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Section 8.1: Simulation

Section 8.1: Simulation. What is a Simulation?. A simulation is a term which describes using a table of random digits, calculator, or computer software to imitate chance behavior. The 3 steps in a simulation are… 1. Give a probability model. 2. Assign digits to represent outcomes.

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Section 8.1: Simulation

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  1. Section 8.1: Simulation

  2. What is a Simulation? • A simulation is a term which describes using a table of random digits, calculator, or computer software to imitate chance behavior. • The 3 steps in a simulation are… • 1. Give a probability model. • 2. Assign digits to represent outcomes. • 3. Simulate many repetitions.

  3. Is it random???

  4. The 3 Steps • Give a probability model. • List all the possible values (yes/no, heads/tails, etc.). • Assign digits to represent outcomes. • For example, if 70% said “yes”, 30% said “no”, you can assign 0-6 for “yes”, 7-9 for “no”. • For example, if 45% said “A”, 25% said “B”, and 30% said “C”, you can assign 00-44 for “A”, 45-69 for “B”, and 70-99 for “C”. • Simulate many repetitions. • Use the table of random digits or the randint function on the calculator or computer to simulate repetitions. • The repetitions must consist of independent trials (each trial cannot have an effect on any other trial).

  5. Tree Diagram of a Probability Model • It is predicted that 80% of all students have Internet access at home. A simulation can be performed to confirm this statement. • What numbers can be assigned to represent those with Internet access and those without? • 0-7, 8-9 if one digit; 00-79, 80-99 if two digit

  6. Tree Diagram of a Probability Model

  7. Tree Diagram of a Probability Model • Using a calculator’s randint function or a table of random digits, you can perform several simulations to see if your statement is correct. • Make sure that you start over each time (don’t use the same line in the table, for example) when you conduct a simulation, as each simulation must be independent. • Remember, simulations are only estimates.

  8. What to remember: Simulations are only estimated probabilities.

  9. Homework • Pages 452-453, #8.1, 8.2, 8.3 • Pages 459-460, #8.10 • Page 462, #8.11, 8.12

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