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

1 2 3 4

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 numbers96299 07196 98642 20639 23185 56282 69929 14125 38872 94168 71622 35940

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

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 31087 42430 60322 34765 15757 53300 97392

98035 05228 68970 84432 04916 52949 78533 316

Using random numbers Throw out 0,7,8,9

31424363223465155533323552264432416524533316

Trial 1: 3142436 ___ rolls Trial 2: 322346 ___ rolls Trial 3: 515553332355226 ___ rolls Trial 4: 4432416 ___ rolls Trial 5: 524533316 ___ 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 numbers47119 76651 21732 32364 58545 50277 57558 30390 18771 72703 11232 99884 05087 76839 65142 19994 91397 29350 83852 04905

By twos47 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

Using Random Numbers

Throw out 40,41,…,9911 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 _________

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?