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A random experiment has an unpredictable outcome.
  Examples include tossing a coin, playing the lottery, driving a car, taking an exam......

Interpretations of Probability

Long term frequency, as in the limit of the number of 6's that appear in many tosses of a fair dice.
Measure of belief:
P(I survive surgical operation)
This experiment cannot be repeated, the only interpretation would be that of a measure of belief.

Our first intuitive ideas about probability can be fraught with fallacies, in that they sometimes do not obey the axioms they should.

Susan Holmes