PROBABILITY

                                        PROBABILITY

                         INTRODUCTION
                                   
                              The word probability has two meaning:(1) a quantitative measure of uncertainty and (2) a measure of degree of belief in a particular or problem.

                               Probability and statistic are fundamentally interrelated. probability is often called the vehicle of statistics. the area of inferential statistics in which we are mainly concerned with drawing inferences from experiments or situations involving an element of uncertainty, leans heavily upon probability theory. Uncertainty is also an inherent part of statistics inference as inferences are based on a sample, and a sample being a small part of larger population, contains incomplete information. A similar type of uncertainty occurs when we toss a coin, draw a card or throw dice,etc. The uncertainty in all these cases is measured in terms of probability.

                             It is always clear what we mean when we make statement of the type that it is very likely to rain today or I have a fair chance of passing the annual examination or A will probably win a prize, etc. In each of these statements, the natural state of uncertainty is expressed, but on the basis of part evidence, we have some degree of personal belief in the truth of each statement.
                           
                             The foundations of probability were laid by french mathematician of the seventeenth century - Blaise pascal (1623-1662) and Pierre De Fermat (1601-1665) in connection with gambling problems. Later on it was developed by Jakob Bernoulli (1654-1605), Abraham De Moire (1667-1754) and Pierre Simon Laplace (1749-1827). The modern treatment of probability theory which consists of stating a few axioms and rules resulting from these axioms, was developed during the twenties and thirties of twentieth century.

                             Today the probability theory has a wider field of application and is used to make intelligent decisions in Economics, Management, operations Research Sociology, Astronomy, Physics, Engineering and Genetics where risk and uncertainty are involved.

                              
                              As the probability theory these days is best understood through the application of the modern set theory, therefore brief descriptions of the basic concepts, notation and operations of set theory that are relevant to probability,