Simulations

1. Simulations

2. Simulations – What’s That? • Simulations are used to solve probability problems when it is difficult to calculate the answer theoretically. You may be asked to calculate • The long run frequency of an event happening • The average number of times needed to carry out a ‘trial’ until a certain condition is met

3. Simulations – How? • When designing a simulation a tool must be chosen that matches the situation. Possible tools include; • Coins, Dice, Spinners • Random number tables • Random numbers on the calculator • Random number generator on a spreadsheet

4. Simulations – Random Numbers? One of the best tools for simulation is the calculator How to produce random number on a calculator… Example: If I wanted to produce 10 random numbers from 0 to 30 I would… Type 31Ran# - and press = 10 times – only read the digits before the decimal place

5. Simulations – Random Numbers? Produce 10 random numbers from 1 to 50 Produce 4 random numbers from 5 to 20 Produce 6 random numbers from 0 to 1000

6. Simulations – Random Numbers? • simulate a situation where there is a 14% chance of success • 101Ran# = , taking only the digits before the decimal place and ignoring 0, • allocating 1 to 14 for success, 15 to 100 for failure • Keep pressing = until you have the required number of random numbers.

7. Simulation

8. Cereal Box http://mste.illinois.edu/reese/cereal/cereal.php

9. Simulation

10. Example On average four out of every six kiwifruit selected at the orchard, are suitable for export. Use a simulation technique (with random numbers or dice) to estimate the probability that all of the next five kiwifruit which are tested will be up to the export standard.

11. Discussion

12. Task Cambridge Textbook – p398 ex 10E and 10F