Theory of Probability
May 6th 2015 Posted at Uncategorized
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Probability, the formal term for the concept of ‘chance’, is an integral part of our life and our conversations. We often discuss matters such as whether a new baby would be a boy or a girl, whether there will be a good monsoon this year; whether a student will get admission to a MBA program me, etc. During such conversations, normally, we do not attempt to measure the degree of chance. However, sometimes, we do mention. “1 am 90%, 95% or 99% certain” about a particular aspect, if someone were to counter why not 95.5%— well there would be any answer. A person makes a quantitative statement just to emphasise a point. It is not that one measures and then makes the statement of the above type. That is how, sometimes, one makes a statement, “I am 100% certain or sometimes, even 101% certain? However, one thing is agreed by every one that if there were a measure of chance, the measure would vary from zero (impossible) to one (certain). From time immemorial, human beings have been endeavoring to develop professional skills to enable them to predict the likelihood of various types of events. Two persons (whose names have been lost in the sands of time, so let us call them 4A* and 4B*), were playing a match of tennis. Both of them put SI000 each at stake on the understanding that whoever wins the match would take the total amount of $ 2,000.
As is well known in tennis, usually the best of 5 sets is the winner i.e. whoever is the first to win three sets is the winner, and there is no draw in a set—the set being played till one player wins the set. Thus the total number of sets that could be played is 3, 4 or 5. Now, it so happened that on the day when ‘A’ and *B’ started playing the match, they could play only 3 sets—out of which A won 2 and B won 1. Somehow, they were not in a position to continue the match further, because A had to go to some other place. Now the problem arose as to how to divide the total stake money of $ 2,000. Everyone agreed that ‘A* should get more than ‘B* but exactly how much was the issue. ‘A’ argued that, he should get two-thirds of the amount as he had won two out of three sets but ‘B’ did not agree saying that if the match could be continued, he would win both the remaining matches, and thus get the entire amount.
However, instead of arguing over the issue, they approached their common friend who happened to be a mathematician. They thought that he would be able to measure their chances of winning the match if the game was continued further, and then the total amount could be divided in that ratio. Even he could not resolve the issue, as till that time there was no formal method for measuring the chance factor. That mathematician approached his mathematician friends and the resulting research triggered the development of the theory of Probability.
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