B \u003d (point falls into triangle B) IN
A
A + B \u003d (the point falls into at least one figure A and B).
Basic concepts
A-B \u003d (the point will fall into circle A
and will not fall into triangle B)
A
IN
A
Basic concepts
IN
A AB \u003d (the point falls into both figures A and B).
Basic concepts
An event is called opposite to an event if it occurs if and only if the event does not occur.
A
A \u003d (the point falls into circle A) =(point is not in circle A)
Basic concepts
Events A and B are called incompatible if they cannot occur together in the same experiment.
IN
A A \u003d (the point falls into circle A) B \u003d (point falls into triangle B) A and B are incompatible events
Operation Properties
A+B=B+A
(A+B)+C=A+(B+C)
A + Ǿ \u003d A
A+ Ω = Ω
AB=BA A(BC)=(AB)C And Ǿ = Ǿ A Ω = A Ǿ ( A + B ) C=A C + B C (D.z.)
Space of elementary events
Consider a stochastic experiment.
1. Events ω mutually exclude each other.
2. As a result of the experiment, be sure
one of them comes.
3. For any event A,
upon the occurrence of the event ω , we can say that
event A occurred or did not occur.
The events ω are elementary .
Space of elementary events
Example 3. Throwing a dice.
=(drop number 1)
=(drop number 2)
- - - - - - - - - - - - - - - - -
=(drop number 6)
Space of elementary events
Example 4
A factory produces N items of the same type.
To assess the quality, m products are selected and examined.
ω is any set of m products.
- space of elementary events .
