Introduction to Probability

We live in a world of uncertainty, and we are surrounded by situations which are not fully under our control. Nature commands these situations. A person on the road does not know whether or not they will reach their destination safely. A patient in the hospital is never sure about their survival after a delicate operation. We can't know for sure what the weather will be like tomorrow, but we always like to have an idea about the weather conditions in the future. Whether a flight will be on time, or if the road will be clear or have traffic jams; we face these problems daily in our lives. We are always curious to know what will happen in the future, and this knowledge can be important. These future events are based on what is known as chance or probability. If we have a numerical measure of uncertainty, this measure is called probability. We may find a numerical measure for a bulb to be defective, or a numerical measure of how much rain will fall.

The belief or confidence associated with a certain situation can also be measured, and it is also called probability. In statistics there are various situations where uncertainty is involved.

Such situations need the application of probability. Probability is widely 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 where uncertainty is involved. Knowledge of probability is used in space research, astronomy, business, weather studies, economics, genetics and many other fields. It is simple to explain the various concepts of probability with the help of set theory. Thus we shall use the set theory notation in these tutorials.