Page 12 - 6880

where P(A+B) – probability of implementation of at least one event (A or B, or
both A and B together).
For three or more events it is better to use a formula by the probability of the
opposite event:

P A В С  1 P А В  С  1 P       1СPВPА      1 P    1 PА      1 PВ    ,С
(2.3)
Addition theorem for incompatible events is:



P  ВA   P А    P  ,  В (2.4)
     
where P(A+B) – probability of a single event (A or B).
2) dependent and independent.
Dependent events are the events, when the probability of one of them
depends on the occurrence or no occurrence of another one, and independent
events are the events, when the probability of one of them doesn’t depend on the
occurrence or no occurrence of another one.
Multiplication theorem of probability for dependent events is:
P A В  P   PА  А  ,В (2.5)
where P (B) – conditional probability of event B under the condition, that
A
event A has already occurred.
Multiplication theorem of probability for independent events is:
P A В  P    ,ВPА  (2.6)
where P(A*B) – probability of events, together A and B.

3.2 Determining the value of acceptable risk
An economic approach is often used for determining the value of acceptable
risk. This approach is based on the accounting for safety costs.
For this should take into consideration the following:
– absolute safety can not be ensured, the object can be only relatively safe;
– risk value shall not exceed the level that has already been achieved for
complex technical objects taking into account the natural influences;
– the risk must be reduced as much as practically possible to achieve within
constraints;
– should not be parts of the risk that far exceed others (analogy with the
principle of equal reliability, which is used for ensuring the reliability of system).
The essence of the concept of a reasonable (acceptable) risk consists in the
desire to establish such a level of safety that a society can let at this stage of its
development, taking into account technical and economic, and social opportunities
(Figure 2.1).

12