We live in the world of uncertainties. Man is surrounded by situations which are not fully under his control. The nature commands these situations. A person on a road does not know whether or not he will reach his destination safely. A patient in the hospital is never sure about his survival after a delicate operation. What will be the weather conditions tomorrow, nothing is known with certainty but we always like to have an idea about the weather conditions in future. A flight will be in time, the road will be clear or there will be some traffic jam. We face this of problem in our daily life. Man is always curious to know as to what will happen in future. The things which happen are important for the man today. These things are based on what is called chance or probability. If we have some numerical measure of uncertainty, this measure is called probability. We may find a numerical measure for a bulb to be defective, some numerical measure for the rain to fall.
The belief or confidence associated with a certain situation can also be measured. It is also called probability. In statistics there are various situations where uncertainty in involved.
Such situations need the application of probability. Probability is widely and rightly used in statistical decisions. The areas of statistics where probability is used are called the areas of statistical inference. Statistical inference is not possible without the use of probability. Probability is also used in different fields of life where uncertainty is involved. Knowledge of probability is used in space research, astronomy, business, weather studies, economics, genetics and various other fields of life. It is simple to explain various concepts of probability with the help of set theory. Thus we shall use here the set theory notation.