Why Be Random? What is it about chance outcomes being random that makes random selection seem fair? Two things: Nobody can guess the outcome before it happens. When we want things to be fair, usually some underlying set of outcomes will be equally likely (although in many games some combinations of outcomes are more likely than others).

A simulation is a sequence of random outcomes that model a situation. What is a simulation? A simulation is a sequence of random outcomes that model a situation.

Vocabulary Breakdown: Random – An event in which we know what outcomes can occur but not what outcome actually will happen. Outcome- The individual results of a single sequence of events Trial – A single run of sequence of events being simulated. Response Variable – Values that record the results of each trial

Simulation Steps Identify the component to be repeated. Explain how you will model the outcome. Explain how you will simulate the trial. State clearly what the response variable is. Run several trials. Analyze the response variable. State your conclusion (in the context of the problem, as always).

Example: You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right?

I Step 1- Identify the component to be repeated. One multiple choice question Step 2 – Explain how you will model the outcome. Since I have 80% chance of getting a question right, I will use random digits 0 -9 by assigning 0 -7 for a correct answer and 8 and 9 for an incorrect answer.

Step 4 – State clearly what the response variable is. Step 3 – Explain how you will simulate the trial Each trial will consist of 6 random digits since there are 6 multiple choice questions. Step 4 – State clearly what the response variable is. I want to know what my chance of getting them all right is. Thus I will count the number of trials that give us all 6 numbers being 0 -7.

Step 6 – Analyze the response variable Step 5 – Run several trials. (you can create a chart to keep track of what happened). Recommend 20 trials Step 6 – Analyze the response variable Count the number of times I got all the problems right and divide it by the total number of trials Step 7 – State you conclusion(in the context of the problem, as always). If I were to have about an 80% chance of getting an individual problem correct, I would have about 26% chance of getting them all right on a quiz with 6 multiple choice questions according to this simulation.