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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
Ð
(
À
)
corresponds to each event
À
Å
, that:
Then we say, that the probability is
defined on events of
E
, and the number
Ð
(
À
) 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
Ð
(
À
) = 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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