Probability: A Very Short Introduction (Very Short Introductions) by Haigh John

Author:Haigh, John [Haigh, John]
Language: eng
Format: mobi, epub
Tags: A Very Short Introduction
Publisher: Oxford University Press
Published: 2012-04-25T16:00:00+00:00

Combining tiny probabilities

How likely is it that at least one among an enormous number of events, each having a tiny probability, will occur? This can be the pertinent question when considering the probability of a catastrophe. Complex systems or machinery may fail if any one of a myriad of components fails; will two aircraft collide, or might a nuclear power station suffer a meltdown? The so-called Borel-Cantelli Lemmas give some pointers. These mathematical results show that, in many circumstances, the key quantity is the sum of all those tiny probabilities: if it grows without bound, catastrophe is certain.

One consequence is that we can never be satisfied with current safety standards. It is essential to continue to make improvements. For, no matter how high our standards, there is some non-zero probability of failure during any given month: and however small this value, if it remains unchanged (or even if it decreases too slowly) the sum over many months will grow indefinitely large, and disaster will occur sometime.

A sound programme of continual improvement does not guarantee that disaster will be averted: but to be ever satisfied with the status quo is to invite doom.

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