NCERT Solutions for Class 12 Maths Chapter 13: Probability - Exercise 13.1

The different properties of Conditional Probability are mentioned below in detail :  Let A and B be events of a sample space S of an experiment, then;

• Property 1: P(S|B) = P(B|B) = 1

• Property 2: If E and F are two events in a sample space S and B is an event of S, such that P(B)≠0, then;

         P((E ∪ F)|B) = P(E|B) + P(F|B) – P((E ∩ F)|B)

• Property 3: P(A′|B) = 1 − P(A|B)

Two experiments or events are said to be independent if for every pair of events A and B, where A is associated with the first experiment or event and B is associated with the second experiment or event, then the probability of the simultaneous occurrence of the events A and B when the two experiments are performed is the product of P(A) and P(B) calculated separately on the basis of two experiments, i.e.,

P (A ∩ B) = P (A) . P(B).

The topics covered in the 12 maths chapter 13 exercise 13.1 are:

• Introduction: Basic sums for a better understanding of the concept.

• Conditional Probability: Sums related to the same.

• Properties of conditional probability: Problems related to the three properties of conditional probability. 

Apart from NCERT solutions, Vedantu also provides students with revision notes, previous years solved question papers, sample papers, exemplar answers etc. to make the process of studying all the more easy and productive for the students.

The following concepts have been covered in NCERT Solutions for Class 12 Maths Chapter 13 for the students to learn easily: 

• Conditional probability and its properties 

• Multiplication theorem, 

• Independent events

• Bayes’ Theorem

• Partition of a space

• Random variables, their probability distributions, and their mean/variance 

• Bernoulli trials

• Binomial distribution

Chapter 13, Probability exercise 13.1 of Class 12 is easy to solve if you understand concepts related to the conditional probability of a given event when another event has already occurred. This will lead to understanding Bayes' theorem, the independence of events as well as the multiplication rule of probability.  A binomial distribution, which is actually a discrete probability distribution and is explained in detail in the chapter for solving questions. 

The multiplication theorem of probability is used to explain the condition relating to two events. In the case of two events, i.e., A and B related with the sample space denoted by S, set A∩B are the events where both event A, as well as event B, take place. Therefore, (A∩B) refers to the occurrence of event A and event B simultaneously.

Exercise 13.1 Bayes' theorem is used to describe the probability of one particular occurrence of a given event in relation to a condition. For proving Bayes' theorem, the formula of conditional probability is used: P(Ei|A)=P(Ei∩A)P(A). To understand more about the theorem in detail, visit Vedantu website or the app. You can also talk to an expert to clear all your doubts and enjoy video lessons, revision notes, important questions and a lot more. Vedantu offers all this and more free of cost.

Any random variable (denoted by X) with values 0, 1, 2, 3... n is considered as having binomial distribution with given parameters (denoted by n and p), when the probability distribution is: 

P (X = r) = ncr p^r q^(n–r),

Here, q = 1 – p 

r = 0, 1, 2, ..., n.