**
Events
**

*
Event. Elementary event. Space of
elementary events.
*

*
Certain event. Impossible event.
Identical events.
*

*
Sum, product, difference of
events. Complementary events.
*

*
Mutually exclusive events.
Equally likely events.
*

**
An event
**
in probability theory is any
fact, which may occur as a result of an experiment with a random outcome or may
not. The simplest result of such experiment is called

**( for instance, an appearance of heads or tails at throwing of a coin, shooting hit, an appearance of an ace at taking a card out of a pack, a random appearance of number at throwing of a die etc.).**

*an elementary event*

A
set
of all elementary
events
*
E
*
is
called
**
a space of
elementary
**

**. So, this space consists of six elementary events at throwing of a die and 52 elementary events at taking a card out of a pack. An event can consist of one or several elementary events, for example, an appearance of two aces one after the other at taking a card out of a pack, or an appearance of the same number at triple throwing of a die. Then it's possible to define**

*events***as an arbitrary subset of a space of elementary events.**

*an event*

**
A
certain event
**
is
all space
of elementary
events.
Thus,

**is an event, which must happen as a result of the experiment without fail. Such event at throwing of a die is a fall of the die on one of its faces.**

*a certain event*

**
An impossible event
**
(
)
is called an empty subset of a space of elementary events.
That is,

**cannot happen as a result of the experiment. So, such event at throwing of a die is a fall of the die on its edge.**

*an impossible event*

Events
*
A
*
and
*
B
*
are
called
**
identical events
**
(

*A*=

*B*), if the event

*A*occurs if and only if the event

*B*occurs. An event

*A*

*involves the event**B*(

*À*

*Â*), if the condition

*"the event B occurred*

*"*follows from the condition

*"the event A occurred*

*"*.

An event
*
*
*
C
*
is called
**
a sum of the events
**

*A*and

*B*(

*Ñ*=

*À*

*Â*), if the event

*C*happens if and only if either the event

*A*happens or the event B happens.

An event
*
*
*
C
*
is called
**
a product of the events
**

*A*and

*B*(

*Ñ*=

*À*

*Â*), if the event

*C*happens if and only if both event

*A*and event B happen.

An event
*
C
*
is called
**
a
difference of the events
**

*A*and

*B*(

*Ñ*=

*À*–

*Â*), if the event

*C*happens if and only if the event

*A*happens and the event B doesn't.

An event
*
A'
*
is
**
a
complementary event
**
to the event

*A*,

*if the event*

*A*doesn't occur.

*So, shooting hit and miss are complementary events.*

Events
*
A
*
and
*
B
*
are
called
*
mutually exclusive
*
(

*À*

*Â*= ),

**if their simultaneous occurrence is impossible. For instance, an occurrence both heads and tails at throwing of a coin.**

If several events can happen as
a result
of an experiment,
and each
of them isn't more possible
than others according to objective conditions, then such events are called
**
equally likely events
**
.
Examples of equally likely events are: an appearance of two, an ace and a knave
at taking a card out of a pack, an appearance of any number from 1 to 6 at
throwing of a die etc.