1. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 11 Understanding Randomness

2. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Random Structure??? Constant probability - no certain outcome Set of outcomes equally likely (all have a chance, doesn’t have to be equal) of happening

3. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Random Numbers From Table From TI Computer generated numbers are pseudorandom Generated in a fixed sequence with a finite number of distinct values

4. Copyright © 2010, 2007, 2004 Pearson Education, Inc. MATH -- PRB menu

5. Copyright © 2010, 2007, 2004 Pearson Education, Inc. randInt command (starting number, ending number, # digits chosen) Ex: rolling a dice Ex: rolling 2 dice

6. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Slide 11 - 6 It’s Not Easy Being Random It’s surprisingly difficult to generate random values even when they’re equally likely. Computers have become a popular way to generate random numbers. Even though they often do much better than humans, computers can’t generate truly random numbers either. Since computers follow programs, the “random” numbers we get from computers are really pseudorandom. Fortunately, pseudorandom values are good enough for most purposes.

7. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Slide 11 - 7 It’s Not Easy Being Random (cont.) There are ways to generate random numbers so that they are both equally likely and truly random. The best ways we know to generate data that give a fair and accurate picture of the world rely on randomness, and the ways in which we draw conclusions from those data depend on the randomness, too.

8. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Slide 11 - 8 Practical Randomness We need an imitation of a real process so we can manipulate and control it. In short, we are going to simulate reality.

9. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Slide 11 - 9 A Simulation The sequence of events we want to investigate is called a trial. The basic building block of a simulation is called a component. Trials usually involve several components. After the trial, we record what happened—our response variable. There are seven steps to a simulation…

10. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Slide 11 - 10 Simulation Steps 1.Identify the component to be repeated. 2.Explain how you will model the component’s outcome. 3.Explain how you will combine the components to model a trial. 4.State clearly what the response variable is. 5.Run several trials. 6.Collect and summarize the results of all the trials. 7.State your conclusion.

11. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Arranged Marriages!!!

12. Copyright © 2010, 2007, 2004 Pearson Education, Inc. The proposal

13. Copyright © 2010, 2007, 2004 Pearson Education, Inc. The big day!!!

14. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Little ones??? How many & what gender???

15. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Free Throws 80% free throw shooter # made in a row until a miss Points scored in a bonus situation (2 automatic shots) Points scored in a one-&-one situation (2 nd shot only if make the first) Run 10 trials of each!!!

16. Copyright © 2010, 2007, 2004 Pearson Education, Inc.

17. We are opening a new frozen yogurt store. Other store sales indicate the following flavor preferences Chocolate – 38% Vanilla – 42% Strawberry – 20% We predict that we will average 20 customers per hour. How many servings of each should we prepare?

18. Copyright © 2010, 2007, 2004 Pearson Education, Inc.

19. Slide 11 - 19 What have we learned? How to harness the power of randomness. A simulation model can help us investigate a question when we can’t (or don’t want to) collect data, and a mathematical answer is hard to calculate. How to base our simulation on random values generated by a computer, generated by a randomizing device, or found on the Internet. Simulations can provide us with useful insights about the real world.

20. Copyright © 2010, 2007, 2004 Pearson Education, Inc. Simulation Exit Slip Bob is trying to get his C.D.L. in order to drive trucks. He has heard that you have a 2 out of 10 chance of passing based on guessing alone. He gets three chances to pass the test. (Assume the attempts are independent because he takes a different test every time). Should he study or just go in there and play the odds??? Conduct a simulation, run 20 trials using the table of random digits and support your conclusion.