TABLE OF CONTENTS Suppose that we conduct an experiment and observe its results. In fire engineering we obtain quite often widely varying results as we repeat the experiment, even though we have tried to keep the conditions constant.
To model this situation formally we introduce a set which we call the sample space. A set is a collection of elements. Here the elements of the sample space are all the possible outcomes of the experiment. The sample space is usually denoted by S.
For example, if we light a fire in a compartment, we could consider three possible outcomes: a smouldering fire, a flaming fire and a flashover fire. In that case, the sample space of the experiment consists of three elements. If we repeat the experiment often enough we may be able to state that we get a smouldering fire 30% of the time, a flaming fire 50% of the time and a flashover fire 20% of the time. In this way, we can attach probabilities to the elements of the sample space. Probabilities are expressed as fractions, not percentages. Here the three outcomes will be said to have probabilities of 0.3, 0.5 and 0.2, respectively.
Sometimes there is an infinity of possible outcomes. For example, we might be measuring the maximum temperature reached in a compartment. It might be any number between, say, 500 C and 1500 C. The sample space in this case is the interval (500, 1500).
An event is a...
