# Probability Chapter 13 Class 12 Maths NCERT Textbook PDF

NCERT Solutions for Class 12 Maths Chapter 13‘ PDF Quick download link is given at the bottom of this article. You can see the PDF demo, size of the PDF, page numbers, and direct download Free PDF of ‘Ncert Class 12 Maths Chapter 13 Exercise Solution’ using the download button.

### Chapter 13: Probability

#### 13.1 Introduction

In earlier classes, we studied probability as a measure of uncertainty of events in a random experiment.

We discussed the axiomatic approach formulated by Russian Mathematician, A.N. Kolmogorov (1903-1987) and treated probability as a function of the outcomes of the experiment.

We have also established the equivalence between the axiomatic theory and the classical theory of probability in the case of equally likely outcomes.

On the basis of this relationship, we obtained probabilities of events associated with discrete sample spaces.

We have also studied the addition rule of probability.

In this chapter, we shall discuss the important concept of the conditional probability of an event given that another event has occurred, which will be helpful in understanding the Bayes’ theorem, multiplication rule of probability, and independence of events.

We shall also learn an important concept of random variables and their probability distribution and also the mean and variance of a probability distribution.

In the last section of the chapter, we shall study an important discrete probability distribution called the Binomial distribution. Throughout this chapter, we shall take up the experiments having equally likely outcomes, unless stated otherwise.

### NCERT Solutions Class 12 Maths Chapter 13 Probability

1. Given that E and F are events such that P (E) = 0.6, P (F) = 0.3 and P (E ∩ F) = 0.2, find P (E|F) and P (F|E)

Solution:

2. Compute P (A|B), if P (B) = 0.5 and P (A ∩ B) = 0.32

Solution:

3. If P (A) = 0.8, P (B) = 0.5 and P (B|A) = 0.4, find
(i) P (A ∩ B)

(ii) P (A|B)

(iii) P (A ∪ B)

Solution:

4. Evaluate P (A ∪ B), if 2P (A) = P (B) = 5/13 and P (A|B) = 2/5.

Solution:

5. If P (A) = 6/11, P (B) = 5/11 and P (A ∪ B) = 7/11, find
(i) P (A∩B)

(ii) P (A|B)

(iii) P (B|A)

Solution: