## Course 1, Unit 7 - Simulation Models

Summary
In the "Simulation Models" unit, students learn to design and carry out simulations to estimate answers to questions about probability. Situations involving uncertainty surround us, from weather forecasts to stock markets. Many of these situations are too complex to be handled theoretically, but some of them are quite accessible through the technique of simulation. This technique has a history that is concurrent with the development of computing technology, and your student uses methods that make good use of the graphing calculator. Theoretical probability is developed in Courses 2 and 3.

Key Ideas from Course 1, Unit 7

• Simulation model: A way of modeling a real situation that involves randomly occurring events. For example, suppose that 45% of a population has type O blood. Here's how to use simulation to estimate the probability that 4 random people entering a blood donor bank have blood type O. Model the selection of one person chosen at random from the population by assigning the numbers 1-45 to represent people with type O blood and 46-100 to represent other people. Choosing 4 numbers at random from 1 to 100 and counting how many are 1-45 would simulate 4 random people entering a blood donor clinic and being identified by blood type.
• Trial: In the above example, if 4 random numbers between 1 and 100 are drawn and the result is "12, 46, 70, 31," then there are 2 type O blood persons (represented by numbers 1-45) in this one trial of the simulation.
• Law of Large Numbers: The more trials you do, the more likely that your result will be close to the exact, theoretical probability.
• Probability distribution: A list of all possible outcomes of a chance situation along with the probability that each occurs.