Chapter 11 Understanding Randomness

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.

Pick a Number

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

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

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.

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?

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

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

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

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

Using random numbers  Throw out 0,7,8,  Trial 1: ___ rolls  Trial 2: ___ rolls  Trial 3: ___ rolls  Trial 4: ___ rolls  Trial 5: ___ rolls

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

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

Using Random Numbers  Look at random numbers  By twos

Using Random Numbers  Throw out 40,41,…,  Trial 1: _________  Trial 2: _________  Trial 3: _________  Trial 4: _________  Trial 5: _________  Trial 6: _________  Trial 7: _________

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?