# NCERT Solutions for Class 12 Maths Chapter 13

## NCERT Solutions for Class 12 Maths Chapter 13 - Probability

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1. Explain the discovery of probability.

Chevalier de Méré, a gambler in the 16th century wanted to find out about the chances of a number appearing on the roll of dice so he approached a French Philosopher and Mathematician Blaise Pascal. Blaise Pascal got interested in the concept of possibility and discussed it with another Mathematician, Pierre de Fermat. Since then both the Mathematicians started working on the concept of probability separately. Later, this caught the attention of some of the great Mathematicians and A.N.Kolmogorov, a Russian mathematician, treated probability as a function of outcomes of the experiment. Therefore, with the help of this concept, we are able to find the probability of events allied with discrete sample spaces.

2. What is theoretical probability?

Probability in other words is prediction, so theoretical probability is a probability about a particular event that can be precisely done with the access of statistical data which is based on the possibility of the occurrence of an outcome. For example, the theoretical probability of getting a number '3' on rolling a die is 1:6 because the total number of possible outcomes are 6, (i.e, 1,2,3,4,5,6) and the possibility of getting 5 is one.

3. What are the three axioms of axiomatic probability?

Axiomatic Probability unifies the probability where there is an application of a set of rules made by Kolmogorov. The three axioms are given below:

1) The probability of an event X is always greater than or equal to zero but it can never be less than zero.

2) If there is a sample space S, then the probability of occurrence of the sample space is always 1. Which means that if the experiment is surely performed then getting one of the sample spaces is confirmed.

3) In case of mutually exclusive events, the probability of any of the events happening is the addition of the probability of both the events happening.

4. How does NCERT solution for class 12 Maths Chapter 13 by Vedantu is beneficial?

NCERT solution for class 12 Maths Chapter 13 by Vedantu is prepared by the subject matter experts keeping in mind the problems and complications faced by the average students in understanding and solving problems. The solutions are broken into simple steps and yet it is kept precise. Greater emphasis is paid to the concept clearing. The solutions cover all the important points, formulas and key facts of the chapter.