Life safety. Calculating the probability of an emergency (most important)

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Life safety. Calculating the probability of an emergency (most important)

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47. CALCULATION OF THE PROBABILITY OF AN EMERGENCY

Emergencies create damage that may or may not be quantifiable (for example, deaths, personal injury, property damage, environmental damage, etc.). For the purpose of unification, various consequences and harm are denoted by the term "damage". Damage is measured in monetary terms or the number of deaths, number of people injured, etc. To measure damage in monetary terms, an equivalent must be found between these units of measurement.

Calculation of emergency probabilities (state of emergency). Let P{E} denote its probability. The probability of a certain event P{E} = 1, the probability of an impossible event P{E} = 0, the probability of the sum of pairwise incompatible PE (E_j E_jis not equal to zero if i ≠ j) is equal.

PE E_i, And_j,...,E_n, form a complete group of events if they are pairwise incompatible and one of them necessarily occurs for the complete group of events

In particular, for equally possible emergency situations (P{E} = p, i =1, 2,..., n), forming a complete group of events, the probability of an emergency

P = 1/n.

Opposite events E and E form a complete group, so

A complete group of events can be identified using the Karnot map. Three emergencies X, Y, Z form a Karnot map. The PEs written in the cells are pairwise incompatible.

When the number of emergencies exceeds five, Karnot cards are inconvenient to use. Then the complete group of events can be generated using binary numbers. For n emergencies, write decimal numbers from 0 to (2ⁿ - 1) and their representations in the binary system.

Let us determine the probability (P) of the emergency. R-PE is the sum a and N. Accident N and accident A can occur together. Therefore, the formula for determining the probability of pairwise incompatible events P{S} is unsuitable. Using a Karnaugh map to identify a complete group of events, we find the probability of an R-emergency:

P{A + N} = P{A} + P{N} - P{AN}.

If catastrophe (K) is impossible, K = AN is not equal to zero, then P{AN} = 0.

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