Impossible event

Impossible event

In the mathematics of probability, an impossible event is an event "x" with a probability Pr of zero, or Pr("x") = 0. [Tannenbaum & Arnold, p. 468]

An impossible event is not the same as the stronger concept of logical impossibility. For any continuous probability distribution the probability of any single elementary event is 0, yet the event is not logically impossible as an event outside the distribution. For instance, hitting any specific point on a dart board, let's say a square cartesian grid [-10,10] x [-10,10] and point (4.5678,-8.4568), is 0, because there is an infinite number of points on the board, while hitting a point outside of the space considered, is logically impossibe.

References

*Tannenbaum, Peter and Robert Arnold (1992). "Excursion in Modern Mathematics." Englewood Cliffs, New Jersey: Prentice Hall. ISBN 0132982331

Notes


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