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Probability is something we use everyday, from evaluating the chances of it raining, to winning…or losing a bet. Yet what lies behind the decisions we make about probability?
Many of the things that statisticians and others investigate involve uncertainty. What will be the UK level of unemployment in a year’s time? If I take this drug my doctor has prescribed, will my health improve? If I drink a glass or two of red wine every day, will I live a longer or shorter time than if I don't drink wine at all? Will it rain tomorrow? The mathematical tool that is generally used to deal with such uncertainty is called probability.
Probability is a way of expressing the uncertainty of an event in terms of a number on a scale. The most common way, among statisticians at least, of expressing this uncertainty is on a scale going from 0 to 1, where impossible events are given a probability of 0 and events that will certainly happen are given a probability of 1.
Other events, that might or might not happen, are given probabilities at intermediate events on the scale. So an event that is as likely to happen as not is given a probability halfway along the scale, at ½ or 0.5. An event that is pretty likely to happen, but could possibly not happen, might have a probability of 0.95.
Other scales are used for probabilities. Sometimes they are expressed on a percentage scale, where impossible events have a probability of 0%, events that are certain get a probability of 100%, an event as likely as not to happen has a probability of 50% and so on. Bookmakers (and statisticians in some contexts) usually express uncertainty in terms of odds rather than probability.
If a horse-racing expert says that the odds on a particular horse winning a particular race are 1 to 2, he or she means that the chance of the horse not winning is twice as big as the chance of the horse winning. Expressing this on a probability scale going from 0 to 1, the probability that the horse will win the race is 1/3, and the chance that it doesn’t win is 2/3.
Probabilities obey various mathematical rules, many of which are quite simple and straightforward. For instance, tomorrow it will either rain or not rain. If the Met Office gives the probability of rain tomorrw as, let's say, 0.2 (that is, 20%), then then the probability that it won’t rain is 1 – 0.2 which comes to 0.8. In general, if the probability of an event is p, the probability that the event won’t happen is 1 – p. Using this and many other mathematical rules, a large body of mathematical theory about probabilities has been built up over several centuries.
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Content last updated: 05/01/2005
About our expert
Kevin McConway is a Senior Lecturer in the Department of Mathematics and Statistics at the Open University, where he teaches statistics and health studies, and researches in several areas including statistical theory, health service organization, ecology and evolution.
He has degrees in mathematics, statistics, psychology and business from the Universities of Cambridge and London and the Open University. Kevin originally comes from rural Northumberland but is now a long-term Milton Keynes resident.
