__Introduction__

__Introduction__

The theory of probability originated in the middle of the seventeenth century has its origin in the context of the correspondence between *Pascal* and *Fermat* while dealing with a problem of a game of chance posed by a *gambler Chavalier de Mere*. Such games present situations where under given conditions more than one result are possible and the occurrence of a particular result is unpredictable and remains uncertain.

As for example, consider the tossing of a coin. When it falls, the result may be either a head or a tail. We know what the possible results are; but we are not quite sure which one of these results will actually turn up. Similar situation arises when we roll a die whose six faces are marked with 1, 2, 3, 4, 5, 6.

A numerical measure of such an uncertainty is known as the probability. Sometimes, we use “most likely”, probably, almost certain or chance as the synonym of the world probability by saying “almost it is certain that it may rain today”, “probably you may pass +2 level this year”.

### Some Basic Terms incuding Independent Cases

Before giving the definition of probability, we explain some terms which are used in the definition of probability.

#### Experiment

The processes, which when performed result different possible outcomes or cases, are known as the experiments. While performing an experiment repeatedly under the same condition if the result obtained is not unique, but may be any one of the possible outcomes, then the experiment is known as a random experiment. The set of all possible outcomes is called the sample space of the random experiment.

#### Trial and Event

Performing of a random experiment is called a trial and outcome or a combination of outcomes of an experiment is termed as an event.

Drawing a card from a deck of 52 cards, is a trial or an experiment and getting any one of the cards is an event. An event is said to be a sure event if its occurrence is certain and an event which can never occur is said to be an impossible event. We use the term “success” whenever an event of an experiment under consideration, takes place and failure whenever it does not.

#### Exhaustive cases

The number of cases which include all possible outcomes of a random experiment is said to be the exhaustive cases for the experiment. In throwing a die, the turning up of 1, 2, 3, 4, 5 and 6 marked in a die made exhaustive cases. Thus the total number of exhaustive cases in throwing a die is 6.

#### Equally likely cases

While performing experiments if any one of the possible outcomes may occur but no one case can be expected to occur more than the other then the cases are said to be equally likely. If a die is rolled, any one of the six numbers marked in the faces of a die, may turn up. So there are 6 equally likely cases in throwing a die.

#### Mutually exclusive cases (events)

Two or more events are said to be mutually exclusive if their simultaneous occurrence is not possible. If a coin is tossed either head or tail will occur, so head and tail are two mutually exclusive events.

#### Favourable cases

The cases or the outcomes of a random experiment which entail the happening of an event are known as the cases favourable to that event.

In throwing a die, the cases favourable to “getting an odd numbers” are 3.