What is probability


probability


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The probability (English: probability) is a measure to quantify the certainty or uncertainty of the occurrence of a certain event in the context of a »random experiment«. There are different opinions in the literature on how to determine the probability empirically:
  • The classic The concept of probability by Pierre-Simon Laplace (1749-1827) defines probability as the quotient of the number of favorable and equally possible cases.
  • The statistical Richard von Mises' (1883-1953) concept of probability defines probability as the limit value of the relative frequency of occurrence of the event.
  • The subjective The concept of probability by Leonard J. Savage (1917-1971) defines probability as the subjectively perceived chance of betting.
Regardless of the question of how one has to determine the probability of an event, the formal properties of this mathematical construct and the rules of how to use it are bypass (calculate), clearly. They are based on three axioms formulated by Andrej N. Kolmogorov (1903-87):
  • A probability is a number between 0 and 1 (including the two limits).
  • An event that always occurs, the so-called safe Event, has the probability 1.
  • Close two events and off, corresponds to the probability that either the event or the event occurs, the sum of the two individual probabilities.
All further rules for calculating probabilities result from these axioms. The second axiom, for example, results in the knowledge that the sum of the probabilities of all elementary events of a random experiment is equal to 1. In other words, the probability that any of the possible events will occur corresponds to the probability of the certain event. Furthermore, one can specify calculation rules how the probability of event combinations is calculated from the individual probabilities of the events involved.

notation: is the probability of the event . is the conditional probability of the event provided that event has occurred.



Next page:Random variable Upwards:Random variables Previous page:Random experiment & nbsp index HJA 2001-10-01