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## NCERT Class 12 Maths Textbook Chapter 13 With Answer PDF Free Download

### 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.

Author | NCERT |

Language | English |

No. of Pages | 57 |

PDF Size | 800 KB |

Category | Mathematics |

Source/Credits | ncert.nic.in |

### 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:**

NCERT Class 12 Maths Textbook Chapter 13 With Answer PDF Free Download