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Designing Simulations

Designing Simulations. Section 7.7. Monty Hall Problem. Break up into teams of 2 and complete the activity on page 464. Fill in the chart for number 5, and answer questions 6 and 7. Definitions.

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Designing Simulations

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  1. Designing Simulations Section 7.7

  2. Monty Hall Problem • Break up into teams of 2 and complete the activity on page 464. Fill in the chart for number 5, and answer questions 6 and 7.

  3. Definitions • Simulation: a way to test the results of an experiment without actually conducting the experiment. • Trial: each repetition of the experiment

  4. Monte Carlo Simulations • 1. determine how it will be simulated • 2. Define what constitutes a single trial and what data will be recorded. • 3. Specify the number of trials that will be run and how the estimated answer will be obtained. **very helpful – p. 874 (random numbers) BEGIN AT ANY NUMBER(not beginning)!!!

  5. Example 1 • Four darts are thrown randomly at a coordinate plane and the quadrants are recorded. It is desired to simulate the probability that all 4 darts land in at most 2 quadrants. Design a simulation with 50 trials to estimate this probability. Sample: roll two dice, 1 – 4 stand for quadrants. Re-roll if it lands on 5 or 6. Roll die 4 times – record answer. Repeat 50 times.

  6. Example 2 • Explain how to use a table of random numbers to simulate the trials in Example 1. Take the numbers in pairs. If the number is between 0 – 24  quad 1 25 – 49  quad 2 50 – 74  quad 3 75 – 99  quad 4 Look at 8 numbers. Record results. Repeat 50 times!

  7. Example 3 • Run the simulation mentioned in example 2. I began my random number at row 23, column 10. 1, 4, 1, 3 1, 3, 1, 1 4, 4, 1, 4 … 18 / 50 = .36 Theoretical probability: 1/16 + ¼ + 1/16 = 3/8

  8. Homework Page 469 3, 4, 6 – 8 (skip 8 b)

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