Understanding Randomness

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Chapter 11

• Understanding Randomness

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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.

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Pick a Number

• 1 2 3 4

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What Number did you pick?

• Class picks
• ______ select 1
• ______ select 2
• ______ select 3
• ______ select 4

• If selected randomly
• ______ select 1
• ______ select 2
• ______ select 3
• ______ select 4

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People are BAD at being random

• Basic lesson from this example Peoples idea of
  randomness is really, really bad!
• Were bad at generating random numbers
• Were also bad at identifying randomness
• So, we need some tool to get randomness
• Cards/dice/slips of paper out of a hat
• Computer applications
• Random number table (pg. A 81)

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What is Randomness?

• An event is random if the individual outcome is
  uncertain but the distribution of outcomes over
  the long run (or the distribution of many
  repetitions of the event) is predictable

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What is Randomness?
Random events Outcome unknown before event
(but all possibilities are known) ______________
________ ______________________ No Structure in
Short Term Structure in Long Term
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How do we get random numbers?

• Computers?
• Pseudorandom numbers
• Table in Appendix E A-81
• List of numbers 0 through 9.
• Organized by rows and in columns of 5.

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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?

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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

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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
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Using random numbers

• Out of 10 trials
• - mean _______ boxes
• More trials more accurate result.
• Out of 200 trials
• - mean _______ boxes.

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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

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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

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Using random numbers

• Out of 5 trials
• - mean number of rolls ___
• More trials more accurate result.
• Out of 200 trials
• - mean number of rolls ___ .

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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

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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

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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 ___

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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?