Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Introduction and historical background

The foundation of the theory of Probability are believed to have been laid by French Mathematicians Fermat  \left( 1604-1665 \right) ,Pascal  \left( 1623-1662 \right) and Laplace, Italian Mathematician Bernoulli   \left( 1654-1705 \right) and a host of others.

An Italian mathematician Jerome Cardan  \left( 1501-1576 \right) in his little book `Liber de Ludo Aleae’, considered to be a gambler’s manual, gave most of the laws of Probability.

A solid Mathematical foundation to the modern theory of probability was given by the Russian Mathematician A.N. Kolmogorov.

The theory of Probability had its origin in the exchange of a series of letters between Pascal and Fermat in the year  \left( 1654 \right) ; it involved a very simple question posed by a gambler named ‘Chevalier de Mere’, how fairly the stakes at a game of dice were the be distributed if the game was abruptly halted at some point before completion. The answer to this question involved a sample space that is not uniform.

Basic Concepts:

Probability is the branch of mathematics concerning numerical descriptions on how likely an event is to occur; or how likely it is that a proposition is true. The Probability of an event is a number between  0\  \text{and}\ 1 , where roughly speaking,  0  indicates the impossibility of the event and  1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.

Tossing off a fair Coin:

When a coin is tossed, the two outcomes (“heads and tails”) are both equally probable; the probability of “heads” equals the probability of “tails”, and since no other outcomes are possible the probability of either “heads” or “tails” is  \dfrac{1}{2}\ \text{ or }\ 0.5\ \text{ or}\ 50\% that is i.e. If a coin is tossed then either “head” or “tail” will be a possible outcome, not both at a time.

Rolling of a Dice:

A dice have  6 faces occurring  1,2,3,4,5,6. When a dice is rolled  6 outcomes are equally probable; the probability of  "1" , the probability of  ``2''... the probability of  ``6'' are equal. The probability of occurring one of the faces is  \dfrac{1}{6} .

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