3.7 Simulations Unit 1: Statistics

Today’s Objectives I can… Use design simulations to model experiments.

Simulation Why run a simulation? Simulation is a way to model random events, to closely match real-world outcomes. Why run a simulation? Some situations may be difficult, time-consuming, or expensive to analyze. In these situations, simulation may approximate real-world results while requiring less time, effort, or money.

Portia and Tafui are playing a dice game Portia and Tafui are playing a dice game. Portia believes that she can roll six dice and get each number, one through six, on a single roll. Tafui knows the probability of this occurrence is low. She bets Portia that she will wear her clothes inside out tomorrow if Portia can get the outcome she wants in twenty tries.

What is the problem that we are simulating? Can Portia roll one of each number in a throw of six dice? What random device will you use to simulate the problem and how will you use it? We will use the calculator to generate random numbers.

Seeding Since a calculator is a type of computer, it can never be truly random. For this reason, we can configure our calculators to give everyone the same set of “random” data (so we can all work together!). The process of calibrating our calculators in this way is called seeding.

How to seed the calculator:

How will you conduct each trial? How many trials will you conduct? I will use the randInt( command in my calculator to generate random integers. randInt(min value, max value, number of data in set) randInt(1, 6, 6) Smallest number on dice Throwing 6 dice at a time Largest number on dice

Let’s perform our simulation! In your groups, complete the simulation 20 times. Record which trials gave you one of each number. _____ 2. _____ 3. _____ 4. _____ 5. _____ 6. _____ 7. _____ 8. _____ 9. _____ 10. _____ 11. _____ 12. _____ 13. _____ 14. _____ 15. _____ 16. _____ 17. _____ 18. _____ 19 . _____ 20. _____

What are the results of these trials? What predictions can be made based on these results? The more trials you run, the closer you will get to the theoretical probability (Law of Large Numbers). What is the theoretical probability that you will get the numbers 1 – 6 on in six rolls of a die?

On a certain day the blood bank needs 4 donors with type O blood On a certain day the blood bank needs 4 donors with type O blood.  If the hospital brings in groups of five, what is the probability that a group would arrive that satisfies the hospitals requirements, assuming that 45% of the population has type O blood?    Remember to seed the calculator to 5

Questions about simulations?