### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Introduction and historical background

The foundation of the theory of Probability are believed to have been laid by French Mathematicians Fermat ,Pascal and Laplace, Italian Mathematician Bernoulli and a host of others.

An Italian mathematician Jerome Cardan 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 ; 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 , where roughly speaking, indicates the impossibility of the event and 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 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 faces occurring When a dice is rolled outcomes are equally probable; the probability of , the probability of the probability of are equal. The probability of occurring one of the faces is .

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