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Definition and basic properties of probability

 

Axiomatic and classical definitions of probability.

Probability of event. Basic properties of probability.

 

The axiomatic definition of probability. Let a space of elementary events  E  be given and such single number ( ) corresponds to each event  , that:

 

 

Then we say, that the probability is defined on events of  E , and the number ( ) is called the probability of an event  A .

 

The classical definition of probability. Let a space of elementary events  E  be given and this space consists of  N  equally likely elementary events, among which there are  n  events, favorable for an event  A. Then the number

 

                                                                                  ( ) = n / N

 

is called the probability of an event  A .

 

Basic properties of probability. Let a space of elementary events  E  be given and probabilities  P  are defined on events of   E . Then:

 

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