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The Mathematics of Maybe: Introduction to Probability

What random means

A coin spins before every cricket match. No one can call it for sure. To call a toss is to name its result before it lands.

Past tosses give no clue about the next one.

Nobody calls the next one

Random — a result nobody can name before it happens. A toss is random. You know the possible results: heads or tails. You cannot say which one will come.

The past tosses do not help. A fair coin is equally likely to show heads or tails. For a fair coin, ten heads in a row change nothing. Each toss is separate from the earlier ones. So the next toss is as uncertain as the first.

A whole run can be described

One toss cannot be called. A long run can be described. A run is many tosses in a row. "About half were heads" is a real claim for a fair coin. You can check it.

Six calls on a class coin (made-up data)
Call numberCalledCoin landedRight?
1headsheadsyes
2headstailsno
3tailstailsyes
4headsheadsyes
5tailsheadsno
6tailstailsyes

Four of six calls were right this time. With a fair coin, no way of calling beats half right. That holds over a long run.

Rule: The next toss cannot be called. A whole run can be described.

Call each toss. See how you score.

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This track

  1. 0 Start here
  2. 1 What random means
  3. 2 A scale from 0 to 1
  4. 3 Counting what happened
  5. 4 More tries, steadier
  6. 5 Counting what could happen
  7. 6 When the two disagree
  8. 7 Two things at once
  9. 8 A tree of results
  10. 9 The big picture
  11. 10 Track quiz

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