From Risk Analysis in Building Fire Safety Engineering

3.3 The Probability Measure

To create a mathematical model which will enable us to quantify the likelihood of the various outcomes of the experiment, we attach to each event a number between 0 and 1 which will be called the probability of the event. It can be thought of as the relative frequency of occurrence of the event in a large number of repetitions of the experiment. The probability of event A will be denoted by P( A). The probability measure satisfies the following axioms:

  1. 0 ? P( A) ? 1 for all P( A).

  2. P( S) = 1 and P( ) = 0.

  3. If A ? B = (i.e. A and B are mutually exclusive), then P( A ? B) = P( A) + P( B).

It follows immediately from the axioms that if { A 1, A 2, , A n} is a partition then


  1. Consider a room of fire origin with one door and one window. There are four possible situations, namely: door and window closed, door and window open, door open and window closed, and door closed and window open. By analysing observations on actual fires, we may come to the conclusion that the relative frequencies of these four events are 0.1, 0.2, 0.4 and 0.3.

  2. Returning to the maximum temperature T in...

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Door Closers close a door after it has been manually opened.
Door Operators
Door operators are devices used to open and close all types of doors or gates. These operators can be powered by a variety of power sources such as electric, hydraulic or pneumatic devices.
Overhead Doors
Garage doors are designed to enclose and protect the entrances to garages and other large structures.
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Door strikes are metal plate devices that are installed within a door jamb to stop and retain a door when closed. Multiple operational configurations are available for differing door bolt options as well as the action of the clasp mechanism and level of security.

Topics of Interest

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Overview Probabilistic thinking is based on very old ideas which go back to De Mere [1], La Place [2], and Bayes [3]. What is probability and how does it relate to frequency, statistics and, finally,...