The Concept of Probability

Probability or more precisely probability theory is a very interesting branch of mathematics that has many applications in practically all the fields of human endeavour – especially in the many areas of engineering, agriculture, medicine and the social sciences.

In simple terms, probability is a mathematical concept that measures the likelihood of an event occurring, taking into account various factors and conditions. For example, in saying that when a fair coin is tossed, the probability of obtaining a head is 1/2, we mean to say if we throw the coin ( which must be fair, or unbiased or not ‘weighted’ ) a large number of times, chances are that we will obtain equal number of heads as tails. So if we throw the unbiased coin say 400 time, we should obtain 200 heads out of the 400 throws. Of course in practice, if you perform the ‘experiment’ of tossing a coin 400 times, you may not get exactly 200 heads; but the odds are that you would get a number very close to 200, say 203 or 197 heads out of the 400 tosses. A probability is therefore a theoretical forecast of the likelihood of obtaining the required result or outcome, given certain conditions and terms.

Now, when an oncologist tells a patient that there is a probability of 1 in 5 of an Asian woman contracting breast cancer, how does he obtain this figure? How is this probability calculated? Similarly if we read in the opinion polls or other surveys about the chances of a candidate getting re-elected or the probability of a person living to age 70 etc, we might wonder how these figures come about. Again these figures are mere theoretical figures arrived at after the relevant personnel ( statisticians, actuaries, etc ) conduct random surveys and applying many statistical tests over a representative population. So it does not mean that whenever 5 Asian women appear before you, you are sure to find one of them suffering from breast cancer. The cold statistic of 1 in 5 means that, on average, over a certain population of Asian women, there is a strong likelihood that one of five women might contract breast cancer. The importance of this is that here the probability of this sinister and unfortunate event ( that of getting breast cancer ) has been quantified; a ratio or fraction has been arrived at, and this gives us an idea of how prevalent or widespread the associated occurrence is. Thus the suicide rate of 16 in 10,000 in a certain city translates into a probability of 1 over 625 meaning that in theory ( though not necessarily in practice ) the odds are that 1 in 625 of the population of this city might attempt suicide.

This article does not intend to delve very deeply into probability and probability theories but it is instructive to note that the study of probablities and the associated theories forms a very important branch of mathematics viz Probability and Statistics. In the mathematical study of probability, various concepts and formulae are introduced e.g. the concept of equiprobable or equally likely events, mutually exclusive and independent events and their diagrammatic representation – the Venn diagrams etc. From the studies of probabilities students of mathematics then proceed to study statistics, which explores how data are collected, collated and analysed. Various statistical techniques are then introduced and various distributions discussed. From a close study of these and a host of others, statisticians learn to represent data and carry out statistical tests to arrive at certain conclusions, both qualitatively and quantitatively.

For the layperson, probablity is just a number forecasting the likelihood of certain events or occurrences. But for those mathematically inclined, probability is an important branch of the subject that is intellectually stimulating and a close examination of the concepts and theories could prove to be a profitable and rewarding exercise.