2. Chapter 11 Understanding Randomness

3. At the end of this chapter, you should be able to  Identify a random event.  Describe the properties of random events.  Use random number table to study random events.

4. Pick a Number 1 2 3 4

5. What Number did you pick?  If selected randomly ______ select 1 ______ select 2 ______ select 3 ______ select 4  Class picks ______ % select 1 ______ % select 2 ______ % select 3 ______ % select 4

6. What is Randomness?  Random events Outcome unknown before event  _______________________ No Structure in Short Term  _______________________ Structure in Long Term  _______________________

7. How do we get random numbers?  Computers? Pseudorandom numbers  Random events Radioactive decay Random movements of molecules  Table in Appendix E List of numbers 0 through 9. Organized by rows and in columns of 5.

8. Using random numbers  A cereal maker has 3 sports cards: Tiger Woods, Lance Armstrong and Serena Williams. 30% - Tiger Woods 30% - Lance Armstrong 40% - Serena Williams  How many boxes do we need to buy before we get all 3 cards?

9. Using random numbers  Simulation 0,1,2: box has Tiger Woods 3,4,5: box has Lance Armstrong 6,7,8,9: box has Serena Williams  Look at random numbers 96299 07196 98642 20639 23185 56282 69929 14125 38872 94168 71622 35940

10. Using random numbers  Trial 1: 96299071969864 ________ boxes  Trial 2: 22063________ boxes  Trial 3: 923________ boxes  Trial 4: 185________ boxes  Trial 5: 562________ boxes  Trial 6: 826992914________ boxes  Trial 7: 12538________ boxes  Trial 8: 87294________ boxes  Trial 9: 168________ boxes  Trial 10: 716223________ boxes

11. Using random numbers  Out of 10 trials - mean = ________ boxes  More trials = more accurate result. Out of 200 trials - mean = _________ boxes.

12. Using random numbers  How many times do we need to roll a die before we get a 6?  Simulation 1,2,3,4,5,6: Roll on die 0,7,8,9: Throw out  Look at random numbers 31087 42430 60322 34765 15757 53300 97392 98035 05228 68970 84432 04916 52949 78533 316

13. Using random numbers  Throw out 0,7,8,9 3142436322346515553332 3552264432416524533316  Trial 1: 3142436___ rolls  Trial 2: 322346___ rolls  Trial 3: 515553332355226___ rolls  Trial 4: 4432416___ rolls  Trial 5: 524533316___ rolls

14. Using random numbers  Out of 5 trials - mean number of rolls = ____  More trials = more accurate result. Out of 200 trials - mean number of rolls = ______.

15. Using Random Numbers  40 people live on a dorm floor; 10 are on soccer team. A lottery was drawn to select 3 people to live in triple suite. All 3 people selected were on soccer team. Is this fair?  Simulation 00,01,02,03,04,05,06,07,08,09: Soccer team 10,11,12,…,39: Non-soccer team 40,41,…,99: Throw out

16. Using Random Numbers  Look at random numbers 47119 76651 21732 32364 58545 50277 57558 30390 18771 72703 11232 99884 05087 76839 65142 19994 91397 29350 83852 04905  By twos 47 11 97 66 51 21 73 23 23 64 58 54 55 02 77 57 55 83 03 90 18 77 17 27 03 11 23 29 98 84 05 08 77 68 39 65 14 21 99 94 91 39 72 93 50 83 85 20 49 05

17. Using Random Numbers  Throw out 40,41,…,99 11 21 23 23 02 03 18 17 27 03 11 23 29 05 08 39 14 21 39 20 05  Trial 1: 11 21 23_________  Trial 2: 23 02 03 _________  Trial 3: 18 17 27_________  Trial 4: 03 11 23 _________  Trial 5: 29 05 08 _________  Trial 6: 39 14 21_________  Trial 7: 39 20 05_________

18. Using Random Numbers  Out of 7 trials - no groups selected had all three people from soccer team.  More trials = more accurate result. Out of 200 trials, - only _______ groups selected had all three people from soccer team.  Was drawing fair?