Importance of Modelling

We can not estimate the probability of most events occurring as easily as estimating the probability of tossing a coin and getting heads or tails. Probabilities like these, which can be accurately calculated, are called theoretical probabilities.
In fact the probabilities of most of the events we are interested in are obtained from observations, testing and historical records. We are very interested in the expected lifetime of aircraft parts, or the average time between major earthquakes in a certain city. We can test aircraft parts in the laboratory or observe them in use to find the average lifetime, and the probability of the part having a certain lifetime,and for earthquakes in a certain area. we must use computer models and historical records.
Using these methods we can build a statistical model of some event occurring and use it to predict the probability of the event in question occurring in any time period, given the age of the part, or the time since the last earthquake. We may want to build in a safety margin, so that the part is replaced well before any calculated failure date, or that intensive monitoring of an earthquake fault zone is undertaken.

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