice
A basketball player makes 70% of free throws. Which assignment of single random digits (0-9) models one shot?
Seven of the ten digits are a make, which is 70%.
A weather event has a 35% chance of happening each day. Which assignment of two-digit random numbers (00-99) models one day?
00 to 34 contains exactly 35 numbers out of 100.
A student runs a simulation 20 times, then again 2,000 times. Which is likely to give a result closer to the true probability?
Relative frequencies settle near the true probability as the number of trials grows.
Ready for more? Take the Unit 8 test.