What does it mean to be random

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What does it mean to be random?
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Randomness
This clip was taken from the very first episode
of the TV series Numb3rs. In the clip a group of
people are asked to arrange themselves randomly
in a space. What they do is spread themselves
evenly to fill the space. The clip ends with the
usual cynic that doesnt understand maths and
it doesnt make sense to which the mathematician
replies by referring to the lotto ticket in his
shirt pocket claiming that that doesnt make any
sense either if you know the maths. Yet another
discussion starter. Series one is available on DVD

• Demonstration video
• More Info

This link provides background information to show
that the mathematics in this series and the
equations used are real.
The activities which follow are adapted from the
worksheets available to support teachers using
this series as the basis for classroom activities.
More Worksheet from the series
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Thinking about Randomness?

• Which of the following is most likely to occur?
• RRRRRRRRRRRRRRRRRRRRRRRRRRBBBBBBBBBBBBBBBBBBBBBBBB
  BBBB
• RBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRB
  RBRB
• BBBRRRBRRRRRRRRRBBBBRRRRRBRBBBBBRRRRBBBBBBBBBRBBBR
  RR

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Thinking about randomness

• Using only your intuition, write a sequence of 52
  Bs and Rs that you think might result from
  cards dealt at random from a shuffled deck.

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• Shuffle a deck of cards very well, deal the cards
  from the top of the deck, and record the sequence
  of the 52 Bs and Rs that results.
• What surprises do you see in this sequence?

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• Write down the lengths of the seven runs of
  consecutive B's as they occur in order from left
  to right in shuffle (C) of Question 1. Then do
  the same for the R's, but count the runs from
  right to left.

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• BBB RRR B RRRRRRRRR BBBB RRRRR B R BBBBB
  RRRR BBBBBBBBB R BBB RRR

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• BBB RRR B RRRRRRRRR BBBB RRRRR B R BBBBB
  RRRR BBBBBBBBB R BBB RRR
• Bs _3_ . __1_ _4_ _1__ _5__ _7_ _3__ Rs _3__
  . _1_ _4_ _1__ _5__ _7_ _3_

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Your Task

• Construct a random sequence of 26Rs and 26Bs.
• How does your procedure ensure that it is random?

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Interesting Links

• www.rand.org/publications/classics/randomdigits
• www.maa.org/mathland/mathtrek_5_7_01.html.
• www.random.org

Historical interest One million random digits.
This link may not open but it is correct. Go to
www.maa.org and follow the to columns and
mathtrek and click on the link to the mathtrek
archives then scroll to 5/72001 column and it
will open (with the same URL as above)
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• As mathematician Robert R. Coveyou of Oak Ridge
  National Laboratory once put it,
• "The generation of random numbers is too
  important to be left to chance."